,transcriber's notes3 #a7 ,peaucillier is a printers error and has been changed to ,peaucellier4 #b7 ,the #d characters at the end of the word ',pafnut7i' denote a letter 'i' with a breve accent4 ,,contributions ,,from ,,the ,,museum ,,of ,,history ,,and ,,technology ,,paper #bg ,,kinematics ,,of ,,mechanisms ,,from ,,the ,,time ,,of ,,watt ,eugene ,s4 ,ferguson ,,james ,,watt1 ,,kinematic ,,synthesist #ahg ,,to ,,draw ,a ,,straight ,,line #aii ,,scholars ,,and ,,machines #bji ,,mechanicians ,,and ,,mechanisms #baf ,,mechanisms ,,in ,,america1 #ahge-aiee #bbc ,,additional ,,references #bbi ,,kinematics ,,of ,,mechanisms ,,from ,,the ,,time ,,of ,,watt ,in an inventive tour de force that seldom1 if ever1 has been equalled for its brilliance and far-reaching consequences1 ,james ,watt radically altered the steam engine not only by adding a separate condenser but by creating a whole new family of linkages4 ,his approach was largely empirical1 as we use the word today4 ,this study suggests that1 despite the glamor of today's sophisticated methods of calculation1 a highly developed intuitive sense1 reinforced by a knowledge of the past1 is still indispensable to the design of successful mechanisms4 ,,the ,,author3 ,eugene ,s4 ,ferguson1 formerly curator of mechanical and civil engineering in the ,united ,states ,national ,museum1 ,smithsonian ,institution1 is now professor of mechanical engineering at ,iowa ,state ,university of ,science and ,technology4 ,in engineering schools today1 a student is introduced to the kinematics of mechanisms by means of a course of kinematic analysis1 which is concerned with principles underlying the motions occurring in mechanisms4 ,these principles are demonstrated by a study of mechanisms already in existence1 such as the linkage of a retractable landing gear1 computing mechanisms1 mechanisms used in an automobile1 and the like4 ,a systematic1 if not rigorous1 approach to the design of gears and cams also is usually presented in such a course4 ,until recently1 however1 no serious attempt was made to apply the principles developed in kinematic analysis to the more complex problem of kinematic synthesis of linkages4 ,by kinematic synthesis is meant the designing of a linkage to produce a given series of motions for a particular purpose4 ,that a rational--numerical or geometrical--approach to kinematic synthesis is possible is a relatively recent idea1 not yet fully accepted2 but it is this idea that is responsible for the intense scholarly interest in the kinematics of mechanisms that has occurred in this country within the last #aj years4 ,this scholarly activity has resulted in the rediscovery of many earlier works on the subject1 and nearly all the scholars now working in this field have acknowledged in one way or another their debt to those who arrived on the scene at an earlier time than they4 ,there have been occasional reviews of the sequence and nature of developments1 but the emphasis naturally has been upon the recent past4 ,it seems to me that there is something to be gained in looking beyond our own generation1 or even beyond the time of ,franz ,reuleaux 7#ahbi-aije71 who is generally credited with originating many of our modern concepts of mechanism analysis and design1 and to inquire into the ideas that made possible ,reuleaux's contributions4 ,take to ,kinematics4 ,it will repay you4 ,it is more fecund than geometry2 it adds a fourth dimension to space4 --,chebyshev to ,sylvester1 #ahgc ,while no pretense of completeness is made1 ,i have tried in this paper to trace the high points in the development of kinematic analysis and synthesis1 both in academic circles and in the workshop1 noting where possible the influence of one upon the other4 ,if ,i have devoted more space to particular people and episodes than is warranted by their contributions to the modern treatment of the subject1 it is because ,i have found that the history of kinematics of mechanisms1 like the history of any other branch of engineering1 is more interesting and more plausible if it is recognized that its evolutionary development is the result of human activity4 ,this history was wrought by people like us1 no less intelligent and no less subject than we are to environment1 to a subjective way of looking at things1 and to a heritage of ideas and beliefs4 ,i have selected the period from the time of ,watt because modern mechanisms originated with him1 and ,i have emphasized the first century of the period because by #ahhe many of the ideas of modern kinematics of mechanisms were well developed4 ,linkages are discussed1 to the virtual exclusion of gears and cams1 because much of the scholarly work in kinematic synthesis is presently directed toward the design of linkages and because linkages provide a convenient thread for a narrative that would have become unnecessarily complex if detailed treatment of gears and cams had been included4 ,i have brought the narrative down to the present by tracing kinematics as taught in ,american engineering schools1 closing with brief mention of the scholarly activity in kinematics in this country since #aiej4 ,an annotated list of additional references is appended as an encouragement to further work in the history of the subject4 ,james ,watt1 ,kinematic ,synthesist ,james ,watt 7#agcf-ahai71 improver of the steam engine1 was a highly gifted designer of mechanisms1 although his background included no formal study of mechanisms4 ,indeed1 the study of mechanisms1 without immediate regard to the machines in which they were used1 was not introduced until after ,watt's important work had been completed1 while the actual design of mechanisms had been going on for several centuries before the time of ,watt4 ,mechanisms that employed screws1 cams1 and gears were certainly in use by the beginning of the ,christian era4 ,while ,i am not aware of unequivocal evidence of the existence of four-bar linkages before the #afth century1 their widespread application by that time indicates that they probably originated much earlier4 ,a tantalizing #acth-century sketch of an up-and-down sawmill 7fig4 #a7 suggests1 but does not prove1 that the four-bar linkage was then in use4 ,leonardo da ,vinci 7#adeb-aeai7 delineated1 if he did not build1 a crank and slider mechanism1 also for a sawmill 7fig4 #b74 ,in the #afth century may be found the conversion of rotary to reciprocating motion 7strictly speaking1 an oscillation through a small arc of a large circle7 and vice versa by use of linkages of rigid members 7figs4 #c and #d71 although the conversion of rotary to reciprocating motion was at that time more frequently accomplished by cams and intermittent gearing4 ,nevertheless1 the idea of linkages was a firmly established part of the repertory of the machine builder before #afjj4 ,in fact one might have wondered in #aehh1 when ,agostino ,ramelli published his book on machines1#a whether linkages had not indeed reached their ultimate stage of development4 ,to illustrate my point1 ,i have selected the plate of ,ramelli that most appeals to me 7fig4 #e71 although the book exhibits more than #bjj other machines of comparable complexity and ingenuity4 ,footnote #a3 ,agostino ,ramelli1 ,le ,diverse et ,artificiose ,machine1 ,paris1 #aehh4 ,illustration3 ,figure #a4--,up-and-down sawmill of the #acth century4 ,the guide mechanism at lower left1 attached to the saw blade1 appears to be a #d-;bar linkage4 ,after ,robert ,willis1 trans4 and ed41 ,facsimile of the ,sketch-,book of ,wilars de ,honecort 7,london1 #ahei1 pl4 #dc74 ,illustration3 ,figure #b4--,slider-crank mechanism of ,leonardo da ,vinci 7#adeb-aeai71 redrawn from his manuscript notebooks4 ,a frame saw is depicted at the lower end of the guides4 ,from ,theodor ,beck1 ,beitrge zur ,geschichte des ,maschinenbaues 7,berlin1 #ahii1 p4 #cbc74 ,illustration3 ,figure #c4--;,blowing engine by ,vanuccio ,biringuccio1 about #aedj1 showing conversion of motion of the waterwheel shaft from rotation to oscillation4 ,from ,theodor ,beck1 ,beitrge zur ,geschichte des ,maschinenbaues 7,berlin1 #ahii1 p4 #abj74 ,illustration3 ,figure #d4--;,grain mill1 #aehh1 showing conversion of motion of the operating bars from oscillation to rotation4 ,note the fly-weights1 predecessors of the flywheel4 ,from ,agostino ,ramelli1 ,le ,diverse et ,artificiose ,machine 7,paris1 #aehh1 pl4 opposite p4 #aii74 ,illustration3 ,figure #e4--,machine for raising water4 ,such a machine was built in ,spain during the #afth century and was operated for some #hj years4 ,from ,agostino ,ramelli1 ,le ,diverse et ,artificiose ,machine 7,paris1 #aehh1 p4 #aii74 ,there was a vast difference1 both in conception and execution1 between the linkages of ,ramelli and those of ,james ,watt some #bjj years later4 ,watt was responsible for initiating profound changes in mechanical technology1 but it should be recognized that the mechanic arts had1 through centuries of slow development1 reached the stage where his genius could flourish4 ,the knowledge and ability to provide the materials and tools necessary for ,watt's researches were at hand1 and through the optimism and patient encouragement of his partner1 ,matthew ,boulton1 they were placed at his disposal4 ,watt's genius was nowhere more evident than in his synthesis of linkages4 ,an essential ingredient in the success of ,watt's linkages1 however1 was his partner's appreciation of the entirely new order of refinement that they called for4 ,matthew ,boulton1 who had been a successful manufacturer of buttons and metal novelties long before his partnership with ,watt was formed1 had recognized at once the need for care in the building of ,watt's steam engine4 ,on ,february #g1 #agfi1 he had written ,watt3#b ,i presumed that your engine would require money1 very accurate workmanship and extensive correspondence to make it turn out to the best advantage and that the best means of keeping up the reputation and doing the invention justice would be to keep the executive part of it out of the hands of the multitude of empirical engineers1 who from ignorance1 want of experience and want of necessary convenience1 would be very liable to produce bad and inaccurate workmanship2 all of which deficiencies would affect the reputation of the invention4 ,boulton expected to build the engines in his shop with as great a difference of accuracy as there is between the blacksmith and the mathematical instrument maker4 ,the ,soho ,works of ,boulton and ,watt1 in ,birmingham1 ,england1 solved for ,watt the problem of producing in great 7that is1 in sizes large enough to be useful in steam engines7 the mechanisms that he devised4#c ,footnote #b3 ,henry ,w4 ,dickinson1 ,james ,watt1 ,craftsman ,engineer1 ,cambridge1 ,cambridge ,university ,press1 #aicf1 pp4 #eb-ec4 ,footnote #c3 ,james ,p4 ,muirhead1 ,the ,origin and ,progress of the ,mechanical ,inventions of ,james ,watt1 ,london1 #ahed1 vol4 #a1 pp4 #ef1 #fd4 ,this work1 in three volumes1 contains letters1 other documents1 and plates of patent specification drawings4 ,the contributions of ,boulton and ,watt to practical mechanics in great cannot be overestimated4 ,there were in the #ahth century instrument makers and makers of timekeepers who had produced astonishingly accurate work1 but such work comprised relatively small items1 all being within the scope of a bench lathe1 hand tools1 and superb handwork4 ,the rapid advancement of machine tools1 which greatly expanded the scope of the machine-building art1 began during the ,boulton and ,watt partnership 7#agge-ahjj74 ,in ,april #agge the skirmish at ,concord between ,american colonists and ,british redcoats marked the beginning of a war that was to determine for the future the course of political events in the ,western ,hemisphere4 ,another event of ,april #agge occurring in ,birmingham now appears to have been one that marked the beginning of a new era of technological advance4 ,it was near the end of this month that ,boulton1 at the ,soho ,works1 wrote to his partner and commented upon receiving the cast iron steam engine cylinder that had been finished in ,john ,wilkinson's boring mill3 444 it seems tolerably true1 but is an inch thick and weighs about #aj cwt4 ,its diameter is about as much above #ah inches as the tin one was under1 and therefore it is become necessary to add a brass hoop to the piston1 which is made almost two inches broad4#d ,footnote #d3 ,ibid41 vol4 #b1 p4 #hd4 ,this cylinder indeed marked the turning point in the discouragingly long development of the ,watt steam engine1 which for #aj years had occupied nearly all of ,watt's thoughts and all the time he could spare from the requirements of earning a living4 ,although there were many trials ahead for the firm of ,boulton and ,watt in further developing and perfecting the steam engine1 the crucial problem of leakage of steam past the piston in the cylinder had now been solved by ,wilkinson's new boring mill1 which was the first large machine tool capable of boring a cylinder both round and straight4 ,the boring mill is pertinent to the development of linkages in great1 being the first of a new class of machine tools that over the next #ej or #fj years came to include nearly all of the basic types of heavy chip-removing tools that are in use today4 ,the development of tools was accelerated by the inherent accuracy required of the linkages that were originated by ,watt4 ,once it had been demonstrated that a large and complex machine1 such as the steam engine1 could be built accurately enough so that its operation would be relatively free of trouble1 many outstanding minds became engaged in the development of machines and tools4 ,it is interesting1 however1 to see how ,watt and others grappled with the solutions of problems that resulted from the advance of the steam engine4 ,during the #aggj's the demand for continuous1 dependable power applied to a rotating shaft was becoming insistent1 and much of ,boulton's and ,watt's effort was directed toward meeting this demand4 ,mills of all kinds used water or horses to turn wheel-work1 but1 while these sources of power were adequate for small operations1 the quantity of water available was often limited1 and the use of enormous horse-whims was frequently impracticable4 ,the only type of steam engine then in existence was the ,newcomen beam engine1 which had been introduced in #agab by ,thomas ,newcomen1 also an ,englishman4 ,this type of engine was widely used1 mostly for pumping water out of mines but occasionally for pumping water into a reservoir to supply a waterwheel4 ,it was arranged with a vertical steam cylinder located beneath one end of a large pivoted working beam and a vertical plunger-type pump beneath the other end4 ,heavy1 flat chains were secured to a sector at each end of the working beam and to the engine and pump piston rods in such a way that the rods were always tangent to a circle whose center was at the beam pivot4 ,the weight of the reciprocating pump parts pulled the pump end of the beam down2 the atmosphere1 acting on the open top of the piston in the steam cylinder1 caused the engine end of the beam to be pulled down when the steam beneath the piston was condensed4 ,the chains would of course transmit force from piston to beam only in tension4 ,it is now obvious that a connecting rod1 a crank1 and a sufficiently heavy flywheel might have been used in a conventional ,newcomen engine in order to supply power to a rotating shaft1 but contemporary evidence makes it clear that this solution was by no means obvious to ,watt nor to his contemporaries4 ,at the time of his first engine patent1 in #agfi1 ,watt had devised a steam wheel1 or rotary engine1 that used liquid mercury in the lower part of a toroidal chamber to provide a boundary for steam spaces successively formed by flap gates within the chamber4 ,the practical difficulties of construction finally ruled out this solution to the problem of a rotating power source1 but not until after ,boulton and ,watt had spent considerable effort and money on it4#e ,footnote #e3 ,henry ,w4 ,dickinson and ,rhys ,jenkins1 ,james ,watt and the ,steam ,engine1 ,oxford1 ,clarendon ,press1 #aibg1 pp4 #adf-adh1 pls4 #ad1 #ca4 ,this work presents a full and knowledgeable discussion1 based on primary material1 of the development of ,watt's many contributions to mechanical technology4 ,it is ably summarized in ,dickinson1 op4 cit4 7footnote #b74 ,in #aggg a speaker before the ,royal ,society in ,london observed that in order to obtain rotary output from a reciprocating steam engine1 a crank naturally occurs in theory1 but that in fact the crank is impractical because of the irregular rate of going of the engine and its variable length of stroke4 ,he said that on the first variation of length of stroke the machine would be either broken to pieces1 or turned back4#f ,john ,smeaton1 in the front rank of ,english steam engineers of his time1 was asked in #agha by ,his ,majesty's ,victualling-,office for his opinion as to whether a steam-powered grain mill ought to be driven by a crank or by a waterwheel supplied by a pump4 ,smeaton's conclusion was that the crank was quite unsuited to a machine in which regularity of operation was a factor4 ,i apprehend1 he wrote1 that no motion communicated from the reciprocating beam of a fire engine can ever act perfectly equal and steady in producing a circular motion1 like the regular efflux of water in turning a waterwheel4 ,he recommended1 incidentally1 that a ,boulton and ,watt steam engine be used to pump water to supply the waterwheel4#g ,smeaton had thought of a flywheel1 but he reasoned that a flywheel large enough to smooth out the halting1 jerky operation of the steam engines that he had observed would be more of an encumbrance than a pump1 reservoir1 and waterwheel4#h ,footnote #f3 ,john ,farey1 ,a ,treatise on the ,steam ,engine1 ,london1 #ahbg1 pp4 #djh-dji4 ,footnote #g3 ,reports of the ,late ,john ,smeaton1 ,f4,r4,s41 ,london1 #ahab1 vol4 #b1 pp4 #cgh-chj4 ,footnote #h3 ,farey1 op4 cit4 7footnote #f71 p4 #dji4 ,the simplicity of the eventual solution of the problem was not clear to ,watt at this time4 ,he was not1 as tradition has it1 blocked merely by the existence of a patent for a simple crank and thus forced to invent some other device as a substitute4 ,matthew ,wasbrough1 of ,bristol1 the engineer commonly credited with the crank patent1 made no mention of a crank in his patent specification1 but rather intended to make use of racks with teeth1 or one or more pullies1 wheels1 segments of wheels1 to which are fastened rotchets and clicks or palls4444 ,he did1 however1 propose to add a fly or flys1 in order to render the motion more regular and uniform4 ,unfortunately for us1 he submitted no drawings with his patent specification4#i ,footnote #i3 ,british ,patent #abac1 ,march #aj1 #aggi4 ,james ,pickard1 of ,birmingham1 like ,boulton1 a buttonmaker1 in #aghj patented a counterweighted crank device 7fig4 #f7 that was expected to remove the objection to a crank1 which operated with changing leverage and thus irregular power4 ,in figure #f1 the counterweighted wheel1 revolving twice for each revolution of the crank 7,a71 would allow the counterweight to descend while the crank passed the dead-center position and would be raised while the crank had maximum leverage4 ,no mention of a flywheel was made in this patent4#aj ,footnote #aj3 ,british ,patent #abfc1 ,august #bc1 #aghj4 ,illustration3 ,figure #f4--,one of the steam engine ,crank ,patents that hindered ,james ,watt's progress4 ,this patent1 granted to ,james ,pickard in #aghj1 claimed only the arrangement of counterweights1 not the crank4 ,the crank pin to which the connecting rod was attached is at ,aa4 ,from ,british ,patent #abfc1 ,august #bc1 #aghj4 ,wasbrough1 finding that his rotchets and clicks did not serve1 actually used1 in #aghj1 a crank with a flywheel4 ,watt was aware of this1 but he remained unconvinced of the superiority of the crank over other devices and did not immediately appreciate the regulating ability of a flywheel4#aa ,in ,april #agha ,watt wrote to ,boulton1 who was then out of town3 ,i know from experiment that the other contrivance1 which you saw me try1 performs at least as well1 and has in fact many advantages over the crank4#ab ,the other contrivance probably was his swash wheel which he built and which appeared on his next important patent specification 7fig4 #g;a74 ,also in this patent were four other devices1 one of which was easily recognizable as a crank1 and two of which were eccentrics 7fig4 #g;a1 b74 ,the fourth device was the well-known sun-and-planet gearing 7fig4 #g;e74#ac ,in spite of the similarity of the simple crank to the several variations devised by ,watt1 this patent drew no fire from ,wasbrough or ,pickard1 perhaps because no reasonable person would contend that the crank itself was a patentable feature1 or perhaps because the similarity was not at that time so obvious4 ,however1 ,watt steered clear of directly discernible application of cranks because he preferred to avoid a suit that might overthrow his or other patents4 ,for example1 if the ,wasbrough and ,pickard patents had been voided1 they would have become public property2 and ,watt feared that they might get into the hands of men more ingenious1 who would give ,boulton and ,watt more competition than ,wasbrough and ,pickard4#ad ,footnote #aa3 ,dickinson and ,jenkins1 op4 cit4 7footnote #e71 pp4 #aej1 #aed4 ,footnote #ab3 ,ibid41 p4 #aed4 ,footnote #ac3 ,william ,murdock1 at this time a ,boulton and ,watt erector1 may have suggested this arrangement4 ,ibid41 p4 #ef4 ,footnote #ad3 ,muirhead1 op4 cit4 7footnote #c71 vol4 #c1 note on p4 #ci4 ,illustration3 ,figure #g4--;,james ,watt's five alternative devices for the conversion of reciprocating motion to rotary motion in a steam engine4 7,british ,patent #acjf1 ,october #be1 #agha74 ,from ,james ,p4 ,muirhead1 ,the ,origin and ,progress of the ,mechanical ,inventions of ,james ,watt 7,london1 #ahed1 vol4 #c1 pls4 #c-e1 #g74 ,illustration3 7a7 ,inclined wheel4 ,the vertical shaft at ,d is rotated by action of wheels ,h and ,j on cam1 or swash plate1 ,,abc4 ,boulton and ,watt tried this device but discarded it4 ,illustration3 7b7 ,counterweighted crank wheel4 ,illustration3 7c7 ,eccentric wheel with external yoke hung from working beam4 ,the wheel pivots at ,c4 ,illustration3 7d7 ,eccentric wheel with internal driving wheel hung from working beam4 ,wheel ,b is pivoted at center of shaft ,a4 ,illustration3 7e7 ,sun-and-planet gearing4 ,this is the idea actually employed in ,boulton and ,watt engines4 ,as the optional link ,,jk held the gearwheel centers always equidistant1 the annular guide ,g was not used4 ,the sun-and-planet arrangement1 with gears of equal size1 was adopted by ,watt for nearly all the rotative engines that he built during the term of the crank patents4 ,this arrangement had the advantage of turning the flywheel through two revolutions during a single cycle of operation of the piston1 thus requiring a flywheel only one-fourth the size of the flywheel needed if a simple crank were used4 ,the optional link 7,,jk of fig4 #g;e7 was used in the engines as built4 ,from the first1 the rotative engines were made double-acting--that is1 work was done by steam alternately in each end of the cylinder4 ,the double-acting engine1 unlike the single-acting pumping engine1 required a piston rod that would push as well as pull4 ,it was in the solution of this problem that ,watt's originality and sure judgment were most clearly demonstrated4 ,a rack and sector arrangement 7fig4 #h7 was used on some engines4 ,the first one1 according to ,watt1 has broke out several teeth of the rack1 but works steady4#ae ,a little later he told a correspondent that his double-acting engine acts so powerfully that it has broken all its tackling repeatedly4 ,we have now tamed it1 however4#af ,footnote #ae3 ,james ,watt1 ,march #ca1 #aghc1 quoted in ,dickinson and ,jenkins1 op4 cit4 7footnote #e71 p4 #adj4 ,footnote #af3 ,watt to ,de ,luc1 ,april #bf1 #aghc1 quoted in ,muirhead1 op4 cit4 7footnote #c71 vol4 #b1 p4 #agd4 ,illustration3 ,figure #h4--,watt engine of #aghb 7,british ,patent #acba1 ,march #ab1 #aghb7 showing the rack and sector used to guide the upper end of the piston rod and to transmit force from piston to working beam4 ,this engine1 with a #cj-;inch cylinder and an #h-;foot stroke1 was arranged for pumping4 ,pump rod ,,ss is hung from sector of the working beam4 ,from ,james ,p4 ,muirhead1 ,the ,origin and ,progress of the ,mechanical ,inventions of ,james ,watt 7,london1 #ahed1 vol4 #c1 pl4 #ae74 ,it was about a year later that the straight-line linkage#ag was thought out4 ,i have started a new hare1 ,watt wrote to his partner4 ,i have got a glimpse of a method of causing the piston-rod to move up and down perpendicularly1 by only fixing it to a piece of iron upon the beam1 without chains1 or perpendicular guides1 or untowardly frictions1 arch-heads1 or other pieces of clumsiness4444 ,i have only tried it in a slight model yet1 so cannot build upon it1 though ,i think it a very probable thing to succeed1 and one of the most ingenious simple pieces of mechanism ,i have contrived4444#ah ,footnote #ag3 ,watt's was a four-bar linkage4 ,all four-bar straight-line linkages that have no sliding pairs trace only an approximately straight line4 ,the exact straight-line linkage in a single plane was not known until #ahfd 7see p4 #bjd74 ,in #ahec ,pierre-,frdric ,sarrus 7#agih-ahfa71 a ,french professor of mathematics at ,strasbourg1 devised an accordion-like spatial linkage that traced a true straight line4 ,described but not illustrated 7,acadmie des ,sciences1 ,paris1 ,comptes rendus1 #ahec1 vol4 #cf1 pp4 #ajcf-ajch1 #aabe71 the mechanism was forgotten and twice reinvented2 finally1 the original invention was rediscovered by an ,english writer in #aije4 ,for chronology1 see ,florian ,cajori1 ,a ,history of ,mathematics1 ed4 #b1 ,new ,york1 #aiai1 p4 #cja4 ,footnote #ah3 ,muirhead1 op4 cit4 7footnote #c71 vol4 #b1 pp4 #aia-aib4 ,watt's marvelously simple straight-line linkage was incorporated into a large beam engine almost immediately1 and the usually pessimistic and reserved inventor was close to a state of elation when he told ,boulton that the new central perpendicular motion answers beyond expectation1 and does not make the shadow of a noise4#ai ,this linkage1 which was included in an extensive patent of #aghd1 and two alternative devices are illustrated here 7fig4 #i74 ,one of the alternatives is a guided crosshead 7fig4 #i1 top right74 ,footnote #ai3 ,ibid41 p4 #bjb4 ,illustration3 ,figure #i4--,watt's mechanisms for guiding the upper end of the piston rod of a double-acting engine 7,british ,patent #adcb1 ,april #bh1 #aghd74 ,top left1 straight-line linkage2 top right1 crosshead and guide arrangement2 lower left1 piston rod ,a is guided by sectors ,d and ,e1 suspended by flexible cords4 ,from ,james ,p4 ,muirhead1 ,the ,origin and ,progress of the ,mechanical ,inventions of ,james ,watt 7,london1 #ahed1 vol4 #c1 pls4 #ba1 #bb74 ,brilliant as was the conception of this linkage1 it was followed up by a synthesis that is very little short of incredible4 ,in order to make the linkage attached to the beam of his engines more compact1 ,watt had plumbed his experience for ideas2 his experience had yielded up the work done much earlier on a drafting machine that made use of a pantograph4#bj ,watt combined his straight-line linkage with a pantograph1 one link becoming a member of the pantograph4 ,footnote #bj3 ,it has only one fault1 he had told a friend on ,december #bd1 #aggc1 after describing the drafting machine to him1 which is1 that it will not do1 because it describes conic sections instead of straight lines4 ,ibid41 p4 #ga4 ,the length of each oscillating link of the straight-line linkage was thus reduced to one-fourth instead of one-half the beam length1 and the entire mechanism could be constructed so that it would not extend beyond the end of the working beam4 ,this arrangement soon came to be known as ,watt's parallel motion 7fig4 #aj74ba ,years later ,watt told his son3 ,though ,i am not over anxious after fame1 yet ,i am more proud of the parallel motion than of any other mechanical invention ,i have ever made4#bb ,footnote #ba3 ,throughout the #aith century the term parallel motion was used indiscriminately to refer to any straight-line linkage4 ,i have not discovered the origin of the term4 ,watt did not use it in his patent specification1 and ,i have not found it in his writings or elsewhere before #ahjh 7see footnote #bb74 ,the ,cyclopaedia 7,abraham ,rees1 ed41 ,london1 #ahai1 vol4 #bf7 defined parallel motion as a term used among practical mechanics to denote the rectilinear motion of a piston-rod1 c4 in the direction of its length2 and contrivances1 by which such alternate rectilinear motions are converted into continuous rotatory ones1 or vice versa4444 ,robert ,willis in his ,principles of ,mechanism 7,london1 #ahda1 p4 #cii7 described parallel motion as a term somewhat awkwardly applied to a combination of jointed rods1 the purpose of which is to cause a point to describe a straight line4444 ,a4 ,b4 ,kempe in ,how to ,draw a ,straight ,line 7,london1 #ahgg1 p4 #di7 wrote3 ,i have been more than once asked to get rid of the objectionable term 'parallel motion4' ,i do not know how it came to be employed1 and it certainly does not express what is intended4 ,the expression1 however1 has now become crystallised1 and ,i for one cannot undertake to find a solvent4 ,footnote #bb3 ,muirhead1 op4 cit4 7footnote #c71 vol4 #c1 note on p4 #hi4 ,illustration3 ,figure #aj4--,watt's parallel motion4 ,engine's working beam is pivoted at ,a4 ,pivot ,f is attached to the engine frame4 ,from ,dyonysius ,lardner1 ,the ,steam ,engine 7,philadelphia1 #aheb71 pl4 #e 7,american ed4 #e from ,london ed4 #e74 ,the ,watt four-bar linkage was employed #ge years after its inception by the ,american ,charles ,b4 ,richards when1 in #ahfa1 he designed his first high-speed engine indicator 7fig4 #aa74 ,introduced into ,england the following year1 the ,richards ,indicator was an immediate success1 and many thousands were sold over the next #bj or #cj years4#bc ,footnote #bc3 ,charles ,t4 ,porter1 ,engineering ,reminiscences1 ,new ,york1 #aijh1 pp4 #eh-ei1 #ij4 ,illustration3 ,figure #aa4--,richards high-speed engine indicator of #ahfa1 showing application of the ,watt straight-line linkage4 7,,usnm #cjgeae2 ,smithsonian photo #dfegj74 ,in considering the order of synthetic ability required to design the straight-line linkage and to combine it with a pantograph1 it should be kept in mind that this was the first one of a long line of such mechanisms4#bd ,once the idea was abroad1 it was only to be expected that many variations and alternative solutions should appear4 ,one wonders1 however1 what direction the subsequent work would have taken if ,watt had not so clearly pointed the way4 ,footnote #bd3 ,at least one earlier straight-line linkage1 an arrangement later ascribed to ,richard ,roberts1 had been depicted before ,watt's patent 7,pierre ,patte1 ,mmoirs sur les objets les plus importants de l'architecture1 ,paris1 #agfi1 p4 #bbi and pl4 #aa74 ,however1 this linkage 7reproduced here in figure #ah7 had no detectable influence on ,watt or on subsequent practice4 ,in #ahbg ,john ,farey1 in his exhaustive study of the steam engine1 wrote perhaps the best contemporary view of ,watt's work4 ,farey as a young man had several times talked with the aging ,watt1 and he had reflected upon the nature of the intellect that had caused ,watt to be recognized as a genius1 even within his own lifetime4 ,in attempting to explain ,watt's genius1 ,farey set down some observations that are pertinent not only to kinematic synthesis but to the currently fashionable term creativity4 ,in ,farey's opinion ,watt's inventive faculty was far superior to that of any of his contemporaries2 but his many and various ideas would have been of little use if he had not possessed a very high order of judgment1 that faculty of distinguishing between ideas2 decomposing compound ideas into more simple elements2 arranging them into classes1 and comparing them together4444 ,farey was of the opinion that while a mind like ,watt's could produce brilliant new ideas1 still the common stock of ideas which are current amongst communities and professions1 will generally prove to be of a better quality than the average of those new ideas1 which can be produced by any individual from the operation of his own mind1 without assistance from others4 ,farey concluded with the observation that the most useful additions to that common stock1 usually proceed from the individuals who are well acquainted with the whole series4#be ,footnote #be3 ,farey1 op4 cit4 7footnote #f71 pp4 #fea1 #feb4 ,to ,draw a ,straight ,line ,during most of the century after ,james ,watt had produced his parallel motion1 the problem of devising a linkage1 one point of which would describe a straight line1 was one that tickled the fancies of mathematicians1 of ingenious mechanics1 and of gentlemanly dabblers in ideas4 ,the quest for a straight-line mechanism more accurate than that of ,watt far outlasted the pressing practical need for such a device4 ,large metal planing machines were well known by #ahcj1 and by midcentury crossheads and crosshead guides were used on both sides of the ,atlantic in engines with and without working beams4 ,by #ahai ,john ,farey had observed quite accurately that1 in ,england at least1 many other schemes had been tried and found wanting and that no methods have been found so good as the original engine2 and we accordingly find1 that all the most established and experienced manufacturers make engines which are not altered in any great feature from ,mr4 ,watt's original engine4444#bf ,footnote #bf3 ,in ,rees1 op4 cit4 7footnote #ba71 vol4 #cd 7,steam ,engine74 ,john ,farey was the writer of this article 7see ,farey1 op4 cit41 p4 vi74 ,two mechanisms for producing a straight line were introduced before the ,boulton and ,watt monopoly ended in #ahjj4 ,perhaps the first was by ,edmund ,cartwright 7#agdc-ahbc71 who is said to have had the original idea for a power loom4 ,this geared device 7fig4 #ab71 was characterized patronizingly by a contemporary ,american editor as possessing as much merit as can possibly be attributed to a gentleman engaged in the pursuit of mechanical studies for his own amusement4#bg ,only a few small engines were made under the patent4#bh ,footnote #bg3 ,emporium of ,arts and ,sciences1 ,december #ahac1 new ser41 vol4 #b1 no4 #a1 p4 #ha4 ,footnote #bh3 ,farey1 op4 cit4 7footnote #f71 p4 #fff4 ,illustration3 ,figure #ab4--;,cartwright's geared straight-line mechanism of about #ahjj4 ,from ,abraham ,rees1 ,the ,cyclopaedia 7,london1 #ahai1 ,steam ,engine1 pl4 #e74 ,the properties of a hypocycloid were recognized by ,james ,white1 an ,english engineer1 in his geared design which employed a pivot located on the pitch circle of a spur gear revolving inside an internal gear4 ,the diameter of the pitch circle of the spur gear was one-half that of the internal gear1 with the result that the pivot1 to which the piston rod was connected1 traced out a diameter of the large pitch circle 7fig4 #ac74 ,white in #ahja received from ,napoleon ,bonaparte a medal for this invention when it was exhibited at an industrial exposition in ,paris4#bi ,some steam engines employing ,white's mechanism were built1 but without conspicuous commercial success4 ,white himself rather agreed that while his invention was allowed to possess curious properties1 and to be a pretty thing1 opinions do not all concur in declaring it1 essentially and generally1 a good thing4#cj ,footnote #bi3 ,h4 ,w4 ,dickinson1 ,james ,white and ,his ',new ,century of ,inventions1' ,transactions of the ,newcomen ,society1 #aidi-aiea1 vol4 #bg1 pp4 #age-agi4 ,footnote #cj3 ,james ,white1 ,a ,new ,century of ,inventions1 ,manchester1 #ahbb1 pp4 #cj-ca1 #cch4 ,a hypocycloidal engine used in ,stourbridge1 ,england1 is in the ,henry ,ford ,museum4 ,illustration3 ,figure #ac4--;,james ,white's hypocycloidal straight-line mechanism1 about #ahjj4 ,the fly-weights 7at the ends of the diagonal arm7 functioned as a flywheel4 ,from ,james ,white1 ,a ,new ,century of ,inventions 7,manchester1 #ahbb1 pl4 #g74 ,the first of the non-,watt four-bar linkages appeared shortly after #ahjj4 ,the origin of the grasshopper beam motion is somewhat obscure1 although it came to be associated with the name of ,oliver ,evans1 the ,american pioneer in the employment of high-pressure steam4 ,a similar idea1 employing an isosceles linkage1 was patented in #ahjc by ,william ,freemantle1 an ,english watchmaker 7fig4 #ad74ca ,this is the linkage that was attributed much later to ,john ,scott ,russell 7#ahjh-ahhb71 the prominent naval architect4#cb ,an inconclusive hint that ,evans had devised his straight-line linkage by #ahje appeared in a plate illustrating his ,abortion of the ,young ,steam ,engineer's ,guide 7,philadelphia1 #ahje71 and it was certainly used on his ,columbian engine 7fig4 #ae71 which was built before #ahac4 ,the ,freemantle linkage1 in modified form1 appeared in ,rees's ,cyclopaedia of #ahai 7fig4 #af71 but it is doubtful whether even this would have been readily recognized as identical with the ,evans linkage1 because the connecting rod was at the opposite end of the working beam from the piston rod1 in accordance with established usage1 while in the ,evans linkage the crank and connecting rod were at the same end of the beam4 ,it is possible that ,evans got his idea from an earlier ,english periodical1 but concrete evidence is lacking4 ,footnote #ca3 ,british ,patent #bgda1 ,november #ag1 #ahjc4 ,footnote #cb3 ,william ,j4 ,m4 ,rankine1 ,manual of ,machinery and ,millwork1 ed4 #f1 ,london1 #ahhg1 p4 #bge4 ,illustration3 ,figure #ad4--;,freemantle straight-line linkage1 later called the ,scott ,russell linkage4 ,from ,british ,patent #bgda1 ,november #ag1 #ahjc4 ,illustration3 ,figure #ae4--,oliver ,evans' ,columbian engine1 #ahac1 showing the ,evans1 or grasshopper1 straight-line linkage4 ,from ,emporium of ,arts and ,sciences 7new ser41 vol4 #b1 no4 #c1 ,april #ahad1 pl4 opposite p4 #chj74 ,illustration3 ,figure #af4--,modified ,freemantle linkage1 #ahai1 which is kinematically the same as the ,evans linkage4 ,pivots ,d and ,e are attached to engine frame4 ,from ,abraham ,rees1 ,the ,cyclopaedia 7,london1 #ahai1 ,parallel ,motions1 pl4 #c74 ,if the idea did in fact originate with ,evans1 it is strange that he did not mention it in his patent claims1 or in the descriptions that he published of his engines4#cc ,the practical advantage of the ,evans linkage1 utilizing as it could a much lighter working beam than the ,watt or ,freemantle engines1 would not escape ,oliver ,evans1 and he was not a man of excessive modesty where his own inventions were concerned4 ,footnote #cc3 ,greville and ,dorothy ,bathe1 ,oliver ,evans1 ,philadelphia1 #aice1 pp4 #hh1 #aif1 and passim4 ,another four-bar straight-line linkage that became well known was attributed to ,richard ,roberts of ,manchester 7#aghi-ahfd71 who around #ahbj had built one of the first metal planing machines1 which machines helped make the quest for straight-line linkages largely academic4 ,i have not discovered what occasioned the introduction of the ,roberts linkage1 but it dated from before #ahda4 ,although ,roberts patented many complex textile machines1 an inspection of all of his patent drawings has failed to provide proof that he was the inventor of the ,roberts linkage4#cd ,the fact that the same linkage is shown in an engraving of #agfi 7fig4 #ah7 further confuses the issue4#ce ,footnote #cd3 ,robert ,willis 7op4 cit4 ,footnote #ba p4 #daa7 credited ,richard ,roberts with the linkage4 ,roberts' #ae ,british patent drawings exhibit complex applications of cams1 levers1 guided rods1 cords1 and so forth1 but no straight-line mechanism4 ,in his patent no4 #fbeh of ,april #ac1 #ahcb1 for a steam engine and locomotive carriage1 ,roberts used ,watt's parallel motion on a beam driven by a vertical cylinder4 ,footnote #ce3 ,this engraving appeared as plate #aa in ,pierre ,patte's #agfi work 7op4 cit4 footnote #bd74 ,patte stated that the machine depicted in his plate #aa was invented by ,m4 de ,voglie and was actually used in #agef4 ,illustration3 ,figure #ag4--,straight-line linkage 7before #ahda7 attributed to ,richard ,roberts by ,robert ,willis4 ,from ,a4 ,b4 ,kempe1 ,how to ,draw a ,straight ,line 7,london1 #ahgg1 p4 #aj74 ,illustration3 ,figure #ah4--,machine for sawing off pilings under water1 about #agfj1 designed by ,de ,voglie4 ,the ,roberts linkage operates the bar 7,q in detailed sketch7 at the rear of the machine below the operators4 ,the significance of the linkage apparently was not generally recognized4 ,a similar machine depicted in ,diderot's ,encyclopdie1 published several years later1 did not employ the straight-line linkage4 ,from ,pierre ,patte1 ,memoirs sur les objets plus importants de l'architecture 7,paris1 #agfi1 pl4 #aa74 ,the appearance in #ahfd of ,peaucellier's exact straight-line linkage went nearly unnoticed4 ,a decade later1 when news of its invention crossed the ,channel to ,england1 this linkage excited a flurry of interest1 and variations of it occupied mathematical minds for several years4 ,for at least #aj years before and #bj years after the final solution of the problem1 ,professor ,chebyshev1#cf a noted mathematician of the ,university of ,st4 ,petersburg1 was interested in the matter4 ,judging by his published works and his reputation abroad1 ,chebyshev's interest amounted to an obsession4 ,footnote #cf3 ,this is the ,library of ,congress spelling ,pafnut7i ,l'vovich ,chebyshev was born in #ahba1 near ,moscow1 and entered the ,university of ,moscow in #ahcg4 ,in #ahec1 after visiting ,france and ,england and observing carefully the progress of applied mechanics in those countries1 he read his first paper on approximate straight-line linkages1 and over the next #cj years he attacked the problem with new vigor at least a dozen times4 ,he found that the two principal straight-line linkages then in use were ,watt's and ,evans'4 ,chebyshev noted the departure of these linkages from a straight line and calculated the deviation as of the fifth degree1 or about #j4jjjh inch per inch of beam length4 ,he proposed a modification of the ,watt linkage to refine its accuracy but found that he would have to more than double the length of the working beam4 ,chebyshev concluded ruefully that his modification would present great practical difficulties4#cg ,footnote #cg3 ,oeuvres de ,p4 ,l4 ,tchebychef1 #b vols41 ,st4 ,petersburg1 #ahii-aijg1 vol4 #a1 p4 #ech2 vol4 #b1 pp4 #eg1 #he4 ,at length an idea occurred to ,chebyshev that would enable him to approach if not quite attain a true straight line4 ,if one mechanism was good1 he reasoned1 two would be better1 et cetera1 ad infinitum4 ,the idea was simply to combine1 or compound1 four-link approximate linkages1 arranging them in such a way that the errors would be successively reduced4 ,contemplating first a combination of the ,watt and ,evans linkages 7fig4 #ai71 ,chebyshev recognized that if point ,d of the ,watt linkage followed nearly a straight line1 point ,a of the ,evans linkage would depart even less from a straight line4 ,he calculated the deviation in this case as of the #aath degree4 ,he then replaced ,watt's linkage by one that is usually called the ,chebyshev straight-line mechanism 7fig4 #bj71 with the result that precision was increased to the #acth degree4#ch ,the steam engine that he displayed at the ,vienna ,exhibition in #ahgc employed this linkage--the ,chebyshev mechanism compounded with the ,evans1 or approximate isosceles1 linkage4 ,an ,english visitor to the exhibition commented that the motion is of little or no practical use1 for we can scarcely imagine circumstances under which it would be more advantageous to use such a complicated system of levers1 with so many joints to be lubricated and so many pins to wear1 than a solid guide of some kind2 but at the same time the arrangement is very ingenious and in this respect reflects great credit on its designer4#ci ,footnote #ch3 ,ibid41 vol4 #b1 pp4 #ic1 #id4 ,footnote #ci3 ,engineering1 ,october #c1 #ahgc1 vol4 #af1 p4 #bhd4 ,illustration3 ,figure #ai4--,pafnut7i ,l'vovich ,chebyshev 7#ahba-ahid71 ,russian mathematician active in analysis and synthesis of straight-line mechanisms4 ,from ,ouvres de ,p4 ,l4 ,tchebychef 7,st4 ,petersburg1 #aijg1 vol4 #b1 frontispiece74 ,illustration3 ,figure #bj4--;,chebyshev's combination 7about #ahfg7 of ,watt's and ,evans' linkages to reduce errors inherent in each4 ,points ,c1 ,c'1 and ,c are fixed2 ,a is the tracing point4 ,from ,oeuvres de ,p4 ,l4 ,tchebychef 7,st4 ,petersburg1 #aijg1 vol4 #b1 p4 #ic74 ,illustration3 ,figure #ba4--,top3 ,chebyshev straight-line linkage1 #ahfg2 from ,a4 ,b4 ,kempe1 ,how to ,draw a ,straight ,line 7,london1 #ahgg1 p4 #aa74 ,bottom3 ,chebyshev-,evans combination1 #ahfg2 from ,oeuvres de ,p4 ,l4 ,tchebychef 7,st4 ,petersburg1 #aijg1 vol4 #b1 p4 #id74 ,points ,c1 ,c'1 and ,c are fixed4 ,a is the tracing point4 ,there is a persistent rumor that ,professor ,chebyshev sought to demonstrate the impossibility of constructing any linkage1 regardless of the number of links1 that would generate a straight line2 but ,i have found only a dubious statement in the ,grande ,encyclopdie#dj of the late #aith century and a report of a conversation with the ,russian by an ,englishman1 ,james ,sylvester1 to the effect that ,chebyshev had succeeded in proving the nonexistence of a five-bar link-work capable of producing a perfect parallel motion4444#da ,regardless of what tradition may have to say about what ,chebyshev said1 it is of course well known that ,captain ,peaucellier was the man who finally synthesized the exact straight-line mechanism that bears his name4 ,footnote #dj3 ,la ,grande ,encyclopdie1 ,paris1 #ahhf 7,peaucellier74 ,footnote #da3 ,james ,sylvester1 ,recent ,discoveries in ,mechanical ,conversion of ,motion1 ,notices of the ,proceedings of the ,royal ,institution of ,great ,britain1 #ahgc-ahge1 vol4 #g1 p4 #aha4 ,the fixed link was not counted by ,sylvester2 in modern parlance this would be a six-link mechanism4 ,illustration3 ,figure #bb4--,peaucellier exact straight-line linkage1 #ahgc4 ,from ,a4 ,b4 ,kempe1 ,how to ,draw a ,straight ,line 7,london1 #ahgg1 p4 #ab74 ,illustration3 ,figure #bc4--,model of the ,peaucellier ,compas ,compos1 deposited in ,conservatoire ,national des ,arts et ,mtiers1 ,paris1 #ahge4 ,photo courtesy of the ,conservatoire4 ,illustration3 ,figure #bd4--;,james ,joseph ,sylvester 7#ahad-ahig71 mathematician and lecturer on straight-line linkages4 ,from ,proceedings of the ,royal ,society of ,london 7#ahih1 vol4 #fc1 opposite p4 #afa74 ,charles-,nicolas ,peaucellier1 a graduate of the ,ecole ,polytechnique and a captain in the ,french corps of engineers1 was #cb years old in #ahfd when he wrote a short letter to the editor of ,nouvelles ,annales de mathmatiques 7ser4 #b1 vol4 #c1 pp4 #dad-dae7 in ,paris4 ,he called attention to what he termed compound compasses1 a class of linkages that included ,watt's parallel motion1 the pantograph1 and the polar planimeter4 ,he proposed to design linkages to describe a straight line1 a circle of any radius no matter how large1 and conic sections1 and he indicated in his letter that he had arrived at a solution4 ,this letter stirred no pens in reply1 and during the next #aj years the problem merely led to the filling of a few academic pages by ,peaucellier and ,amde ,mannheim 7#ahca-aijf71 also a graduate of ,ecole ,polytechnique1 a professor of mathematics1 and the designer of the ,mannheim slide rule4 ,finally1 in #ahgc1 ,captain ,peaucellier gave his solution to the readers of the ,nouvelles ,annales4 ,his reasoning1 which has a distinct flavor of discovery by hindsight1 was that since a linkage generates a curve that can be expressed algebraically1 it must follow that any algebraic curve can be generated by a suitable linkage--it was only necessary to find the suitable linkage4 ,he then gave a neat geometric proof1 suggested by ,mannheim1 for his straight-line compound compass4#db ,footnote #db3 ,charles-,nicholas ,peaucellier1 ,note sur une question de geomtrie de compas1 ,nouvelles ,annales de mathmatiques1 #ahgc1 ser4 #b1 vol4 #ab1 pp4 #ga-gh4 ,a sketch of ,mannheim's work is in ,florian ,cajori1 ,a ,history of the ,logarithmic ,slide ,rule1 ,new ,york1 about #aiaj1 reprinted in ,string ,figures and ,other ,monographs1 ,new ,york1 ,chelsea ,publishing ,company1 #aifj4 ,on a ,friday evening in ,january #ahgd ,albemarle ,street in ,london was filled with carriages1 each maneuvering to unload its charge of gentlemen and their ladies at the door of the venerable hall of the ,royal ,institution4 ,amidst a mighty rustling of silks1 the elegant crowd made its way to the auditorium for one of the famous weekly lectures4 ,the speaker on this occasion was ,james ,joseph ,sylvester1 a small intense man with an enormous head1 sometime professor of mathematics at the ,university of ,virginia1 in ,america1 and more recently at the ,royal ,military ,academy in ,woolwich4 ,he spoke from the same rostrum that had been occupied by ,davy1 ,faraday1 ,tyndall1 ,maxwell1 and many other notable scientists4 ,professor ,sylvester's subject was ,recent ,discoveries in ,mechanical ,conversion of ,motion4#dc ,footnote #dc3 ,sylvester1 op4 cit4 7footnote #da71 pp4 #agi-aih4 ,it appears from a comment in this lecture that ,sylvester was responsible for the word linkage4 ,according to ,sylvester1 a linkage consists of an even number of links1 a link-work of an odd number4 ,since the fixed member was not considered as a link by ,sylvester1 this distinction became utterly confusing when ,reuleaux's work was published in #ahgf4 ,although link was used by ,watt in a patent specification1 it is not probable that he ever used the term link-work--at any rate1 my search for his use of it has been fruitless4 ,link work is used by ,willis 7op4 cit4 footnote #ba71 but the term most likely did not originate with him4 ,i have not found the word linkage used earlier than ,sylvester4 ,remarking upon the popular appeal of most of the lectures1 a contemporary observer noted that while many listeners might prefer to hear ,professor ,tyndall expound on the acoustic opacity of the atmosphere1 those of a higher and drier turn of mind experience ineffable delight when ,professor ,sylvester holds forth on the conversion of circular into parallel motion4#dd ,footnote #dd3 ,bernard ,h4 ,becker1 ,scientific ,london1 ,london1 #ahgd1 pp4 #de1 #ej1 #ea4 ,sylvester's aim was to bring the ,peaucellier linkage to the notice of the ,english-speaking world1 as it had been brought to his attention by ,chebyshev--during a recent visit of the ,russian to ,england--and to give his listeners some insight into the vastness of the field that he saw opened by the discovery of the ,french soldier4#de ,footnote #de3 ,sylvester1 op4 cit4 7footnote #da71 p4 #ahc2 ,nature1 ,november #ac1 #ahgc1 vol4 #i1 p4 #cc4 ,the perfect parallel motion of ,peaucellier looks so simple1 he observed1 and moves so easily that people who see it at work almost universally express astonishment that it waited so long to be discovered4 ,but that was not his reaction at all4 ,the more one reflects upon the problem1 ,sylvester continued1 he wonders the more that it was ever found out1 and can see no reason why it should have been discovered for a hundred years to come4 ,viewed a priori there was nothing to lead up to it4 ,it bears not the remotest analogy 7except in the fact of a double centring7 to ,watt's parallel motion or any of its progeny4#df ,footnote #df3 ,sylvester1 op4 cit4 7footnote #da71 p4 #aha4 ,it must be pointed out1 parenthetically at least1 that ,james ,watt had not only had to solve the problem as best he could1 but that he had no inkling1 so far as experience was concerned1 that a solvable problem existed4 ,sylvester interrupted his panegyric long enough to enumerate some of the practical results of the ,peaucellier linkage4 ,he said that ,mr4 ,penrose1 the eminent architect and surveyor to ,st4 ,paul's ,cathedral1 had put up a house-pump worked by a negative ,peaucellier cell1 to the great wonderment of the plumber employed1 who could hardly believe his senses when he saw the sling attached to the piston-rod moving in a true vertical line1 instead of wobbling as usual from side to side4 ,sylvester could see no reason why the perfect parallel motion should not be employed with equal advantage in the construction of ordinary water-closets4 ,the linkage was to be employed by a gentleman of fortune in a marine engine for his yacht1 and there was talk of using it to guide a piston rod in certain machinery connected with some new apparatus for the ventilation and filtration of the air of the ,houses of ,parliament4 ,in due course1 ,mr4 ,prim1 engineer to the ,houses1 was pleased to show his adaptation of the ,peaucellier linkage to his new blowing engines1 which proved to be exceptionally quiet in their operation 7fig4 #be74dg ,a bit on the ludicrous side1 also1 was ,sylvester's #gh-;bar linkage that traced a straight line along the line connecting the two fixed centers of the linkage4#dh ,footnote #dg3 ,ibid41 pp4 #ahb1 #ahc1 #ahh1 #aic4 ,footnote #dh3 ,kempe1 op4 cit4 7footnote #ba71 p4 #ag4 ,illustration3 ,figure #be4--,mr4 ,prim's blowing engine used for ventilating the ,house of ,commons1 #ahgg4 ,the crosshead of the reciprocating air pump is guided by a ,peaucellier linkage shown at the center4 ,the slate-lined air cylinders had rubber-flap inlet and exhaust valves and a piston whose periphery was formed by two rows of brush bristles4 ,prim's machine was driven by a steam engine4 ,photograph by ,science ,museum1 ,london4 ,before dismissing with a smile the quaint ideas of our ,victorian forbears1 however1 it is well to ask1 #hh years later1 whether some rather elaborate work reported recently on the synthesis of straight-line mechanisms is more to the point1 when the principal objective appears to be the moving of an indicator on a pleasing1 expanded 7i4e41 squashed flat7 radio dial4#di ,footnote #di3 ,machine ,design1 ,december #aied1 vol4 #bf1 p4 #baj4 ,but ,professor ,sylvester was more interested1 really1 in the mathematical possibilities of the ,peaucellier linkage1 as no doubt our modern investigators are4 ,through a compounding of ,peaucellier mechanisms1 he had already devised square-root and cube-root extractors1 an angle trisector1 and a quadratic-binomial root extractor1 and he could see no limits to the computing abilities of linkages as yet undiscovered4#ej ,footnote #ej3 ,sylvester1 op4 cit4 7footnote #da71 p4 #aia4 ,sylvester recalled fondly1 in a footnote to his lecture1 his experience with a little mechanical model of the ,peaucellier linkage at an earlier dinner meeting of the ,philosophical ,club of the ,royal ,society4 ,the ,peaucellier model had been greeted by the members with lively expressions of admiration when it was brought in with the dessert1 to be seen by them after dinner1 as is the laudable custom among members of that eminent body in making known to each other the latest scientific novelties4 ,and ,sylvester would never forget the reaction of his brilliant friend ,sir ,william ,thomson 7later ,lord ,kelvin7 upon being handed the same model in the ,athenaeum ,club4 ,after ,sir ,william had operated it for a time1 ,sylvester reached for the model1 but he was rebuffed by the exclamation ,no6 ,i have not had nearly enough of it--it is the most beautiful thing ,i have ever seen in my life4#ea ,footnote #ea3 ,ibid41 p4 #ahc4 ,the aftermath of ,professor ,sylvester's performance at the ,royal ,institution was considerable excitement amongst a limited company of interested mathematicians4 ,many alternatives to the ,peaucellier straight-line linkage were suggested by several writers of papers for learned journals4#eb ,footnote #eb3 ,for a summary of developments and references1 see ,kempe1 op4 cit4 7footnote #ba71 pp4 #di-ea4 ,two of ,hart's six-link exact straight-line linkages referred to by ,kempe are illustrated in ,henry ,m4 ,cundy and ,a4 ,p4 ,rollett1 ,mathematical ,models1 ,oxford1 ,oxford ,university ,press1 #aieb1 pp4 #bjd-bje4 ,peaucellier's linkage was of eight links4 ,in the summer of #ahgf1 after ,sylvester had departed from ,england to take up his post as professor of mathematics in the new ,johns ,hopkins ,university in ,baltimore1 ,alfred ,bray ,kempe1 a young barrister who pursued mathematics as a hobby1 delivered at ,london's ,south ,kensington ,museum a lecture with the provocative title ,how to ,draw a ,straight ,line4#ec ,footnote #ec3 ,kempe1 op4 cit4 7footnote #ba71 p4 #bf4 ,in order to justify the ,peaucellier linkage1 ,kempe belabored the point that a perfect circle could be generated by means of a pivoted bar and a pencil1 while the generation of a straight line was most difficult if not impossible until ,captain ,peaucellier came along4 ,a straight line could be drawn along a straight edge2 but how was one to determine whether the straight edge was straight8 ,he did not weaken his argument by suggesting the obvious possibility of using a piece of string4 ,kempe had collaborated with ,sylvester in pursuing the latter's first thoughts on the subject1 and one result1 that to my mind exemplifies the general direction of their thinking1 was the ,sylvester-,kempe parallel motion 7fig4 #bf74 ,illustration3 ,figure #bf4--,sylvester-,kempe translating linkage1 #ahgg4 ,the upper and lower plates remain parallel and equidistant4 ,from ,a4 ,b4 ,kempe1 ,how to ,draw a ,straight ,line 7,london1 #ahgg1 p4 #cg74 ,illustration3 ,figure #bg4--;,gaspard ,monge 7#agdf-ahah71 professor of mathematics at the ,ecole ,polytechnique from #agid and founder of the academic discipline of machine kinematics1 ,from ,livre du ,centenaire1 #agid-ahid1 ,ecole ,polytechnique 7,paris1 #ahie1 vol4 #a1 frontispiece74 ,enthusiastic as ,kempe was1 however1 he injected an apologetic note in his lecture4 ,that these results are valuable cannot ,i think be doubted1 he said1 though it may well be that their great beauty has led some to attribute to them an importance which they do not really possess4444 ,he went on to say that #ej years earlier1 before the great improvements in the production of true plane surfaces1 the straight-line mechanisms would have been more important than in #ahgf1 but he added that linkages have not at present1 ,i think1 been sufficiently put before the mechanician to enable us to say what value should really be set upon them4#ed ,footnote #ed3 ,ibid41 pp4 #f-g4 ,i have not pursued the matter of cognate linkages 7the ,watt and ,evans linkages are cognates7 because the ,roberts-,chebyshev theorem escaped my earlier search1 as it had apparently escaped most others until #aieh4 ,see ,r4 ,s4 ,hartenberg and ,j4 ,denavit1 ,the ,fecund ,four-,bar1 ,transactions of the ,fifth ,conference on ,mechanisms1 ,cleveland1 ,penton ,publishing ,company1 #aieh1 pp4 #aid-bjf1 reprinted in ,machine ,design1 ,april #af1 #aiei1 vol4 #ca1 pp4 #adi-aeb4 ,see also ,a4 ,e4 ,r4 de ,jonge1 ,the ,correlation of ,hinged ,four-,bar ,straight-,line ,motion ,devices by ,means of the ,roberts ,theorem and a ,new ,proof of the ,latter1 ,annals of the ,new ,york ,academy of ,sciences1 ,march #ah1 #aifj1 vol4 #hd1 art4 #c1 pp4 #ge-ade 7published separately74 ,it was during this same summer of #ahgf1 at the ,loan ,exhibition of ,scientific ,apparatus in the ,south ,kensington ,museum1 that the work of ,franz ,reuleaux1 which was to have an important and lasting influence on kinematics everywhere1 was first introduced to ,english engineers4 ,some #cjj beautifully constructed teaching aids1 known as the ,berlin kinematic models1 were loaned to the exhibition by the ,royal ,industrial ,school in ,berlin1 of which ,reuleaux was the director4 ,these models were used by ,prof4 ,alexander ,b4 ,w4 ,kennedy of ,university ,college1 ,london1 to help explain ,reuleaux's new and revolutionary theory of machines4#ee ,footnote #ee3 ,alexander ,b4 ,w4 ,kennedy1 ,the ,berlin ,kinematic ,models1 ,engineering1 ,september #ae1 #ahgf1 vol4 #bb1 pp4 #bci-bdj4 ,scholars and ,machines ,when1 in #ahbi1 ,andr-,marie ,ampre 7#agge-ahcf7 was called upon to prepare a course in theoretical and experimental physics for the ,collge de ,france1 he first set about determining the limits of the field of physics4 ,this exercise suggested to his wide-ranging intellect not only the definition of physics but the classification of all human knowledge4 ,he prepared his scheme of classification1 tried it out on his physics students1 found it incomplete1 returned to his study1 and produced finally a two-volume work wherein the province of kinematics was first marked out for all to see and consider4#ef ,only a few lines could be devoted to so specialized a branch as kinematics1 but ,ampre managed to capture the central idea of the subject4 ,footnote #ef3 ,andr-,marie ,ampre1 ,essai sur la philosophie des sciences1 une exposition analytique d'une classification naturelle de toutes les connaissances humaines1 #b vols41 ,paris1 #ahch 7for origin of the project1 see vol4 #a1 pp4 v1 xv74 ,cinmatique 7from the ,greek word for movement7 was1 according to ,ampre1 the science in which movements are considered in themselves independent of the forces which produce them1 as we observe them in solid bodies all about us1 and especially in the assemblages called machines4#eg ,kinematics1 as the study soon came to be known in ,english1#eh was one of the two branches of elementary mechanics1 the other being statics4 ,footnote #eg3 ,ibid41 vol4 #a1 pp4 #ea-eb4 ,footnote #eh3 ,willis 7op4 cit4 footnote #ba7 adopted the word kinematics1 and this ,anglicization subsequently became the standard term for this branch of mechanics4 ,in his definition of kinematics1 ,ampre stated what the faculty of mathematics at the ,ecole ,polytechnique1 in ,paris1 had been groping toward since the school's opening some #dj years earlier4 ,the study of mechanisms as an intellectual discipline most certainly had its origin on the left bank of the ,seine1 in this school spawned1 as suggested by one ,french historian1#ei by the great ,encyclopdie of ,diderot and d',alembert4 ,footnote #ei3 ,g4 ,pinet1 ,histoire de l',ecole ,polytechnique1 ,paris1 #ahhg1 pp4 viii-ix4 ,in their forthcoming book on kinematic synthesis1 ,r4 ,s4 ,hartenberg and ,j4 ,denavit will trace the germinal ideas of ,jacob ,leupold and ,leonhard ,euler of the #ahth century4 ,because the ,ecole ,polytechnique had such a far-reaching influence upon the point of view from which mechanisms were contemplated by scholars for nearly a century after the time of ,watt1 and by compilers of dictionaries of mechanical movements for an even longer time1 it is well to look for a moment at the early work that was done there4 ,if one is interested in origins1 it might be profitable for him to investigate the military school in the ancient town of ,mzires1 about #aej miles northeast of ,paris4 ,it was here that ,lazare ,carnot1 one of the principal founders of the ,ecole ,polytechnique1 in #aghc published his essay on machines1#fj which was concerned1 among other things1 with showing the impossibility of perpetual motion2 and it was from ,mzires that ,gaspard ,monge and ,jean ,hachette#fa came to ,paris to work out the system of mechanism classification that has come to be associated with the names of ,lanz and ,btancourt4 ,footnote #fj3 ,lazare ,n4 ,m4 ,carnot1 ,essai sur les machines en gnral1 ,mzires1 #aghc 7later published as ,principes fondamentaux de l'equilibre et du mouvement1 ,paris1 #ahjc74 ,footnote #fa3 ,biographical notices of ,monge and ,hachette appear in ,encyclopaedia ,britannica1 ed4 #aa4 ,see also ,l',ecole ,polytechnique1 ,livre du ,centenaire1 ,paris1 #ahie1 vol4 #a1 p4 #aa;ff4 ,gaspard ,monge 7#agdf-ahah71 who while a draftsman at ,mzires originated the methods of descriptive geometry1 came to the ,ecole ,polytechnique as professor of mathematics upon its founding in #agid1 the second year of the ,french ,republic4 ,according to ,jean ,nicolas ,pierre ,hachette 7#agfi-ahcd71 who was junior to ,monge in the department of descriptive geometry1 ,monge planned to give a two-months' course devoted to the elements of machines4 ,having barely gotten his department under way1 however1 ,monge became involved in ,napoleon's ambitious scientific mission to ,egypt and1 taking leave of his family and his students1 embarked for the distant shores4 ,being left in charge1 wrote ,hachette1 ,i prepared the course of which ,monge had given only the first idea1 and ,i pursued the study of machines in order to analyze and classify them1 and to relate geometrical and mechanical principles to their construction4 ,changes of curriculum delayed introduction of the course until #ahjf1 and not until #ahaa was his textbook ready1 but the outline of his ideas was presented to his classes in chart form 7fig4 #bh74 ,this chart was the first of the widely popular synoptical tables of mechanical movements4#fb ,footnote #fb3 ,jean ,n4 ,p4 ,hachette1 ,trait lmentaire des machines1 ,paris1 #ahaa1 p4 v4 ,illustration3 ,figure #bh4--;,hachette's synoptic chart of elementary mechanisms1 #ahjh4 ,this was the first of many charts of mechanical movements that enjoyed wide popularity for over #ajj years4 ,from ,jean ,n4 ,p4 ,hachette1 ,trait lmentaire des ,machines 7,paris1 #ahaa1 pl4 #a74 ,hachette classified all mechanisms by considering the conversion of one motion into another4 ,his elementary motions were continuous circular1 alternating circular1 continuous rectilinear1 and alternating rectilinear4 ,combining one motion with another--for example1 a treadle and crank converted alternating circular to continuous circular motion--he devised a system that supplied a frame of reference for the study of mechanisms4 ,in the ,u4,s4 ,military ,academy at ,west ,point1 ,hachette's treatise1 in the original ,french1 was used as a textbook in #ahbd1 and perhaps earlier4#fc ,footnote #fc3 ,this work was among the books sent back by ,sylvanus ,thayer when he visited ,france in #ahaf to observe the education of the ,french army cadets4 ,thayer's visit resulted in his adopting the philosophy of the ,ecole ,polytechnique in his reorganization of the ,u4,s4 ,military ,academy and1 incidentally1 in his inclusion of ,hachette's course in the ,academy's curriculum 7,u4,s4 ,congress1 ,american ,state ,papers1 ,washington1 #ahcb-ahfa1 ,class v1 ,military ,affairs1 vol4 #b1 p4 #ffa3 ,sidney ,forman1 ,west ,point1 ,new ,york1 #aiej1 pp4 #cf-fj74 ,there is a collection of miscellaneous papers 7indexed under ,sylvanus ,thayer and ,william ,mc,ree1 ,u4,s4 ,national ,archives1 ,,rg #gg1 ,office1 ,chief of ,engineers1 ,boxes #a and #f7 pertaining to the ,u4,s4 ,military ,academy of this period1 but ,i found no mention of kinematics in this collection4 ,lanz and ,btancourt1 scholars from ,spain at the ,ecole ,polytechnique1 plugged some of the gaps in ,hachette's system by adding continuous and alternating curvilinear motion1 which doubled the number of combinations to be treated1 but the advance of their work over that of ,hachette was one of degree rather than of kind4#fd ,footnote #fd3 ,phillipe ,louis ,lanz and ,augustin de ,btancourt1 ,essai sur la composition des machines1 ,paris1 #ahjh4 ,hachette's chart and an outline of his elementary course on machines is bound with the ,princeton ,university ,library copy of the ,lanz and ,btancourt work4 ,this copy probably represents the first textbook of kinematics4 ,btancourt was born in #agfj in ,teneriffe1 attended the military school in ,madrid1 and became inspector-general of ,spanish roads and canals4 ,he was in ,england before #aghi1 learning how to build ,watt engines1 and he introduced the engines to ,paris in #agij 7see ,farey1 op4 cit41 p4 #fee74 ,he entered ,russian service in #ahjh and died in ,st4 ,petersburg in #ahbf ,j4 ,c4 ,poggendorff1 ,biographisches-literarisches ,handwrterbuch fr ,mathematik 4441 ,leipzig1 #ahfc1 vol4 #a4 ,illustration3 ,figure #bi4--,robert ,willis 7#ahjj-ahge71 ,jacksonian ,professor1 ,cambridge ,university1 and author of ,principles of ,mechanism1 one of the landmark books in the development of kinematics of mechanisms4 ,photo courtesy ,gonville and ,caius ,college1 ,cambridge ,university4 ,giuseppe ,antonio ,borgnis1 an ,italian engineer and member of many academies and professor of mechanics at the ,university of ,pavia in ,italy1 in his monumental1 nine-volume ,trait complet de mchanique applique aux arts1 caused a bifurcation of the structure built upon ,hachette's foundation of classification when he introduced six orders of machine elements and subdivided these into classes and species4 ,his six orders were rcepteurs 7receivers of motion from the prime mover71 communicateurs1 modificateurs 7modifiers of velocity71 supports 7e4g41 bearings71 regulateurs 7e4g41 governors71 and operateurs1 which produced the final effect4#fe ,footnote #fe3 ,giuseppe ,antonio ,borgnis1 ,thorie de la mcanique usuelle in ,trait complet de mcanique applique aux arts1 ,paris1 #ahah1 vol4 #a1 pp4 xiv-xvi4 ,the brilliant ,gaspard-,gustave de ,coriolis 7#agib-ahdc7--remembered mainly for a paper of a dozen pages explaining the nature of the acceleration that bears his name#ff--was another graduate of the ,ecole ,polytechnique who wrote on the subject of machines4 ,his book1#fg published in #ahbi1 was provoked by his recognition that the designer of machines needed more knowledge than his undergraduate work at the ,ecole ,polytechnique was likely to give him4 ,although he embraced a part of ,borgnis' approach1 adopting rcepteurs1 communicateurs1 and operateurs1 ,coriolis indicated by the title of his book that he was more concerned with forces than with relative displacements4 ,however1 the attractively simple three-element scheme of ,coriolis became well fixed in ,french thinking4#fh ,footnote #ff3 ,gaspard-,gustave de ,coriolis1 ,memoire sur les equations du mouvement relatif des systmes de corps1 ,journal de l',ecole ,polytechnique1 #ahce1 vol4 #ae1 pp4 #adb-aed4 ,footnote #fg3 ,gaspard-,gustave de ,coriolis1 ,de ,calcul de l'effet des machines1 ,paris1 #ahbi4 ,in this book ,coriolis proposed the now generally accepted equation1 work force distance 7pp4 iii1 #b74 ,footnote #fh3 ,the renowned ,jean ,victor ,poncelet lent weight to this scheme4 7,see ,franz ,reuleaux1 ,theoretische ,kinematik3 ,grundzge einer ,theorie des ,maschinenwesens1 ,braunschweig1 #ahge1 translated by ,alexander ,b4 ,w4 ,kennedy as ,the ,kinematics of ,machinery3 ,outlines of a ,theory of ,machines1 ,london1 #ahgf1 pp4 #aa1 #dhg4 ,i have used the ,kennedy translation in the ,reuleaux references throughout the present work47 ,michel ,chasles 7#agic-ahhj71 another graduate of the ,ecole ,polytechnique1 contributed some incisive ideas in his papers on instant centers#fi published during the #ahcj's1 but their tremendous importance in kinematic analysis was not recognized until much later4 ,footnote #fi3 ,the instant center was probably first recognized by ,jean ,bernoulli 7#affg-agdh7 in his ,de ,centro ,spontaneo ,rotationis 7,johannis ,bernoulli 444 ,opera ,omnia 4441 ,lausanne1 #agdb1 vol4 #d1 p4 #bfe;ff474 ,illustration3 ,figure #cj4--;,franz ,reuleaux 7#ahbi-aije74 ,his ,theoretische ,kinematik1 published in #ahge1 provided the basis for modern kinematic analysis4 ,photo courtesy ,deutsches ,museum1 ,munich4 ,acting upon ,ampre's clear exposition of the province of kinematics and excluding1 as ,ampre had done1 the consideration of forces1 an ,englishman1 ,robert ,willis1 made the next giant stride forward in the analysis of mechanisms4 ,willis was #cg years old in #ahcg when he was appointed professor of natural and experimental philosophy at ,cambridge4 ,in the same year ,professor ,willis--a man of prodigious energy and industry and an authority on archeology and architectural history as well as mechanisms--read his important paper ,on the ,teeth of ,wheels before the ,institution of ,civil ,engineers#gj and commenced at ,cambridge his lectures on kinematics of mechanisms that culminated in his #ahda book ,principles of ,mechanism4#ga ,footnote #gj3 ,robert ,willis1 ,on the ,teeth of ,wheels1 ,transactions of the ,institution of ,civil ,engineers of ,london1 #ahch1 vol4 #b1 pp4 #hi-aab4 ,footnote #ga3 ,willis1 op4 cit4 7footnote #ba74 ,through the kindness of its owner 7,mr4 ,warren ,g4 ,ogden of ,north ,andover1 ,massachusetts71 ,i have had access to ,willis' own copy of his #ahda edition of ,principles of ,mechanism4 ,the book is interleaved1 and it contains notes made by ,willis from time to time until at least #ahgj1 when the second edition was issued4 ,corrections1 emendations1 notations of some of his sources 7for example1 the ,de ,voglie linkage mentioned in footnote #ce above71 notes to himself to examine the general case and examine the modern forms of straight-line devices are interspersed with references to authors that had borrowed from his work without acknowledgment4 ,of one author ,willis writes an indignant ,he ignores my work4 ,it seemed clear to ,willis that the problem of devising a mechanism for a given purpose ought to be attacked systematically1 perhaps mathematically1 in order to determine all the forms and arrangements that are applicable to the desired purpose1 from which the designer might select the simplest or most suitable combination4 ,at present1 he wrote1 questions of this kind can only be solved by that species of intuition which long familiarity with a subject usually confers upon experienced persons1 but which they are totally unable to communicate to others4 ,in analyzing the process by which a machine was designed1 ,willis observed3 ,when the mind of a mechanician is occupied with the contrivance of a machine1 he must wait until1 in the midst of his meditations1 some happy combination presents itself to his mind which may answer his purpose4 ,he ventured the opinion that at this stage of the design process the motions of the machine are the principal subject of contemplation1 rather than the forces applied to it1 or the work it has to do4 ,therefore he was prepared to adopt without reservation ,ampre's view of kinematics1 and1 if possible1 to make the science useful to engineers by stating principles that could be applied without having to fit the problem at hand into the framework of the systems of classification and description that had gone before4 ,he appraised the celebrated system of ,lanz and ,btancourt as a merely popular arrangement1 notwithstanding the apparently scientific simplicity of the scheme4 ,he rejected this scheme because no attempt is made to subject the motions to calculation1 or to reduce these laws to general formulas1 for which indeed the system is totally unfitted4 ,borgnis had done a better job1 ,willis thought1 in actually describing machinery1 with his orders based upon the functions of machine elements or mechanisms within the machine1 but again there was no means suggested by which the kinematics of mechanisms could be systematically investigated4 ,although ,willis commenced his treatise with yet another synoptical table of the elementary combinations of pure mechanism1 his view shifted quickly from description to analysis4 ,he was consistent in his pursuit of analytical methods for pure mechanism1 eschewing any excursions into the realm of forces and absolute velocities4 ,he grasped the important concept of relative displacements of machine elements1 and based his treatment upon the proportions and relations between the velocities and directions of the pieces1 and not upon their actual and separate motions4#gb ,footnote #gb3 ,ibid41 pp4 iv1 x-xii1 xxi1 #ae4 ,that he did not succeed in developing the formulas that would enable the student to determine all the forms and arrangements that are applicable to the desired purpose--that he did not present a rational approach to synthesis--is not to be wondered at4 ,well over a century later we still are nibbling at the fringes of the problem4 ,willis did1 nonetheless1 give the thoughtful reader a glimpse of the most powerful tool for kinematic synthesis that has yet been devised2 namely1 kinematic analysis1 in which the argument is confined to the relative displacements of points on links of a mechanism1 and through which the designer may grasp the nature of the means at his disposal for the solution of any particular problem4 ,as remarked by ,reuleaux a generation later1 there was much in ,professor ,willis's book that was wrong1 but it was an original1 thoughtful work that departed in spirit if not always in method from its predecessors4 ,principles of ,mechanism was a prominent landmark along the road to a rational discipline of machine-kinematics4 ,a phenomenal engineer of the #aith century was the ,scottish professor of civil engineering at the ,university of ,glasgow1 ,william ,john ,mac,quorn ,rankine4 ,although he was at the ,university for only #ag years--he died at the age of #eb1 in #ahgb--;he turned out during that time four thick manuals on such diverse subjects as civil engineering1 ship-building1 thermodynamics1 and machinery and mill-work1 in addition to literally hundreds of papers1 articles1 and notes for scientific journals and the technical press4 ,endowed with apparently boundless energy1 he found time from his studies to command a battalion of rifle volunteers and to compose and sing comic and patriotic songs4 ,his manuals1 often used as textbooks1 were widely circulated and went through many editions4 ,rankine's work had a profound effect upon the practice of engineering by setting out principles in a form that could be grasped by people who were dismayed by the treatment usually found in the learned journals4 ,when ,rankine's book titled ,a ,manual of ,machinery and ,millwork was published in #ahfi it was accurately characterized by a reviewer as dealing with the principles of machinery and millworks1 and as such it is entirely distinct from other works on the same subject which treat more of the practical applications of such principles than of the principles themselves4#gc ,footnote #gc3 ,engineering1 ,london1 ,august #ac1 #ahfi1 vol4 #h1 p4 #aaa4 ,rankine borrowed what appeared useful from ,willis' ,principles of ,mechanism and from other sources4 ,his treatment of kinematics was not as closely reasoned as the later treatises of ,reuleaux and ,kennedy1 which will be considered below4 ,rankine did1 however1 for the first time show the utility of instant centers in velocity analysis1 although he made use only of the instant centers involving the fixed link of a linkage4 ,like others before him1 he considered the fixed link of a mechanism as something quite different from the movable links1 and he did not perceive the possibilities opened up by determining the instant center of two movable links4 ,many other books dealing with mechanisms were published during the middle third of the century1 but none of them had a discernible influence upon the advance of kinematical ideas4#gd ,the center of inquiry had by the #ahfj's shifted from ,france to ,germany4 ,only by scattered individuals in ,england1 ,italy1 and ,france was there any impatience with the well-established1 general understanding of the machine-building art4 ,footnote #gd3 ,several such books are referred to by ,reuleaux1 op4 cit4 7footnote #fh71 pp4 #ab-af4 ,in ,germany1 on the other hand1 there was a surge of industrial activity that attracted some very able men to the problems of how machines ought to be built4 ,among the first of these was ,ferdinand ,redtenbacher 7#ahji-ahfc71 professor of mechanical engineering in the polytechnic school in ,karlsruhe1 not far from ,heidelberg4 ,redtenbacher1 although he despaired of the possibility of finding a true system on which to base the study of mechanisms1 was nevertheless a factor in the development of such a system4 ,he had young ,franz ,reuleaux in his classes for two years1 from #ahej4 ,during that time the older man's commanding presence1 his ability as a lecturer1 and his infectious impatience with the existing order influenced ,reuleaux to follow the scholar's trail that led him to eminence as an authority of the first rank4#ge ,footnote #ge3 ,see ,carl ,weihe1 ,franz ,reuleaux und die ,grundlagen seiner ,kinematik1 ,deutsches ,museum1 ,munich1 ,abhandlung und ,berichte1 #aidb1 p4 #b2 ,friedrich ,klemm1 ,technik3 ,eine ,geschichte ihrer ,probleme1 ,freiburg and ,munich1 ,verlag ,karl ,alber1 #aied1 translated by ,dorothea ,w4 ,singer as ,a ,history of ,western ,technology1 ,new ,york1 ,charles ,scribner's ,sons1 #aiei1 p4 #cag4 ,before he was #be years old ,franz ,reuleaux published1 in collaboration with a classmate1 a textbook whose translated title would be ,constructive ,lessons for the ,machine ,shop4#gf ,his several years in the workshop1 before and after coming under ,redtenbacher's influence1 gave his works a practical flavor1 simple and direct4 ,according to one observer1 ,reuleaux's book exhibited a recognition of the claims of practice such as ,englishmen do not generally associate with the writings of a ,german scientific professor4#gg ,footnote #gf3 ,see ,weihe1 op4 cit4 7footnote #ge71 p4 #c2 ,hans ,zopke1 ,professor ,franz ,reuleaux1 ,cassier's ,magazine1 ,december #ahif1 vol4 #aa1 pp4 #acc-aci2 ,transactions of the ,american ,society of ,mechanical ,engineers1 #aijd-aije1 vol4 #bf1 pp4 #hac-hag4 ,footnote #gg3 ,engineering1 ,london1 ,september #h1 #ahgf1 vol4 #bb1 p4 #aig4 ,reuleaux's original ideas on kinematics1 which are responsible for the way in which we look at mechanisms today1 were sufficiently formed in #ahfd for him to lecture upon them4#gh ,starting in #ahga1 he published his findings serially in the publication of the ,verein zur ,befrderung des ,gewerbefleisses in ,preussen 7,society for the ,advancement of ,industry in ,prussia71 of which he was editor4 ,in #ahge these articles were brought together in the book that established his fame--,theoretische ,kinematik4444#gi ,footnote #gh3 ,a4 ,e4 ,richard de ,jonge1 ,what is ,wrong with ,kinematics and ,mechanisms8 ,mechanical ,engineering1 ,april #aidb1 vol4 #fd1 pp4 #bgc-bgh 7comments on this paper are in ,mechanical ,engineering1 ,october #aidb1 vol4 #fd1 pp4 #gdd-gea72 ,zopke1 op4 cit4 7footnote #gf71 p4 #ace4 ,footnote #gi3 ,reuleaux1 op4 cit4 7footnote #fh74 ,this was not the last of ,reuleaux's books4 ,his trilogy on kinematics and machine design is discussed by ,de ,jonge1 op4 cit4 7footnote #gh74 ,in the introduction of this book1 ,reuleaux wrote3 ,in the development of every exact science1 its substance having grown sufficiently to make generalization possible1 there is a time when a series of changes bring it into clearness4 ,this time has most certainly arrived for the science of kinematics4 ,the number of mechanisms has grown almost out of measure1 and the number of ways in which they are applied no less4 ,it has become absolutely impossible still to hold the thread which can lead in any way through this labyrinth by the existing methods4#hj ,footnote #hj3 ,reuleaux1 op4 cit4 7footnote #fh71 p4 #bc4 ,reuleaux's confidence that it would be his own work that would bring order out of confusion was well founded4 ,his book had already been translated into ,italian and was being translated into ,french when1 only a year after its publication1 it was presented by ,prof4 ,alexander ,b4 ,w4 ,kennedy in ,english translation4#ha ,footnote #ha3 ,ibid41 p4 iii4 ,the book was enthusiastically reviewed by the weekly ,london journal ,engineering1#hb and it was given lengthy notice by the rival journal1 ,the ,engineer4 ,the editor of ,the ,engineer thought that the mechanician would find in it many new ideas1 that he would be taught to detect hitherto hidden resemblances1 and that he must part--reluctantly1 perhaps--with many of his old notions4 ,but1 added the editor with considerable justice1 that he the mechanician would suddenly recognize in ,professor ,reuleaux's 'kinematic notation1' 'analysis1' and 'synthesis1' the long-felt want of his professional existence we do not for a moment believe4#hc ,indeed1 the fresh and sharp ideas of ,reuleaux were somewhat clouded by a long 7#fjj-page7 presentation2 and his kinematic notation1 which required another attempt at classification1 did not simplify the presentation of radically new ideas4#hd ,footnote #hb3 ,engineering1 loc4 cit4 7footnote #gg74 ,footnote #hc3 ,the ,engineer1 ,london1 ,march #cj and ,april #ac1 #ahgg1 vol4 #dc1 pp4 #baa-bab1 #bdg-bdh4 ,footnote #hd3 ,it is perhaps significant that the first paper of the ,first ,conference on ,mechanisms at ,purdue ,university was ,allen ,s4 ,hall's ,mechanisms and ,their ,classification1 which appeared in ,machine ,design1 ,december #aiec1 vol4 #be1 pp4 #agd-ahj4 ,the place of classification in kinematic synthesis is suggested in ,ferdinand ,freudenstein's ,trends in ,kinematics of ,mechanisms1 ,applied ,mechanics ,reviews1 ,september #aiei1 vol4 #ab1 pp4 #ehg-eij4 ,illustration3 ,figure #ca4--;,alexander ,blackie ,william ,kennedy 7#ahdg-aibh71 translator of ,reuleaux' ,theoretische ,kinematik and discoverer of ,kennedy's ,law of ,three ,centers4 ,from ,minutes of the ,proceedings of the ,institution of ,civil ,engineers 7#aijg1 vol4 #afg1 frontispiece74 ,nevertheless1 no earlier author had seen the problem of kinematic analysis so clearly or had introduced so much that was fresh1 new1 and of lasting value4 ,reuleaux was first to state the concept of the pair2 by his concept of the expansion of pairs he was able to show similarities in mechanisms that had no apparent relation4 ,he was first to recognize that the fixed link of a mechanism was kinematically the same as the movable links4 ,this led him to the important notion of inversion of linkages1 fixing successively the various links and thus changing the function of the mechanism4 ,he devoted #dj pages to showing1 with obvious delight1 the kinematic identity of one design after another of rotary steam engines1 demolishing for all time the fond hopes of ingenious but ill-informed inventors who think that improvements and advances in mechanism design consist in contortion and complexity4 ,the chapter on synthesis was likewise fresh1 but it consisted of a discussion1 not a system2 and ,reuleaux stressed the idea that ,i have mentioned above in connection with ,willis' book1 that synthesis will be successful in proportion to the designer's understanding and appreciation of analysis4 ,reuleaux tried to put the designer on the right track by showing him clearly the essential simplicity of the means with which we have to work and by demonstrating to him that the many things which have to be done can be done with but few means1 and that the principles underlying them all lie clearly before us4#he ,footnote #he3 ,reuleaux1 op4 cit4 7footnote #fh71 p4 #ehb4 ,it remained for ,sir ,alexander ,blackie ,william ,kennedy 7#ahdg-aibh7 and ,robert ,henry ,smith 7#aheb-aiaf7 to add to ,reuleaux's work the elements that would give kinematic analysis essentially its modern shape4 ,kennedy1 the translator of ,reuleaux's book1 became professor of engineering at the ,university ,college in ,london in #ahgd1 and eventually served as president both of the ,institution of ,mechanical ,engineers and of the ,institution of ,civil ,engineers4 ,smith1 who had taught in the ,imperial ,university of ,japan1 was professor of engineering at ,mason ,college1 now a part of ,birmingham ,university1 in ,england4 ,while ,reuleaux had used instant centers almost exclusively for the construction of centrodes 7paths of successive positions of an instant center71 ,professor ,kennedy recognized that instant centers might be used in velocity analysis4 ,his book1 ,mechanics of ,machinery1 was published in #ahhf 7partly through pressure of work and partly through ill-health1 this book appears only now74 ,in it he developed the law of three centers1 now known as ,kennedy's theorem4 ,he noted that his law of three centers was first given1 ,i believe1 by ,aronhold1 although its previous publication was unknown to me until some years after ,i had given it in my lectures4#hf ,in fact1 the law had been published by ,siegfried ,heinrich ,aronhold 7#ahai-ahhd7 in his ,outline of ,kinematic ,geometry1 which appeared in #ahgb alongside ,reuleaux's series in the journal that ,reuleaux edited4 ,apparently ,reuleaux did not perceive its particular significance at that time4#hg ,footnote #hf3 ,alexander ,b4 ,w4 ,kennedy1 ,the ,mechanics of ,machinery1 ed4 #c1 ,london1 #ahih1 pp4 vii1 x4 ,footnote #hg3 ,siegfried ,heinrich ,aronhold1 ,outline of ,kinematic ,geometry1 ,verein zur ,befrderung des ,gewerbefleisses in ,preussen1 #ahgb1 vol4 #ea1 pp4 #abi-aee4 ,kennedy's theorem is on pp4 #acg-ach4 ,illustration3 ,figure #cb4--,robert ,henry ,smith 7#aheb-aiaf71 originator of velocity and acceleration polygons for kinematic analysis4 ,photo courtesy the ,librarian1 ,birmingham ,reference ,library1 ,england4 ,kennedy1 after locating instant centers1 determined velocities by calculation and accelerations by graphical differentiation of velocities1 and he noted in his preface that he had been unable1 for a variety of reasons1 to make use in his book of ,smith's recent work4 ,professor ,kennedy at least was aware of ,smith's surprisingly advanced ideas1 which seem to have been generally ignored by ,americans and ,englishmen alike4 ,professor ,smith1 in a paper before the ,royal ,society of ,edinburgh in #ahhe1 stated clearly the ideas and methods for construction of velocity and acceleration diagrams of linkages4#hh ,for the first time1 velocity and acceleration images of links 7fig4 #cc7 were presented4 ,it is unfortunate that ,smith's ideas were permitted to languish for so long a time4 ,footnote #hh3 ,robert ,h4 ,smith1 ,a ,new ,graphic ,analysis of the ,kinematics of ,mechanisms1 ,transactions of the ,royal ,society of ,edinburgh1 #ahhb-ahhe1 vol4 #cb1 pp4 #ejg-eag1 and pl4 #hb4 ,smith used this paper as the basis for a chapter in his ,graphics or the ,art of ,calculating by ,drawing ,lines1 ,london1 #ahhi1 pp4 #add-afb4 ,in a footnote of his paper1 ,smith credited ,fleeming ,jenkin 7#ahcc-ahhe7 with suggesting the term image4 ,after discarding as practically useless ,kennedy's graphical differentiation1 ,smith complained that he had failed to find any practical use for ,reuleaux's method of centroids1 more properly called axoids4 ,such statements were not calculated to encourage ,kennedy and ,reuleaux to advertise ,smith's fame2 however1 ,i found no indication that either one took offense at the criticism4 ,smith's velocity and acceleration diagrams were included 7apparently embalmed1 so far as ,american engineers were concerned7 in ,encyclopaedia ,britannica1 ed4 #aa1 #aiaj1 vol4 #ag1 pp4 #ajjh-ajji4 ,illustration3 ,figure #cc4--,smith's velocity image 7the two figures at top71 and his velocity1 mechanism1 and acceleration diagrams1 #ahhe4 ,the image of link ,,bacd is shown as figure bacd4 ,the lines pa1 pb1 pc1 and pd are velocity vectors4 ,this novel1 original1 and powerful analytical method was not generally adopted in ,english or ,american schools until nearly #ej years after its inception4 ,from ,transactions of the ,royal ,society of ,edinburgh 7#ahhb-ahhe1 vol4 #cb1 pl4 #hb74 ,by #ahhe nearly all the tools for modern kinematic analysis had been forged4 ,before discussing subsequent developments in analysis and synthesis1 however1 it will be profitable to inquire what the mechanician--designer and builder of machines--was doing while all of this intellectual effort was being expended4 ,mechanicians and ,mechanisms ,while the inductive process of recognizing and stating true principles of the kinematics of mechanisms was proceeding through three generations of ,french1 ,english1 and finally ,german scholars1 the actual design of mechanisms went ahead with scant regard for what the scholars were doing and saying4 ,after the demonstration by ,boulton and ,watt that large mechanisms could be wrought with sufficient precision to be useful1 the ,english tool builders ,maudslay1 ,roberts1 ,clement1 ,nasmyth1 and ,whitworth developed machine tools of increasing size and truth4 ,the design of other machinery kept pace with--sometimes just behind1 sometimes just ahead of--the capacity and capability of machine tools4 ,in general1 there was an increasing sophistication of mechanisms that could only be accounted for by an increase of information with which the individual designer could start4 ,reuleaux pointed out in #ahge that the almost feverish progress made in the regions of technical work was not a consequence of any increased capacity for intellectual action in the race1 but only the perfecting and extending of the tools with which the intellect works4 ,these tools1 he said1 have increased in number just like those in the modern mechanical workshop--the men who work them remain the same4 ,reuleaux went on to say that the theory and practice of machine-kinematics had carried on a separate existence side by side4 ,the reason for this failure to apply theory to practice1 and vice versa1 must be sought in the defects of the theory1 he thought1 because the mechanisms themselves have been quietly developed in practical machine-design1 by invention and improvement1 regardless of whether or not they were accorded any direct and proper theoretical recognition4 ,he pointed out that the theories had thus far furnished no new mechanisms4#hi ,footnote #hi3 ,reuleaux1 op4 cit4 7footnote #fh71 p4 #h4 ,it is reasonable1 therefore1 to ask what was responsible for the appearance of new mechanisms1 and then to see what sort of mechanisms had their origins in this period4 ,it is immediately evident to a designer that the progress in mechanisms came about through the spread of knowledge of what had already been done2 but designers of the last century had neither the leisure nor means to be constantly visiting other workshops1 near and far1 to observe and study the latest developments4 ,in the #ahjj's1 as now1 word must in the main be spread by the printed page4 ,hachette's chart 7fig4 #bh7 had set the pattern for display of mechanical contrivances in practical journals and in the large number of mechanical dictionaries that were compiled to meet an apparent demand for such information4 ,it is a little surprising1 however1 to find how persistent were some of ,hachette's ideas that could only have come from the uppermost superficial layer of his cranium4 ,see1 for example1 his anchored ferryboat 7fig4 #cd74 ,this device1 employed by ,hachette to show conversion of continuous rectilinear motion into alternating circular motion1 appeared in one publication after another throughout the #aith century4 ,as late as #aijc the ferryboat was still anchored in ,hiscox's ,mechanical ,movements1 although the tide had changed 7fig4 #ce74ij ,footnote #ij3 ,gardner ,d4 ,hiscox1 ed41 ,mechanical ,movements1 ed4 #aj1 ,new ,york1 #aijc1 p4 #aea4 ,the ferryboat did not appear in the #aiag edition4 ,illustration3 ,figure #cd4--;,hachette's ferryboat of #ahjh1 a machine for converting continuous rectilinear motion into alternating circular motion4 ,from ,phillipe ,louis ,lanz and ,augustin de ,btancourt1 ,essai sur la composition des machines 7,paris1 #ahjh1 pl4 #b74 ,illustration3 ,figure #ce4--;,ferryboat from ,gardner ,d4 ,hiscox1 ed41 ,mechanical ,movements 7ed4 #aj1 ,new ,york1 #aijc1 p4 #aea74 ,during the upsurge of the ,lyceum--or working-man's institute--movement in the #ahbj's1 ,jacob ,bigelow1 ,rumford professor of applied science at ,harvard ,university1 gave his popular lectures on the ,elements of ,technology before capacity audiences in ,boston4 ,in preparing his lecture on the elements of machinery1 ,bigelow used as his authorities ,hachette1 ,lanz and ,btancourt1 and ,olinthus ,gregory's mechanical dictionary1 an ,english work in which ,hachette's classification scheme was copied and his chart reproduced4#ia ,footnote #ia3 ,jacob ,bigelow1 ,elements of ,technology1 ed4 #b1 ,boston1 #ahca1 pp4 #bca-bef2 ,olinthus ,gregory1 ,a ,treatise of ,mechanics1 #c vols41 ed4 #c1 ,london1 #ahae4 ,a translation of the work of ,lanz and ,btancourt#ib under the title ,analytical ,essay on the ,construction of ,machines1 was published about #ahbj at ,london by ,rudolph ,ackermann 7for whom the ,ackermann steering linkage was named71 and their synoptic chart was reprinted again in #ahbb in ,durham4#ic ,in the ,united ,states1 ,appleton's ,dictionary of ,machines#id 7#ahea7 adopted the same system and used the same figures4 ,apparently the wood engraver traced directly onto his block the figures from one of the reprints of ,lanz and ,btancourt's chart because the figures are in every case exact mirror images of the originals4 ,footnote #ib3 ,rudolph ,ackermann1 ,analytical ,essay on the ,construction of ,machines1 ,london1 about #ahbj1 a translation of ,lanz and ,btancourt1 op4 cit4 7footnote #fd74 ,footnote #ic3 ,thomas ,fenwick1 ,essays on ,practical ,mechanics1 ed4 #c1 ,durham1 ,england1 #ahbb4 ,footnote #id3 ,appleton's ,dictionary of ,machines1 ,mechanics1 ,engine-,work1 and ,engineering1 #b vols41 ,new ,york1 #ahea 7,motion74 ,in the ,dictionary of ,engineering#ie 7,london1 #ahgc71 the figures were redrawn and dozens of mechanisms were added to the repertory of mechanical motions2 the result was a fair catalog of sound ideas4 ,the ferryboat still tugged at its anchor cable1 however4#if ,knight's ,american ,mechanical ,dictionary1#ig a classic of detailed pictorial information compiled by a ,u4,s4 patent examiner1 contained well over #aj1jjj finely detailed figures of various kinds of mechanical contrivances4 ,knight did not have a separate section on mechanisms1 but there was little need for one of the ,hachette variety1 because his whole dictionary was a huge and fascinating compendium of ideas to be filed away in the synthetic mind4 ,one reason for the popularity and usefulness of the various pictorial works was the peculiar ability of a wood or steel engraving to convey precise mechanical information1 an advantage not possessed by modern halftone processes4 ,footnote #ie3 ,e4 ,f4 and ,n4 ,spon1 ,dictionary of ,engineering1 ,london #ahgc1 pp4 #bdba-bdeb4 ,footnote #if3 ,ibid41 p4 #bddg4 ,footnote #ig3 ,edward ,h4 ,knight1 ,knight's ,american ,mechanical ,dictionary1 #c vols41 ,new ,york #ahgd-ahgf4 ,illustration3 ,figure #cf4--,typical mechanisms from ,e4 ,f4 and ,n4 ,spon1 ,dictionary of ,engineering 7,london1 #ahgc1 pp4 #bdbf1 #bdgh74 ,many patent journals and other mechanical periodicals concerned with mechanics were available in ,english from the beginning of the #aith century1 but few of them found their way into the hands of ,american mechanicians until after #ahbj4 ,oliver ,evans 7#agee-ahai7 had much to say about the difficulties inventive mechanics labored under for want of published records of what had preceded them1 and for works of reference to help the beginner4#ih ,in #ahag the ,north ,american ,review also remarked upon the scarcity of engineering books in ,america4#ii ,footnote #ih3 ,george ,escol ,sellers in ,american ,machinist1 ,july #ab1 #ahhd1 vol4 #g1 p4 #c4 ,footnote #ii3 ,north-,american ,review and ,miscellaneous ,journal1 #ahai1 new ser41 vol4 #h1 pp4 #ac-ae1 #be4 ,the ,scientific ,american1 which appeared in #ahde as a patent journal edited by the patent promoter ,rufus ,porter1 carried almost from its beginning a column or so entitled ,mechanical ,movements1 in which one or two mechanisms--borrowed from an ,english work that had borrowed from a ,french work--were illustrated and explained4 ,the ,american ,artisan began a similar series in #ahfd1 and in #ahfh it published a compilation of the series as ,five ,hundred and ,seven ,mechanical ,movements1 embracing all those which are most important in dynamics1 hydraulics1 hydrostatics1 pneumatics1 steam engines 444 and miscellaneous machinery4#ajj ,this collection went through many editions2 it was last revived in #aidc under the title ,a ,manual of ,mechanical ,movements4 ,this #aidc edition included photographs of kinematic models4#aja ,footnote #ajj3 ,henry ,t4 ,brown1 ed41 ,five ,hundred and ,seven ,mechanical ,movements1 ,new ,york1 #ahfh4 ,footnote #aja3 ,will ,m4 ,clark1 ,a ,manual of ,mechanical ,movements1 ,garden ,city1 ,new ,york1 #aidc4 ,many readers are already well acquainted with the three volumes of ,ingenious ,mechanisms for ,designers and ,inventors1#ajb a work that resulted from a contest1 announced by ,machinery 7vol4 #cc1 p4 #dje7 in #aibg1 in which seven prizes were offered for the seven best articles on unpublished ingenious mechanisms4 ,footnote #ajb3 ,ingenious ,mechanisms for ,designers and ,inventors 7vols4 #a and #b edited by ,f4 ,d4 ,jones1 vol4 #c edited by ,h4 ,l4 ,horton71 ,new ,york1 ,industrial ,press1 #aicj-aiea4 ,there was an interesting class of ,united ,states patents called ,mechanical ,movements that comprised scores of patents issued throughout the middle decades of the #aith century4 ,a sampling of these patents shows that while some were for devices used in particular machines--such as a ratchet device for a numbering machine1 a locking index for gunmaking machinery1 and a few gear trains--the great majority were for converting reciprocating motion to rotary motion4 ,even a cursory examination of these patents reveals an appalling absence of sound mechanical sense1 and many of them appear to be attempts at perpetual motion1 in spite of an occasional disclaimer of such intent4 ,typical of many of these patented devices was a linkage for multiplying the motion of a flywheel1 proposed in #ahda by ,charles ,johnson of ,amity1 ,illinois 7fig4 #cg74 ,it is not pretended that there is any actual gain of power1 wrote ,mr4 ,johnson2 and probably he meant it4 ,the avowed purpose of his linkage was to increase the speed of a flywheel and thus decrease its size4#ajc ,footnote #ajc3 ,u4,s4 ,patent #bbie1 ,october #aa1 #ahda4 ,illustration3 ,figure #cg4--;,johnson's converting motion1 #ahda4 ,the linkage causes the flywheel to make two revolutions for each double-stroke of the engine piston rod ,b4 ,from ,u4,s4 ,patent #bbie1 ,october #aa1 #ahda4 ,an ,englishman who a few years earlier had invented a new ,motion had claimed that his device would supersede the ordinary crank in steam engines1 the beam1 parallel motion1 and external flywheel1 reduce friction1 neutralize all extra contending power1 and leave nothing for the piston to do but the work intended to be done4 ,a correspondent of the ,repertory of ,patent ,inventions made short work of this device3 ,there is hardly one assertion that can be supported by proof1 he wrote1 and most of them are palpable misstatements4 ,the writer attacked the 'beetle impetus wheel1' which he the inventor thinks us all so beetle-headed1 as not to perceive to be a flywheel1 and concluded with the statement3 ,in short the whole production evinces gross ignorance either of machinery1 if the patentee really believed what he asserted1 or of mankind1 if he did not4#ajd ,footnote #ajd3 ,repertory of ,patent ,inventions1 ser4 #c1 ,october #ahbh1 vol4 #g1 pp4 #aif-bjj1 and ,december #ahbh1 vol4 #g1 pp4 #ceg-cfa4 ,although many of the mechanisms for which patents were taken out were designed by persons who would make no use of the principles involved even if such principles could at that time have been clearly stated1 it is a regrettable fact that worthless mechanisms often got as much space as sound ones in patent journals1 and objections such as the one above were infrequent4 ,the slanted information thus conveyed to the young mechanician1 who was just accumulating his first kinematic repertory1 was at times sadly misleading4 ,from even this sketchy outline of the literature on the subject1 it should be fairly evident that there has been available to the mechanician an enormous quantity of information about mechanical linkages and other devices4 ,whatever one may think of the quality of the literature1 it has undoubtedly had influence not only in supplying designers with information but in forming a tradition of how one ought to supply the background that will enable the mind to assemble and synthesize the necessary mechanism for a given purpose4#aje ,footnote #aje3 ,some additional catalogs of mechanical movements are listed in the selected references at the end of this paper4 ,some of the mechanisms that have been given names--such as the ,watt straight-line linkage and the ,geneva stop--have appeared in textbook after textbook4 ,their only excuse for being seems to be that the authors must include them or risk censure by colleagues4 ,such mechanisms are more interesting to a reader1 certainly1 when he has some idea of what the name has to do with the mechanism1 and who originated it4 ,one such mechanism is the drag link4 ,after ,i had learned of the drag link 7as most ,american engineering students do71 ,i wondered for awhile1 and eventually despaired of making any sense out of the term4 ,what1 ,i wanted to know1 was being dragged8 ,recently1 in ,nicholson's ,operative ,mechanic and ,british ,machinist 7#ahbf71 ,i ran across the sketch reproduced here as figure #ch4 ,this figure1 explained ,mr4 ,nicholson 7in vol4 #a1 p4 #cb7 represents the coupling link used by ,messrs4 ,boulton and ,watt in their portable steam engines4 ,a1 a strong iron pin1 projecting from one of the arms of the fly-wheel ,b2 ,d1 a crank connected with the shaft ,c2 and ,e1 a link to couple the pin ,a and the crank ,d together1 so the motion may be communicated to the shaft ,c4 ,so the drag link was actually a link of a coupling4 ,nothing could be more logical4 ,a drag link mechanism now makes sense to me4 ,illustration3 ,figure #ch4--;,drag link coupling used on ,boulton and ,watt portable engines4 ,the link ,e drags one shaft when the other turns4 ,from ,john ,nicholson1 ,the ,operative ,mechanic1 and ,british ,machinist 7,philadelphia1 #ahbf1 vol4 ,i1 pl4 #e74 ,directly related to the drag link coupling were the patents of ,john ,oldham 7#aggi-ahdj71 an ,irish engineer who is remembered mainly for the coupling that bears his name 7fig4 #ci74 ,his three patents1 which were for various forms of steamboat feathering paddle wheels1 involved linkages kinematically similar to the drag link coupling1 although it is quite unlikely that ,oldham recognized the similarity4 ,however1 for his well-known coupling1 which employs an inversion of the elliptical trammel mechanism1 ,i have found no evidence of a patent4 ,probably it was part of the machinery that he designed for the ,bank of ,ireland's printing house1 of which ,oldham was manager for many years4 ,mr4 ,oldham and his beautiful system were brought to the ,bank of ,england in #ahcf1 where ,oldham remained until his death in #ahdj4ajf ,footnote #ajf3 ,oldham's paddle-wheel patents were ,british ,patents #dafi 7,october #aj1 #ahag71 #ddbi 7,january #ae1 #ahbj71 and #edde 7,february #a1 #ahbg74 ,robert ,willis 7op4 cit4 footnote #ba1 p4 #afg7 noticed the existence of the coupling4 ,drawings or descriptions of the banknote machinery apparently have not been published though they probably still exist in the banks' archives4 ,the quotation is from ,frederick ,g4 ,hall1 ,the ,bank of ,ireland #aghc-aidf1 ,dublin1 #aidi4 ,john ,francis in his ,history of the ,bank of ,england 7,london1 #ahdh1 vol4 #b1 p4 #bcb7 wrote3 ,the new machinery for printing the notes1 which was introduced by ,mr4 ,oldham 444 is well worthy of a visit1 but would be uninteresting to delineate4 ,illustration3 ,figure #ci4--,top1 ,original ,oldham coupling built before #ahdj1 using a cross 7instead of a center disk71 as sketched by ,robert ,willis in personal copy of his ,principles of ,mechanism 7,london1 #ahda1 p4 #afg74 ,bottom1 ,oldham coupling as illustrated in ,alexander ,b4 ,w4 ,kennedy1 ,kinematics of ,machinery1 a translation of ,franz ,reuleaux' ,theoretische ,kinematik 7,london1 #ahgf1 pp4 #cae-caf74 ,the ,geneva stop mechanism 7fig4 #dj7 was properly described by ,willis as a device to permit less than a full revolution of the star wheel and thus to prevent overwinding of a watch spring4 ,it was called ,geneva stop because it was used in ,geneva watches4 ,the ,geneva wheel mechanism1 which permits full rotation of the star wheel and which is frequently used for intermittent drives1 was improperly called a ,geneva stop in a recent textbook probably because the logical origin of the term had been lost4 ,illustration3 ,figure #dj4--;,geneva stop mechanism first used in ,geneva watches to prevent overwinding4 ,the starwheel ,b had one convex surface 7g-f1 dotted7 so the wheel could be turned less than a full revolution4 ,after ,robert ,willis1 ,principles of ,mechanism 7,london1 #ahda1 p4 #bff74 ,the name for the ,scotch yoke seems to be of fairly recent origin1 the linkage being called by a ,scotsman in #ahfi a crank and slot-headed sliding rod 7fig4 #da74 ,i suppose that it is now known as a ,scotch yoke because1 in ,america at least1 a ,scotch was a slotted bar that was slipped under a collar on a string of well-drilling tools to support them while a section was being added 7fig4 #db74 ,illustration3 ,figure #da4--,scotch yoke1 described as a crank and slot-headed sliding rod4 ,from ,w4 ,j4 ,m4 ,rankine1 ,a ,manual of ,machinery and ,millwork 7ed4 #f1 ,london1 #ahhg1 p4 #afi74 ,illustration3 ,figure #db4--;,a ,scotch supporting the top member of a string of well-drilling tools while a section is being added1 #ahgf4 ,from ,edward ,h4 ,knight1 ,knight's ,american ,mechanical ,dictionary 7,new ,york1 #ahgf1 p4 #bjeg74 ,it was surprising to me to find that the ,ackermann steering linkage1 used today on most automobiles1 was patented in #ahah when ,detroit was still a frontier town4#ajg ,furthermore1 the man who took out the patent described himself as ,rudolph ,ackermann1 publisher and printseller4 ,i thought ,i had the necessary clue to the linkage's origin when ,i noticed that the first ,english translation of the ,lanz and ,btancourt treatise was published by ,ackermann1 but the connection finally proved to be more logical1 if less direct4 ,ackermann 7#agfd-ahcd71 son of a ,bavarian coach builder1 had spent a number of years designing coaches for ,english gentlemen in ,london1 where he made his home4 ,one of his more notable commissions was for the design of ,admiral ,nelson's funeral car in #ahje4 ,the ,ackermann steering linkage was not actually ,ackermann's invention1 although he took out the ,british patent in his name and promoted the introduction of the running gear of which the linkage was a part 7fig4 #dc74 ,the actual inventor was ,ackermann's friend ,george ,lankensperger of ,munich1 coachmaker to the ,king of ,bavaria4 ,the advantage of being able to turn a carriage around in a limited area without danger of oversetting was immediately obvious1 and while there was considerable opposition by ,english coachmakers to an innovation for which a premium had to be paid1 the invention soon made its way from its own intrinsic merit1 as ,ackermann predicted it would4#ajh ,footnote #ajg3 ,british ,patent #dbab1 ,january #bg1 #ahah4 ,footnote #ajh3 ,rudolph ,ackermann1 ,observations on ,ackermann's ,patent ,moveable ,axles1 ,london1 #ahai4 ,it was interesting to me to note an abstract of ,w4 ,a4 ,wolfe's paper ,analytical ,design of an ,ackermann ,steering ,linkage in ,mechanical ,engineering1 ,september #aieh1 vol4 #hj1 p4 #ib4 ,illustration3 ,figure #dc4--;,ackermann steering linkage of #ahah1 currently used in automobiles4 ,this linkage was invented by ,george ,lankensperger1 coachmaker to the ,king of ,bavaria4 ,from ,dinglers ,polytechnisches ,journal 7#ahbj1 vol4 #a1 pl4 #g74 ,the ,whitworth quick-return mechanism 7fig4 #dd7 was first applied to a slotter1 or vertical shaper1 in #ahdi1 and was exhibited in #ahea at the ,great ,exhibition in ,london4#aji ,willis' comments on the mechanism are reproduced in figure #dd4 ,i hope that ,sir ,joseph ,whitworth 7#ahjc-ahhg7 will be remembered for sounder mechanical contrivances than this4 ,footnote #aji3 ,the quick-return mechanism 7,british ,patent #abijg1 ,december #ai1 #ahdi7 was perhaps first publicly described in ,charles ,tomlinson1 ed41 ,cyclopaedia of ,useful ,arts and ,manufactures1 ,london1 #ahed1 vol4 #a1 p4 cxliv4 ,illustration3 ,figure #dd4--,quick-return mechanism4 ,top1 ,early representation of the quick-return mechanism patented by ,whitworth in #ahdi1 from ,william ,johnson1 ed41 ,the ,imperial ,cyclopaedia of machinery 7,glasgow1 about #ahee1 pl4 #hh74 ,middle1 ,sketch by ,robert ,willis from his copy of ,principles of ,mechanism 7,london1 #ahda1 p4 #bfd71 which shews ,whitworth dissected into a simpler form2 it is as obscure as most subsequent attempts have been to explain this mechanism without a schematic diagram4 ,bottom1 ,linkage that is kinematically equivalent to ,whitworth's1 from ,robert ,willis1 ,principles of ,mechanism 7,london1 #ahda1 p4 #bfd74 ,mechanisms in ,america1 #ahge-aiee ,engineering colleges in the ,united ,states were occupied until the late #aidj's with extending1 refining1 and sharpening the tools of analysis that had been suggested by ,willis1 ,rankine1 ,reuleaux1 ,kennedy1 and ,smith4 ,the actual practice of kinematic synthesis went on apace1 but designers often declined such help as the analytical methods might give them and there was little exchange of ideas between scholars and practitioners4 ,the capability and precision of machine tools were greatly enhanced during this period1 although1 with the exception of the centerless grinder1 no significant new types of tools appeared4 ,the machines that were made with machine tools increased in complexity and1 with the introduction of ideas that made mass production of complex mechanical products economically feasible1 there was an accelerating increase in quantity4 ,the adoption of standards for all sorts of component parts also had an important bearing upon the ability of a designer economically to produce mechanisms that operated very nearly as he hoped they would4 ,the study of kinematics has been considered for nearly #hj years as a necessary part of the mechanical engineer's training1 as the dozens of textbooks that have been published over the years make amply clear4 ,until recently1 however1 one would look in vain for original work in ,america in the analysis or rational synthesis of mechanisms4 ,one of the very earliest ,american textbooks of kinematics was the #ahhc work of ,charles ,w4 ,mac,cord 7#ahcf-aiae71 who had been appointed professor of mechanical drawing at ,stevens ,institute of ,technology in ,hoboken after serving ,john ,ericsson1 designer of the ,monitor1 as chief draftsman during the ,civil ,war4#aaj ,based upon the findings of ,willis and ,rankine1 ,mac,cord's ,kinematics came too early to be influenced by ,kennedy's improvements upon ,reuleaux's work4 ,footnote #aaj3 ,a biographical notice and a bibliography of ,mac,cord appears in ,morton ,memorial3 ,a ,history of the ,stevens ,institute of ,technology1 ,hoboken1 #aije1 pp4 #bai-bbb4 ,when the faculty at ,washington ,university in ,st4 ,louis introduced in #ahhe a curriculum in dynamic engineering1 reflecting a dissatisfaction with the traditional branches of engineering1 kinematics was a senior subject and was taught from ,rankine's ,machinery and ,millwork4#aaa ,footnote #aaa3 ,transactions of the ,american ,society of ,mechanical ,engineers1 #ahhe-ahhf1 vol4 #g1 p4 #geg4 ,at ,massachusetts ,institute of ,technology1 ,peter ,schwamb1 professor of machine design1 put together in #ahhe a set of printed notes on the kinematics of mechanisms1 based on ,reuleaux's and ,rankine's works4 ,out of these notes grew one of the most durable of ,american textbooks1 first published in #aijd4aab ,in the first edition of this work1 acceleration was mentioned only once in passing 7on p4 #d74 ,velocities in linkages were determined by orthogonal components transferred from link to link4 ,instant centers were used only to determine velocities of various points on the same link4 ,angular velocity ratios were frequently noted4 ,in the third edition1 published in #aiba1 linear and angular accelerations were defined1 but no acceleration analyses were made4 ,velocity analyses were altered without essential change4 ,the fourth edition 7#aicj7 was essentially unchanged from the previous one4 ,treatment of velocity analysis was improved in the fifth edition 7#aich7 and acceleration analysis was added4 ,a sixth edition1 further revised by ,prof4 ,v4 ,l4 ,doughtie of the ,university of ,texas1 appeared in #aidg4 ,footnote #aab3 ,peter ,schwamb and ,allyne ,l4 ,merrill1 ,elements of ,mechanism1 ,new ,york1 #aijd4 ,in addition to the work of ,reuleaux and ,rankine1 the authors acknowledged their use of the publications of ,charles ,mac,cord1 ,stillman ,w4 ,robinson1 ,thomas ,w4 ,goodeve1 and ,william ,c4 ,unwin4 ,for complete titles see the list of selected references4 ,before #aijj1 several other books on mechanisms had been published1 and all followed one or another of the patterns of their predecessors4 ,professors ,woods and ,stahl1 at the ,universities of ,illinois and ,purdue1 respectively1 who published their ,elementary ,mechanism in #ahhe1 said in their preface what has been said by many other ,american authors and what should have been said by many more4 ,we make little claim to originality of the subject-matter1 wrote ,woods and ,stahl1 free use having been made of all available matter on the subject4444 ,our claim to consideration is based almost entirely on the manner in which the subject has been presented4 ,not content with this disclaimer1 they continued3 ,there is1 in fact1 very little room for such originality1 the ground having been almost completely covered by previous writers4#aac ,footnote #aac3 ,arthur ,t4 ,woods and ,albert ,w4 ,stahl1 ,elementary ,mechanism1 ,new ,york1 #ahhe4 ,the similarity and aridity of kinematics textbooks in this country from around #aiaj are most striking4 ,the generation of textbook writers following ,mac,cord1 ,woods and ,stahl1 ,barr of ,cornell1 ,robinson of ,ohio ,state1 and ,schwamb and ,merrill managed to squeeze out any remaining juice in the subject1 and the dessication and sterilization of textbooks was nearly complete when my generation used them in the #aicj's4 ,kinematics was then1 in more than one school1 very nearly as it was characterized by an observer in #aidb--on an intellectual par with mechanical drafting4#aad ,i can recall my own nave belief that a textbook contained all that was known of the subject2 and ,i was not disabused of my belief by my own textbook or by my teacher4 ,i think ,i detect in several recent books a fresh1 less final1 and less tidy treatment of the kinematics of mechanisms1 but ,i would yet recommend that anyone who thinks of writing a textbook take time to review1 carefully and at first hand1 not only the desk copies of books that he has accumulated but a score or more of earlier works1 covering the last century at least4 ,such a study should result in a better appreciation of what constitutes a contribution to knowledge and what constitutes merely the ringing of another change4 ,footnote #aad3 ,mechanical ,engineering1 ,october #aidb1 vol4 #fd1 p4 #gde4 ,the author of the contentious article that appeared in ,mechanical ,engineering in #aidb under the title ,what is ,wrong with ,kinematics and ,mechanisms8 made several pronouncements that were questioned by various readers1 but his remarks on the meagerness of the college courses of kinematics and the curious fact that the textbooks are all strangely similar in their incompleteness went unchallenged and were1 in fact1 quite timely4#aae ,footnote #aae3 ,de ,jonge1 op4 cit4 7footnote #gh74 ,it appears that in the early #aidj's the general classroom treatment of accelerations was at a level well below the existing knowledge of the subject1 for in a series of articles by two teachers at ,purdue attention was called to the serious consequences of errors in acceleration analysis occasioned by omitting the ,coriolis component4#aaf ,these authors were reversing a trend that had been given impetus by an article written in #aibj by one of their predecessors1 ,henry ,n4 ,bonis4 ,the earlier article1 appearing in a practical-and-proud-of-it technical magazine1 demonstrated how the acceleration of a point on a flywheel governor might be determined without the use of the fictitious acceleration of ,coriolis4 ,the author's analysis was right enough1 and he closed his article with the unimpeachable statement that it is better psychologically for the student and practically for the engineer to understand the fundamentals thoroughly than to use a complex formula that may be misapplied4 ,however1 many readers undoubtedly read only the lead paragraph1 sagely nodded their heads when they reached the word fictitious1 which confirmed their half-formed conviction that anything as abstruse as the ,coriolis component could have no bearing upon a practical problem1 and turned the page to the practical kinks section4#aag ,footnote #aaf3 ,a4 ,s4 ,hall and ,e4 ,s4 ,ault1 ,how ,acceleration ,analysis ,can ,be ,improved1 ,machine ,design1 ,february #aidc1 vol4 #ae1 pp4 #ajj-ajb1 #afb1 #afd2 and ,march #aidc1 vol4 #ae1 pp4 #ij-ib1 #afh1 #agj4 ,see also ,a4 ,s4 ,hall1 ,teaching ,coriolis' ,law1 ,journal of ,engineering ,education1 ,june #aidh1 vol4 #ch1 pp4 #geg-gfe4 ,footnote #aag3 ,henry ,n4 ,bonis1 ,the ,law of ,coriolis1 ,american ,machinist1 ,november #ah1 #aibj1 vol4 #ec1 pp4 #ibh-icj4 ,see also ,acceleration ,determinations1 ,american ,machinist1 ,november #be and ,december #b1 #aibj1 vol4 #ec1 pp4 #igg-iha and #ajbg-ajbi4 ,less than #bj years ago one might have read in ,mechanical ,engineering that ,practical machinery does not originate in mathematical formulas nor in beautiful vector diagrams4 ,while this remark was in a letter evoked by an article1 and was not a reflection of editorial policy1 it was nevertheless representative of an element in the ,american tradition of engineering4 ,the unconscious arrogance that is displayed in this statement of the practical designer's creed is giving way to recognition of the value of scholarly work4 ,lest the scholar develop arrogance of another sort1 however1 it is well to hear the author of the statement out4 ,a drafting machine is a useful tool1 he wrote4 ,it is not a substitute for a draftsman4#aah ,footnote #aah3 ,mechanical ,engineering1 ,october #aidb1 vol4 #fd1 p4 #gdf4 ,the scholarly interest in a subject is fairly represented by the papers that are published in the transactions of professional societies and1 more recently1 by original papers that appear in specialized magazines4 ,from #aijj to #aicj there were few papers on mechanisms1 and most of those that did appear were concerned with descriptions of new mechanical motions4 ,in the #aicj's the number of papers reported in ,engineering ,index increased sharply1 but only because the editors had begun to include foreign-language listings4 ,there has been in ,germany a thread of continuity in the kinematics of mechanisms since the time of ,reuleaux4 ,while most of the work has had to do with analysis1 the teasing question of synthesis that ,reuleaux raised in his work has never been ignored4 ,the developments in ,germany and elsewhere have been ably reviewed by others1#aai and it is only to be noted here that two of the ,german papers1 published in #aici in ,maschinenbau1 appear to have been the sparks for the conflagration that still is increasing in extent and intensity4 ,according to summaries in ,engineering ,index1 ,r4 ,kraus1 writing on the synthesis of the double-crank mechanism1 drew fire from the ,russian ,z4 ,s4 ,bloch1 who1 in #aidj1 discussed critically ,kraus's articles and proceeded to give the outline of the correct analysis of the problem and a general numerical solution for the synthesis of any four-bar linkage4#abj ,russian work in mechanisms1 dating back to ,chebyshev and following the ,chebyshev theory of synthesis in which algebraic methods are used to determine paths of minimum deviation from a given curve1 has also been reviewed elsewhere1#aba and ,i can add nothing of value4 ,footnote #aai3 ,grodzinski1 ,bottema1 ,de ,jonge1 and ,hartenberg and ,denavit4 ,for complete titles see list of selected references4 ,footnote #abj3 ,my source1 as noted1 is ,engineering ,index4 ,kraus's articles are reported in #aici and ,bloch's in #aidj1 both under the section heading ,mechanisms4 ,footnote #aba3 ,a4 ,e4 ,richard de ,jonge1 ,are the ,russians ,ahead in ,mechanism ,analysis8 ,machine ,design1 ,september #aiea1 vol4 #bc1 pp4 #abg1 #bjj-bjh2 ,o4 ,bottema1 ,recent ,work on ,kinematics1 ,applied ,mechanics ,reviews1 ,april #aiec1 vol4 #f1 pp4 #afi-agj4 ,when1 after ,world ,war ,,ii1 some of the possibilities of kinematic synthesis were recognized in the ,united ,states1 a few perceptive teachers fanned the tinder into an open flame4 ,the first publication of note in this country on the synthesis of linkages was a practical one1 but in conception and undertaking it was a bold enterprise4 ,in a book by ,john ,a4 ,hrones and ,g4 ,l4 ,nelson1 ,analysis of the ,four ,bar ,linkage 7#aiea71 the four-bar crank-and-rocker mechanism was exhaustively analyzed mechanically and the results were presented graphically4 ,this work was faintly praised by a ,dutch scholar1 ,o4 ,bottema1 who observed that the complicated analytical theory of the three-bar sic curve has undoubtedly kept the engineer from using it and who went on to say that we fully understand the publication of an atlas by ,hrones and ,nelson containing thousands of trajectories which must be very useful in many design problems4#abb ,nevertheless1 the authors furnished designers with a tool that could be readily1 almost instantly1 understood 7fig4 #de71 and the atlas has enjoyed wide circulation4#abc ,the idea of a geometrical approach to synthesis has been exploited by others in more recent publications1#abd and it is likely that many more variations on this theme will appear4 ,footnote #abb3 ,bottema1 op4 cit4 7footnote #aba74 ,footnote #abc3 ,in #ahea ,robert ,willis had designed a coupler-point path-generating machine 7fig4 #df7 that could have been used to produce a work similar to that of ,hrones and ,nelson4 ,footnote #abd3 ,r4 ,s4 ,hartenberg and ,j4 ,denavit1 ,systematic ,mechanism ,design1 ,machine ,design1 ,september #aied1 vol4 #bf1 pp4 #afg-age1 and ,october #aied1 vol4 #bf1 pp4 #beg-bfe2 ,a4 ,s4 ,hall1 ,a4 ,r4 ,holowenko1 and ,h4 ,g4 ,laughlin1 ,four-,bar ,lever ,crank ,mechanism1 ,design ,news1 ,september #ae1 #aieg1 vol4 #ab1 pp4 #acj-aci1 ,october #a1 #aieg1 vol4 #ab1 pp4 #ade-aed1 and ,october #ae1 #aieg1 vol4 #ab1 pp4 #acb-ada4 ,for a nomographic approach1 with particular application to computers1 see ,antonin ,svoboda1 ,computing ,mechanisms and ,linkages1 ,new ,york1 #aidh4 ,illustration3 ,figure #de4--,paths of #aa points on the coupler 7horizontal7 link are plotted through one cycle4 ,dashes indicate equal time intervals4 ,from ,john ,a4 ,hrones and ,g4 ,l4 ,nelson1 ,analysis of the ,four ,bar ,linkage 7,new ,york1 #aiea1 p4 #fce74 ,illustration3 ,figure #df4--;,coupler-point path-generating machine for four-bar linkage4 ,this device1 built by ,professor ,willis as a teaching aid for demonstrating straight-line linkages1 could have been adapted to produce a plate like the one shown in figure #de4 ,from ,robert ,willis1 ,a ,system of ,apparatus for the ,use of ,lecturers and ,experimenters 444 7,london #ahea1 pl4 #c74 ,pursuit of solutions to the complicated analytical theory of linkages was stimulated by publication of ,ferdinand ,freudenstein's ,analytical ,approach to the ,design of ,four-,link ,mechanisms in #aied1abe and an increasing interest in the problem is indicated by the extensive literature that has appeared in the last five years4 ,footnote #abe3 ,transactions of the ,american ,society of ,mechanical ,engineers1 #aied1 vol4 #gf1 pp4 #dhc-dib4 ,see also ,transactions of the ,american ,society of ,mechanical ,engineers1 #aiee1 vol4 #gg1 pp4 #hec-hfa1 and #aief1 vol4 #gh1 pp4 #ggi-ghg4 ,the proper role of rational methods in the synthesis of mechanisms is not yet clear4 ,while we may talk about kinematic synthesis1 wrote two of today's leaders in the field1 we are really talking about a hope for the future rather than a great reality of the present4#abf ,when the mental equipment and the enthusiasm of scholars who are devoting their time to the problems of kinematic synthesis are considered1 however1 it is difficult to see how important new ideas can fail to be produced4 ,footnote #abf3 ,r4 ,s4 ,hartenberg and ,j4 ,denavit1 ,kinematic ,synthesis1 ,machine ,design1 ,september #f1 #aief1 vol4 #bh1 pp4 #aja-aje4 ,an annual ,conference on ,mechanisms1 sponsored by ,purdue ,university and ,machine ,design1 was inaugurated in #aiec and has met with a lively response4 ,among other manifestations of current interest in mechanisms1 the contributions of ,americans to international conferences on mechanisms reflects the growing recognition of the value of scholarly investigation of the kind that can scarcely hope to yield immediately tangible results4 ,while we look to the future1 one may ask how a lengthy view of the past can be justified4 ,it seems to me that there is inherent in the almost feverish activity of the present the danger of becoming so preoccupied with operational theory that the goals may become clouded and the synthesis 7let us put it less elegantly3 the design7 of mechanisms may never quite come into focus4 ,if one knows nothing of the past1 ,i wonder how he can with any confidence decide in what direction he must turn in order to face the future4 ,acknowledgment ,i am grateful to ,professors ,richard ,s4 ,hartenberg and ,allen ,s4 ,hall1 ,jr41 for reading the manuscript1 making helpful comments1 and suggesting material that ,i had not found4 ,the errors1 however1 are mine4 ,additional ,references ,the following list of additional reference material on kinematics may be of help to readers who desire to do independent research4 ,the material is listed according to the section headings in the text of the present article4 ,,to ,,draw ,a ,,straight ,,line ,,kempe1 ,a4 ,b4 ,how to ,draw a ,straight ,line4 ,london1 #ahgg4 ,contains a useful bibliography4 ,reprinted in ,squaring the ,circle and ,other ,monographs1 ,new ,york1 ,chelsea ,publishing ,company1 #aiec4 ,much attention has been given to straight-line mechanisms since the time of ,kempe2 at least a half dozen articles have appeared in the ,united ,states since #aiej1 but ,i did not investigate the literature published after #ahgg4 ,,scholars ,,and ,,machines ,,beck1 ,,theodor4 ,beitrge zur ,geschichte des ,maschinenbaues4 ,berlin1 #ahii4 ,reviews of early works1 such as those by ,leonardo da ,vinci1 ,biringuccio1 ,besson1 ,zonca1 etc4 ,,borgnis1 ,,giuseppe ,,antonio4 ,trait complet de mcanique applique aux arts4 ,paris1 #ahah-ahba1 #i vols4 ,contains several hundred finely detailed plates of machines4 ,,laboulaye1 ,,charles4 ,trait de cinmatique ou thorie des mcanismes4 ,paris1 #ahfa 7ed4 #b74 ,this work was quoted frequently by ,laboulaye's contemporaries4 ,,royal ,,society ,,of ,,london4 ,catalogue of ,scientific ,papers1 #ahjj-aijj1 ,author ,index4 ,london1 #ahfg-aijb1 and ,cambridge1 #aiad-aibe4 ----4 ,catalogue of ,scientific ,papers1 #ahjj-aijj1 ,subject ,index4 ,london1 #aiji1 vol4 #b4 ,this subject index was started in #aijh1 and by #aiad three volumes 7the third in two parts7 had been published2 however1 this subject index was never completed4 ,volume #b1 titled ,mechanics1 has some #bjj entries under ,linkages4 ,it is interesting to note that both of the ,royal ,society's monumental catalogs grew out of a suggestion made by ,joseph ,henry at a ,british ,association meeting in ,glasgow in #ahee4 ,,weisbach1 ,,julius4 ,the ,mechanics of the ,machinery of ,transmission1 vol4 #c1 pt4 #a1 sec4 #b of ,mechanics of ,engineering and ,machinery1 translated by ,j4 ,f4 ,klein4 ,new ,york1 #ahij 7ed4 #b74 ,,mechanisms ,,and ,,mechanicians ,,barber1 ,,thomas ,w4 ,engineer's ,sketch-,book4 ,london1 #ahij 7ed4 #b74 ,,herkimer1 ,,herbert4 ,engineer's ,illustrated ,thesaurus4 ,new ,york1 #aieb4 ,,periodicals4 ,artizan1 from #ahdc2 ,practical ,mechanic and ,engineer's ,magazine1 from #ahda2 ,repertory of ,arts and ,manufactures1 from #agid2 ,newton's ,london ,journal of ,arts and ,science1 from #ahbj4 7,the preceding periodicals have many plates of patent specification drawings47 ,the ,engineer1 ,november #aj1 #aicc1 vol4 #aef1 p4 #dfc1 and ,engineering1 ,november #aj1 #aicc1 vol4 #acf1 p4 #ebe4 7,recent ,english views questioning the utility of kinematics47 ,,tate1 ,,thomas4 ,elements of ,mechanism4 ,london1 #ahea4 ,contains figures from ,lanz and ,btancourt 7#ahjh74 ,,wylson1 ,,james4 ,mechanical ,inventor's ,guide4 ,london1 #ahei4 ,contains figures from ,henry ,adcock1 ,adcock's ,engineers' ,pocket-,book1 #aheh4 ,,mechanisms ,,in ,,america1 #ahge-aiee ,,albert1 ,,calvin ,d41 ,,and ,,rogers1 ,f4 ,d4 ,kinematics of ,machinery4 ,new ,york1 #aica4 ,contains a bibliography that includes works not mentioned in the present paper4 ,,barr1 ,,john ,h4 ,kinematics of ,machinery4 ,new ,york1 #ahii4 ,an early textbook4 ,the author taught at ,cornell ,university4 ,,beggs1 ,,joseph ,s4 ,mechanism4 ,new ,york1 #aiee4 ,contains an extensive and useful bibliography4 ,,bottema1 ,o4 ,recent ,work on ,kinematics1 ,applied ,mechanics ,reviews1 ,april #aiec1 vol4 #f1 pp4 #afi-agj4 ,,conference ,,on ,,mechanisms4 ,this conference was sponsored by ,purdue ,university and ,machine ,design4 ,transactions of the first two conferences appeared as special sections in ,machine ,design1 ,december #aiec1 vol4 #be1 pp4 #agc-bbj1 ,december #aied1 vol4 #bf1 pp4 #ahg-bcf1 and in collected reprints4 ,papers of the third and fourth conferences 7,may #aief and ,october #aieg7 appeared in ,machine ,design over several months following each conference and in collected reprints4 ,papers of the fifth conference 7,october #aieh7 were collected and preprinted for conference participants2 subsequently1 all papers appeared in ,machine ,design4 ,collected reprints and preprints are available 7,may #aifj7 from ,penton ,publishing ,company1 ,cleveland1 ,ohio4 ,,de ,,jonge1 ,a4 ,e4 ,,richard4 ,kinematic ,synthesis of ,mechanisms1 ,mechanical ,engineering1 ,july #aidj1 vol4 #fb1 pp4 #ecg-edb4 ----4 ,a ,brief ,account of ,modern ,kinematics1 ,transactions of the ,american ,society of ,mechanical ,engineers1 #aidc1 vol4 #fe1 pp4 #ffc-fhc4 ,,goodeve1 ,,thomas ,m4 ,the ,elements of ,mechanism4 ,london1 #aijc4 ,an early textbook4 ,,grodzinski1 ,,paul1 ,,and ,,mcewen1 ,,ewen4 ,link ,mechanisms in ,modern ,kinematics1 ,journal and ,proceedings of the ,institution of ,mechanical ,engineers1 #aied1 vol4 #afh1 pp4 #hgg-hif4 ,this article evoked interesting discussion4 ,it is unfortunate that ,grodzinski's periodical1 ,mechanism1 ,an ,international ,bibliography1 which was published in ,london in #aief-aieg and which terminated shortly after his death1 has not been revived4 ,grodzinski's incisive views and informative essays are valuable and interesting4 ,,hartenberg1 ,r4 ,s4 ,complex ,numbers and ,four-,bar ,linkages1 ,machine ,design1 ,march #bj1 #aieh1 vol4 #cj1 pp4 #aef-afc4 ,this is an excellent primer4 ,the author explains complex numbers in his usual lucid fashion4 ,,hartenberg1 ,r4 ,s41 ,,and ,,denavit1 ,j4 ,kinematic ,synthesis1 ,machine ,design1 ,september #f1 #aief1 vol4 #bh1 pp4 #aja-aje4 ,,maccord1 ,,charles4 ,kinematics4 ,new ,york1 #ahhc4 ,an early textbook4 ,,robinson1 ,,stillman ,w4 ,principles of ,mechanism4 ,new ,york1 #ahif4 ,an early textbook4 ,the author taught at ,ohio ,state ,university4 ,,unwin1 ,,william ,c4 ,the ,elements of ,machine ,design4 ,new ,york1 #ahhb 7ed4 #d74 ,an early textbook4 ,the author taught at ,royal ,indian ,engineering ,college1 in ,england4 ,,government ,,printing ,,office3 #aifb ,for sale by the ,superintendent of ,documents1 ,u4,s4 ,government ,printing ,office ,washington #be1 ,d4 ,c4--,price #dj cents