The Reuleaux Collection

of Kinematic Mechanisms

at Cornell University

Francis C. Moon

Joseph Ford Professor of Mechanical Engineering

July 1999


In an age of computer simulation and multibody dynamics codes one can easily assume that engineers of earlier generations lacked the ability to visualize complex motions of machines and mechanisms. But the use of three-dimensional drawings and physical models of scientific and engineering devices goes back to the Renaissance engineers of Italy, including Leonardo di Vinci (see e.g., Ramelli, 1588). Eugene Ferguson, a former curator at the Smithsonian, has reviewed the history of non-verbal and non-mathematical communication of technical information in his book Engineering and the Mind's Eye (Ferguson, 1992), and in an earlier articles (Ferguson, 1977, 1962). In his reviews, he points out the use of machine models in the teaching of engineering in the late 19th and early 20th century. One of the more popular collections of models for teaching, especially in Germany and in North America, was the reproductions of kinematic mechanisms of Franz Reuleaux. At the end of this millennium, it is fitting for engineers not only to review the progress made in the last century, but also to review what has been lost in the way of technical knowledge.

I will describe one of the largest remaining 19th century collections of kinematic models in North America and perhaps in the world, namely the Reuleaux models at Cornell University. Collections of Reuleaux models were widely used in Europe, especially in Germany, before the Second World War. Most and maybe all have been lost in the destruction of 1941-45. The Cornell Reuleaux Collection seems to be the last remaining large set of 219 models out of the original 800 that Reuleaux had built in his laboratory in Berlin over a century ago.

In this paper I will review Reuleaux's contributions to kinematics in the context of these models. I will also describe how Cornell University acquired its collection through the vision of its first president, Andrew Dickson White. This acquisition took place amidst a crisis in mechanical engineering education at Cornell which involved ASME's first president Professor Robert H. Thurston of Stevens Institute of Hobocken, New Jersey. I will also describe the current state of the Reuleaux collection at Cornell and a smaller collection of Darmstadt models and a plan for making the models available on the web through construction of a virtual kinematic museum.

As a recently appointed curator of the kinematic models collection at Cornell, I found that I had to learn a lot about the history of kinematics and nineteenth century machines in order to understand the role of the Reuleaux models in teaching kinematics. As a result I realized the shortcomings in my knowledge of kinematics and the history of technology which the reader might discover and I hope will understand.

Franz Reuleaux

Franz Reuleaux was born in Eschweiler (near Aachen), Germany on September 30, 1829. He is regarded as the founder of modern kinematics and as one of the forerunners of modern design theory of machines. [A brief biography in English may be found in Gillispie (1970). Another excellent, short biography of Reuleaux has been written by Ferguson as an introduction to the 1963 Dover edition of Reuleaux's 1875 book on kinematics. A separate annotated list of references to Reuleaux in German is provided in the Appendix.] At the time that Cornell's President A.D. White acquired the Collection in 1882, Reuleaux was rector of the Technische Hochschule at Charlottenburg near Berlin. Earlier he was professor of machine design at the Swiss Federal Polytechnic Institute in Zurich where he developed many of his ideas in kinematics. Of his two major books, Der Constructor and Theoretische Kinematik; Grundzüge einer Theorie des Maschinenwesens, the second had a wider impact. It was immediately translated into English by Professor Alexander B.W. Kennedy of Great Britain titled, The Kinematics of Machinery; Outlines of a Theory of Machines (Reuleaux, 1876), after being translated into French and Italian. This pioneering book dealt with both analysis and synthesis of machine kinematics. Kennedy also wrote a book review on Reuleaux's work in the London based journal, Engineering (Kennedy, 1876a). In the earlier sections of his book Reuleaux states that he is interested in how the mind creates new inventions as well as kinematic analysis. Some of his ideas are captured in the quotes in Table 1 below.

Reuleaux was one of the first to use an abstract symbol representation of machines. He is also credited with inventing the idea of a kinematic pair (Kennedy, 1881). Each pair had a different symbol, and each mechanism would be described by a collection of symbols or word. A complete assembly of mechanisms is then a sentence of words in this symbol language.

Reuleaux's symbol notations was based on his ideas of a kinematic chain and pair elements. There were three kinds of signs denoting; i) class or name for a body or link, ii) form of the body, i.e., solid, hollow, etc, iii) relation of one element to its pair. Thus, the four bar linkage shown in Figure 1, without specifying the fixed link has the contracted symbol (C). If the bottom link is called d and is fixed, then the symbol becomes (C)d. The C stands for cylindrical motion, the primes stand for parallel axes and the subscript denotes the four links.

Another example is the cylindric slider-crank chain. The classic slider-crank would have the contracted symbol (CD^) where the P indicates one of the pair elements is a prismatic joint. If the slider follows an arc as in Figure 2, Reuleaux uses the symbol (CA) where A stands for a circular sector. By reducing mechanisms to a symbol set he is able to show how many apparently different devices are similar or identical in a kinematic sense. Also, by changing the fixed link in the chain Reuleaux was able to generate inversions of the same kinematic chain. The details of this system may be found in Reuleaux (1876), Chapter XII.

This abstract methodology for kinematic mechanisms did not propagate in later textbooks in the early 20th century. However, the idea of symbols for machine elements has been renewed in modern design synthesis theory (see e.g., Hartenburg and Denevit, 1964). Reuleaux's contributions to kinematics have recently been recognized in a recent review of modern developments in kinematics (Erdman, 1993). Quotes on Reuleaux from modern practitioners are given in Table 2.

Besides his influence on kinematics, Reuleaux was active in the technological politics of the newly united German Empire. He had an important role in developing German patent legislation and with the founding of the Mannesmann steel works, as well as a member of juries of international exhibitions. Reuleaux was also active in improving the quality of German manufacturing. [See the short biography by Otto Mayr in Gillispie (1970).]

Nineteenth century kinematics flourished because of the need for machine inventors to transmit information and forces (power) from one element in the machine to another. Thus, we see the names of James Watt (1736-1819) and Rankine (1820-1872) among earlier inventors of mechanisms for the new steam and water based machines that revolutionized the 19th century. Also, water and steam power generated circular motions and the need arose to convert these steady circular motions into nonsteady linear and curvilinear motion for machine applications. The challenge to create input-output kinematic devices that could convert circular motion into noncircular, complex, three-dimensional, intermittent motions attracted both practical inventors as well as mathematicians in the nineteenth century. Analysis of mechanisms attracted mathematicians of the likes of Ampere (1775-1836) and Chebyshev (1821-1894) (Ferguson, 1962). Thousands of mechanisms were invented, designed and built in the last century which helped nurture the widespread use and manufacture of machines analogous to the plethora of electronic circuits in the early 20th century and software in the late 20th century.

In Reuleaux's work we see an interest in kinematics–namely the relationship of input and output velocities and motion paths (e.g., in the design of straight line mechanisms). However, by the mid 20th century dynamics became important in machine design with kinematics as one part of a mathematical tool kit to be used to solve the rigid body equations of Newton and Euler. Also important in 20th century machine design was stress analysis and materials science.

The study of kinematics as a separate discipline in mechanical engineering all but died out in many universities by the early 1950's, partly because it became recognized that dynamics was as important in the design of machines as kinematics. Dynamics had all but been ignored by Reuleaux and other 19th century kinematicians. In the late 20th century, kinematics has seen a renaissance with the development of high-speed computers, robotics, the growth of design synthesis theory and mechatronics.

The Reuleaux Collection of Mechanisms

In the mid 19th century, Franz Reuleaux embarked on a method to codify, analyze and synthesize kinematic mechanisms so that engineers could approach machine design in a rational way. To this end, he created at Berlin a collection of over 800 models of mechanisms based on his book. Reuleaux's models were apparently influenced by a model collection of his former professor at Karlsruhe, F.J. Redtenbacher [see footnote 37 in Ferguson (1977).] At the time (c. 1876) he authorized a German Company, Gustav Voigt, Mechanische Werkstatt, in Berlin, to manufacture these models so that technical schools could use them for teaching engineers about machines. From Reuleaux's letter to A.D. White in 1882, Voigt had apparently worked for Reuleaux or had been a student when Reuleaux taught at the Gewerbe Schule in Berlin.

By 1907 some 368 were available in the Voigt catalog and the Cornell collection was reported to number 266 items (Hartenberg and Denavit, 1964). The present inventory as of December 1998 is 219 models from the Voigt catalog of the Reuleaux kinematic models. The classes of models are listed in Table 3. Because of widespread destruction in Germany in World War II, it is believed that Cornell has the largest remaining collection of Reuleaux models. A curator in mechanical engineering at the American Museum of Industry at the Smithsonian Institution said he did not know of any other large collections in the United States or Canada.

Reuleaux's models go beyond the collection of kinematic pairs as in Christopher Polhem's "mechanical alphabet" models of 1729 now at the Teknista Museet in Stockholm. There are numerous Reuleaux models of complete machines such as eight fully operating clock escapements, and several complex winch machine models. The clock escapements have as many as fifteen moving parts, constructed from over two dozen manufactured machine elements.

The models are clearly designed for teaching kinematics. Some are demountable so that a different link can be fixed. Some are inscribed with letters and numbers on the links corresponding to Reuleaux's books. Many have adjustments built in so the user can find the optimum setting for proper motion.

At the time of Reuleaux's book on theoretical kinematics in 1875, he began to travel abroad, and became a member of juries of world exhibitions. Of particular interest are the world exhibitions in Vienna (1873) and Philadelphia (1876) where Reuleaux served as the German commissioner (Gillispie, 1970).

Robert H. Thurston was a member of the Scientific Commission of the United States to the Vienna International Exhibition of 1873. Thurston was then at Stevens Institute in Hoboken, N.J. Thurston's report on the Vienna Exhibition of 1873 (Thurston, 1875) is titled Machinery and Manufactures, with an account of European Manufacturing Districts. On page 367, Thurston mentions visiting Dr. Reuleaux' as director of the Gewerbe Schule, a forerunner of the Technische Hochschule in Berlin. Thurston mentions "the fine collection of geometrical and mechanical apparatus." "The models are lighter and neater than those usually seen in our own cases" and that "none are for sale."

These are several documents in the Cornell University Library archives that confirm that Cornell acquired the collection in 1882 or thereafter.

First there is a letter in English (hand written) from Professor Reuleaux to A.D. White dated 27th June 1882. This letter establishes that there was earlier correspondence between White and Reuleaux and that Reuleaux would supervise the shipping of the Voigt manufactured models to Ithaca.

Second, the minutes of the Cornell University Board of Trustees, June 14, 1882, "Acknowledges a pledge of $8,000 from the Honorable Hiram Sibley of Rochester to secure the duplicate of the Reuleaux models in the possession of the Imperial Government of Germany." (Hiram Sibley and Ezra Cornell both formed the Western Union Telegraph Company in 1854.)

Concerning the International Exhibition of 1876 at Philadelphia there is evidence in the reports of the U.S. Centennial Commission (Walker, 1877, 1878) that A.D. White, Reuleaux, and Robert H. Thurston were all there at some time during the fair. The Exhibition was open for six months. Over ten million people visited the fair to see over 30,000 exhibitors from all over the world. Reuleaux is listed in the volume on Group XXVIII, (p. 203) Education and Science as a Commissioner-General for the German Empire and having assisted the judging of this group. The official list of judges include Andrew D. White of Ithaca, New York. However, in the list of awards, no mention is made of Reuleaux's models nor is he listed in the overall index of awards in the multi-volume report on the Exhibition.

Robert Thurston is mentioned in Group XXV on Instruments of Precision, Research Equipment, etc. as having exhibited his Machine for Testing Strength of Materials. He is identified as a professor at Stevens Institute of Technology. This machine, or a copy of it, is likely the one now in the strength of materials laboratory of the Department of Theoretical and Applied Mechanics in Thurston Hall at Cornell University. This Group had judges which included Joseph Henry, the discoverer of electromagnetism who was then Secretary of the Smithsonian Institute in Washington, D.C. In Reuleaux's letter to White (see Document 1), he mentions the Smithsonian, but not Henry.

Thus, it is possible that Reuleaux met A.D. White and, perhaps, Thurston in Philadelphia. We have no direct evidence so far of how President White learned of the Reuleaux models though perhaps he saw them in London. There is evidence that 300 of Reuleaux's models were actually on display at the Exhibition of Scientific Apparatus at the South Kensington Museum in London in September 1876 (Kennedy, 1876). In the Cornell Archives on A.D. White, there is also evidence that White had traveled to Europe in the Fall of 1876. Thus, it is possible he saw the Reuleaux models at South Kensington. The South Kensington Museum was the predecessor of the Victoria and Albert Museum built in Kensington around 1900. There is a wonderful little book by Professor A.B.W. Kennedy of University College, London with a 19 page introduction by Robert Thurston (Kennedy 1881). The book title is The Kinematics of Machinery: Two Lectures Relating to Reuleaux Methods. These lectures (88 pages) were given by Kennedy at the Museum. Kennedy describes Reuleaux's theory of kinematic pairs and his symbol representation of complex mechanisms. This small book illustrates the high esteem that Reuleaux was held both in Europe and the U.S. and the relation of his theory to his models. (Kennedy became the President of the Institute of Mechanical Engineers in Great Britain and Thurston was the first president of ASME.) Kennedy mentions the loan to the Museum of the Kinematic Collection of the Gewerbe-Academe in Berlin, designed by Reuleaux. He also mentions a set of models at Dresden as being essentially the same as the Berlin models.

To understand the complete collection of models, one has to reference not only Reuleaux's 1876 book on kinematics, but also his 4th edition of his earlier book The Constructor, translated by Henry Suplee in 1893. Reuleaux offers two prefaces, one for the German edition and one for the English edition in which he says he has added many aspects of kinematics in this 4th edition from his theoretical book on kinematics. There are many figures of mechanisms which appear to be directly related to the models especially those dealing with belt drives, water chamber wheels, pumps, couplings and escapements. Many of these are not shown in his earlier 1876 book on kinematics. In The Constructor Reuleaux gives the history, application, inventor and detailed information on the operation of the mechanisms which is lacking in his 1876 kinematics book. According to his Preface, he wrote The Constructor as a handbook on machine construction for the practical engineer.

A Reuleaux Collection Sampler

Along with the Voigt catalog of 1907 and the English translation of Reuleaux's book on kinematics by Kennedy, there is a set of 40, 5 x 7 inch cards, with descriptions of various mechanisms in the Cornell Collection. The cards reference Reuleaux's Kinematics of Machinery as well as other books on kinematics in the late 19th and early 20th century. The cards were written around 1940's-1950's by Harvey Roehl then a student in mechanical engineering. There is no other complete description of the 219 models although we hope to assembly one as part of a new Library effort to catalog the colleciton and to create a virtual museum on the web.

The following descriptions of mechanisms are based on the material in Reuleaux's books. The last item is from the 1962 Smithsonian article by Eugene Ferguson on the history of mechanisms and Reuleaux.

The pump mechanism (F4) known as Ramelli's Rotary Pump (Figure 3) was first described in 1588 by the Italian military engineer, Agostino Ramelli (1531-1610). This mechanism found application in mid twentieth century household refrigerator compressors (Reuleaux, 1876, p. 365).

The Pappenheim Chamber Wheel (I1) (Figure 4) is the forerunner of modern gear pumps. Versions of this mechanism have been in existence for over 350 years (Reuleaux, 1876, p. 403).

The Isosceles Slider Crank Train (S2) (Figure 5) was used in an early steam engine in 1816. This mechanism can be used to form ellipses. Its invention has been attributed to Leonardo da Vinci (1452-1519) for machining elliptical surfaces.

The Crown-Wheel Escapement (X1) (Figure 6) is associated with the Dutch scientist, Christian Huygens who designed the first pendulum clock in 1657. This mechanism allowed the weight of a hanging mass to regularly impart energy to the oscillating pendulum. The Cornell Collection contains eight of these beautiful clock escapement mechanisms. They are the most elaborate devices in the set and can run for a short time by suspended weights. They are the jewels of the Collection.

The Pin-Wheel Escapement (X4) (Figure 7) was invented by Amant in 1741. It was employed in French made pendulum clocks. It was also used in tower clocks.

Chebyshev Mechanism (S19) (Figure 8). For a period in the early 19th century, there was a concerted effort to invent a mechanism that would convert rotary motion into a straight-line motion. This quest occupied mathematicians as well as practical mechanikers. The famous Russian mathematician, Professor P.L. Chebyshev (1821-1894), of the University of St. Petersberg invented his own straight-line mechanisms. Such devices were important in metal planing machines and textile manufacturing.

Other Reuleaux and Modern Kinematic Model Collections

During a sabbatic leave in 1995 at the University of Hannover in Germany, I met Professor Reinhard Braune, a professor of kinematics and computer aided design. He proudly showed me about ten models from the original Reuleaux collection. (These were from Reuleaux's own laboratory, not Voigt's reproductions.) He told me virtually all the collections in Germany were destroyed. However, from recent correspondence with the Deutsche Museum in Munich, it appears that they may have about hundred models, though they could not send an itemized list. In Hannover, they have reproduced several models and displayed them so they can be actuated. The display also includes modern applications of kinematic mechanisms in manufacturing, automotive design and aerospace technology.

There is also a wonderful modern kinematic model collection of about 300 devices at the Technische Hochschule Aachen under Professor Dittrich. However, they do not have any Reuleaux models. (Their web site also describes all the institutes of kinematic research in Germany.)

Professor Braune was kind enough to give me copies of articles on Reuleaux in German (see Appendix). These articles, dating from around 1899-1940, suggested there were other North American Reuleaux collections at McGill University in Montreal, and Stevens Institute in Hoboken, N.J. Inquiries at McGill indicate that their collection, if it existed in any great number, is gone. One colleague remembers seeing one model several years ago. A call to the curator at the Stevens Institute Library revealed that they have, at most, a few and perhaps only one on display in their library. Also from a phone conversation, the Smithsonian does not have any Reuleaux models either. Professor Dittrich in Aachen thought there was also a collection in St. Petersberg in Russia. However, through his conversation with Professor Artobolesvsky, he believes they were also lost during the War.

In addition to the Reuleaux models, Cornell has about ten old kinematic models by Professor Schröder of the Polytechnisches Arbeits Institute, Darmstadt. These models were cited for an award at the Philadelphia Exposition of 1876 in the section judged by A.D. White of Cornell and Reuleaux. We are currently trying to obtain a biography on Schröder.

It is a paradox of Reuleaux influence on kinematics, that although he himself built over 800 models and used over a thousand images of these machines and components in his 1893 edition of The Constructor, educators in kinematics in the early twentieth century substituted mathematics for visual pictures in their textbooks. For example, Kennedy who was such an enthusiastic Reuleaux supporter, does not show any of the models or related mechanisms in his own textbook of 1886. Also, although Cornell university had a large collection of over 250 Reuleaux models, the textbook by Barr and Wood (1916) which was based on a course taught at Cornell, has no figures showing Reuleaux's models and has only 220 figures (mostly live drawings) with very few artifacts except gears. However, unlike Reuleaux's books, Barr and Wood incorporate more detailed velocity and acceleration analysis which became the pattern for later textbooks. An exception to this trend was the book by Durley (1903) who was a professor at McGill University. McGill at one time had a collection of Reuleaux models and Durley's book contains a dozen figures based on these models. But the trend in the 20th century was to use a mathematical approach to kinematic analysis to the detriment of visual, historical and case method studies. Another exception was the work of Hartenburg and Denivit (1964) who devoted a Chapter (3) to kinematic models.

Reuleaux Collection, Thurston and Engineering Education

The acquisition of Reuleaux' famous collection of kinematic models in 1882 by Cornell President White took place amidst a watershed for Cornell's mechanical engineering program as well as American engineering education (Calvert, 1967). For seven years between 1878 and 1886 the University was struggling to resolve a nasty feud between professors, students and alumni about the teaching of mechanical engineering. In the first decade of its existence, the University had developed a curricula in the "mechanic arts" as required of a land grant recipient, based on a shop culture model (Calvert, 1967). Young men were recruited with a farm or mechanical skills background to learn how to construct mechanical machines and machine components. The major proponent of this system was Professor John Sweet (3rd president of ASME) who was supposedly hostile to book learning. At the same time, Professor Robert Henry Thurston (1st president of ASME) of the Stevens Institute in Hoboken, New Jersey was developing a different curriculum based on laboratory testing, and scientific and mathematical principles.

In 1878 Sweet decided to leave Cornell which prompted a crisis over the teaching philosophy. A Trustee Committee was set up to reform the mechanical engineering program helped by a generous gift from a successful businessman, Hiram Sibley of Rochester. It was during this time that Andrew White acquired the Reuleaux models although on whose recommendation we don't know. One possibility is that he met both Reuleaux and Thurston at the Worlds Fair in 1876 in Philadelphia, as discussed above. Reuleaux' letter of 1882 to White suggests that the two men had been in contact between 1876 and 1882. (Reuleaux thanked White for help in contacting the Smithsonian.) Then in 1886, White proposed to the Trustees to appoint Robert Thurston as Director of the newly organized Sibley College of Mechanic Arts and Mechanical Engineering. Shortly after his arrival, Thurston wrote to Andrew D. White in a letter dated July 8, 1885 (typed). Thurston had recently been appointed as Director of the newly revised College of Mechanic Arts in a Board of Trustee meeting of June 17, 1885. Thurston notes the need to "equip the department of mechanical engineering." "With the exception of the Reuleaux collection" he asks for funds to buy more models, plans, charts and a "complete collection needs to be obtained." It is not clear whether this refers to the Reuleaux models or other teaching models. In Thurston's letter to White in 1886 asking for financial resources to rebuild the College, he comments that the Reuleaux collection of models, paid for with a Sibley gift of $8,000, was one of the few strong assets of the College.

In the period of 1886 to 1900, Thurston built the mechanical engineering program on a new educational model based on a balance of scientific and mathematical fundamentals, engineering science and practical shop experience. The use of extensive laboratories and collections of teaching models of mechanisms and machines as well as technical artifacts of the day were essential to the students all round education. Using this new philosophy, Thurston catapulted Cornell's Sibley College of Mechanical Engineering into the top rated program in the United States (Calvert, 1967).

The Reuleaux Collection at Cornell is a reminder of how the vision of A.D. White, H. Sibley and Robert Thurston helped change the nature of engineering education in the United States.

The Cornell Collection–Current Status

The collection of mechanisms is housed in the Sibley School of Mechanical and Aerospace Engineering. When it was originally acquired in 1882 it was housed in the old Engineering campus at the north end of the University. According to an article in the October 17, 1885 issue of Scientific American there was originally a museum of mechanisms and a museum of machines in the then Sibley College of Mechanical Engineering. After the second world war Cornell moved its entire engineering college to the south end of the campus and the kinematic collection was housed in special cabinets in one of the new buildings. By the 1970's, however, space assignments in the College shifted and the Collection space was occupied by Computer Science, so that Mechanical Engineering faculty and students rarely saw or used the models. One of the last faculty to use the collection for teaching was retired Professor Richard Phelan whose design text was well known in earlier decades. After a hiatus of over a decade, however, several younger faculty in design discovered the use of these wonderful machines for teaching. Today the collection is back on the turf of Mechanical and Aerospace Engineering and are publicly on display for students and visitors to view. A few faculty such as myself make use of a dozen or more of the models each year for design and dynamics courses. Inspired by the wonderful kinematic collection in Aachen and Hannover we have motorized one model and hope to motorize reproductions of many other models so that visitors can actuate the models from outside the display cases.

The Engineering Library has embarked on a conservancy program to catalog and make images of the models available on the web. To date we have photographed all 219 Reuleaux models on color slides and hope to make their images available on the web in the form of a virtual museum. Plans are also proposed for quicktime computer movies of selected models, again inspired by the modern German collections.

The state of the models are remarkable. Except for one model, the mechanisms show no rust, Reuleaux having designed the cast iron alloy himself to resist rust. All but a half dozen models actually work and can be actuated by hand. The most marvelous models are the clock and power escapement mechanisms which were designed by Reuleaux to exhibit self excited oscillations driven by a weight on each model. While most of the models represent devices that were common to various technical machines, such as four bar linkages, pumps, or intermittent mechanisms, a small subset actually simulate mathematical curves attendant to kinematic motions, such as cycloid and trochoid curves related to rolling mechanisms.

As noted above, these models were reproduced by the Voigt workshop from Reuleaux's original models under his supervision. Cornell has copies of the Voigt catalog which consists of pictures and a separate list of short descriptions in German. We are using the Reuleaux-Voigt numbering system to catalog the collection (see Table 3).

Researchers from outside Cornell can have access to these models for study by contacting the author of this article.


Reuleaux on the Study of Machines

He who best understands the machine, who is best acquainted with its essential nature, will be able to accomplish the most by its means.

...if the new theory is to lay claim to general interest, it must be capable of producing something new; it must make problems solvable which before could not be solved in any systematic way. This may certainly be said to be the case if it succeeds in making Machine-Kinematics, down to its simplest problems, truly scientific.

What is left unexamined is however the other, immensely deeper part of the problem, the question: How did the mechanism, or the elements of which it is composed, originate? What laws govern its building up?

In other words, the invention of a mechanism will be to the scientific kinematist a synthetic problem,–which he can solve by the use of systematic, if also difficult, methods.





Modern Quotes on Reuleaux' Contribution to Kinematics


[All quotes from the review book Modern Kinematics,

Edited by Arthur G. Erdman, John Wiley & Sons, Inc., New York, 1992.]


1. It was Reuleaux, however, who presented (Kinematics of Machinery) an extensive description and symbolic representation of the mechanisms that are used in engineering. He also addressed important aspects of kinematics, such as pairing and inversion of mechanisms. Reuleaux stated at the outset of his project that he would be concentrating on the theoretical aspects of kinematics of machinery, not the applied subjects. His aim was not to deal with the kinematic behavior of any particular machine, but " determine the conditions which are common to all machines...."

§1.2 The Origins of the Theory of Machines and Mechanisms,

A.D. Dimarogonas, p. 15



2. Reuleaux's work is the first work devoted to modern kinematic synthesis and, further, to symbolic representation of knowledge. Synthesis, in the Reuleauxian sense, is limited to type synthesis. The systematic study of type and dimensional synthesis, although identified long ago, were later developments. However, Reuleaux can also be considered the father of group technology.

§1.2 The Origins of the Theory of Machines and Mechanisms,

A.D. Dimarogonas, p. 15



3. Reuleaux recognized the preeminence of the joints and identified them as kinematic pairs. He laid the foundation for a systematic study of machines by 1) defining machine and mechanism in a meaningful and unambiguous manner, 2) defining the basic building blocks, and 3) establishing a classification of known mechanism types.

§3.2 Historical Review,

G.K. Ananthasuresh, S. Kota, p. 31


4. Reuleaux identified two different methods of synthesis: direct and indirect. Direct Synthesis should yield all the links and pairs required to accomplish a specified motion transformation. Indirect synthesis" provides beforehand the solutions of all those problems under which it is possible for the given problem to fall." Since the number of possible pairs is limited, the number of possible combinations of pairs, although great, is s till manageable. Therefore, all possible combinations can be enumerated and investigated systematically.

§3.3 Methods and Tools for Type Synthesis

S. Kota, et al., p. 36

Table 3


Kinematic Models After Reuleaux

Gustav Voigt Catalog, 1907

Series Description Number of Models

A Lower element pairs 3

B Higher element pairs 4

C Simple kinematic chains (including 4 bar mechanisms) 9

D Crank mechanisms (including slider crank mechanisms) 14

E Crank mechanisms with a pivot 7

F Chamber wheel mechanisms (fluid motors/pumps) 6

G Compound wheel trains (gearing) 7

H Vise stands to create inversions of 4-bar linkage 2

I Chamber wheels (pump mechanisms) 9

K Angular loop chain-crossed axes slider mechanisms 2

L Cam drives of constant breadth 6

M Screw mechanisms 9

N Ratchet and intermittent mechanisms 28

(including power escapements)

O Planetary wheel chains 5

P Hinged couplings (universal joints) 5

Q Gear tooth profiles 8

R Spherical cycloid rolling models 7

S Straight-line mechanisms 39

T Parallel guide mechanisms 14

U Water-wheel paddle mechanisms 2

V Belt guides 16

W Friction wheel mechanisms 7

X Clock escapements 12

Y Reversing shift transmissions 20

Z Clutches 7


References in English

Barr, John H. and Wood, Edgar H., 1916, Kinematics of Machinery, 2nd edition, J. Wiley & Sons, New York.

Calvert, Monte, 1967, History of Mechanical Engineering, J. Hopkins Press.

Durley, R.J., 1907, Kinematics of Machines, J. Wiley & Sons.

Erdman, Arthur G., 1993, editor, Modern Kinematics; Developments in the last Forty Years, J. Wiley & Sons.

Ferguson, E.S., 1992, Engineering and the Mind's Eye, MIT Press, Cambridge, Mass.

Ferguson, E.S., 1977, "The Mind's Eye: Nonverbal Thought in Technology," Science, Vol. 197, No. 4300, pp. 827-836.

Ferguson, E.S., 1962, "Contributions From the Museum of History and technology", Kinematics of Mechanisms from the Time of Watt, from United States National Museum Bulletin, 228, Smithsonian Institution, Washington, D.C. paper 27, pp. 185-230.

Gillispie, Charles C., 1970, Dictionary of Scientific Biography, Charles C. Gillispie, editor, Charles Scribners Sons, New York , Vol. XI, "Reuleaux, Franz", by Otto Mayr, p. 383-385.

Hartenberg, R.S. and Denavit, J., 1964, Kinematic Synthesis of Linkages, McGraw-Hill Book Co., New York, p. 75.

Kennedy, A.B.W., 1886, The Mechanics of Machinery, MacMillan and Co., London.

Kennedy, A.B.W., 1881, The Kinematics of Machinery: Two Lectures Relating to Reuleaux Methods. Delivered at the South Kensington Museum with an Introduction by Professor R.H. Thurston, A.M., C.E. Reprinted from Van Nostrand's Magazine. D. Van Nostrand, Publisher, New York.

Kennedy, A.B.W., 1876a, Book Review, "The Kinematics of Machinery; Outlines of a Theory of Machines", F. Reuleaux, translated by A.B.W. Kennedy, Engineering, Vol. 22, p. 197, London.

Kennedy, Alex. B.W., 1876b, "The Berlin Kinematic Models," Engineering, Vol. 22, p. 239-240, London.

Reuleaux, F., 1876, Kinematics of Machinery; Outlines of a Theory of Machines, A.B.W. Kennedy, Transl., MacMillan and Co., London.

Reuleaux, F., 1872, Der Constructeur : Ein Handbuch zum Begrauch beim Maschinen-Entwerfen (1872), Verlag von Friedrich Voeweg und Sohn, Braunschweig (in German).

Reuleaux, F., 1892, The Constructor; A Handbook of Machine Design H.H. Suplee, Transl. 1892, Philadelphia.

Ramelli, Agostino, 1588, Le Diverse et Artificiose Machine, Paris.

Scientific American, October 17, 1885, Vol. LIII, No. 16 [New Series]. The cover shows a montage of pictures of the Sibley College, Cornell University. The upper left corner shows cabinets with kinematic models and the footnote says this is the "Sibley College Museum of Mechanisms." The text (p. 249) refers to the Reuleaux collection of models in one museum display as well as to a museum of machines. Thus, if Reuleaux' shipment in 1882 arrived at Ithaca in the same year or 1883, then this article is consistent with the letter to A.D. White. The view in Figure 1 on the cover shows eight display cases which could well have contained over 200 models. The Sibley Journal of Engineering, June 1894, Vol. VIII, No. 9, published by the Students of Sibley College, Cornell University. The first article notes the progress in the College from 1885 to 1894. On page 382, the article notes that Mr. Hiram Sibley had given money for the Reuleaux collection. No other mention of the models is given.

Thurston, Robert H., Machinery and Manufacturers with an Account of European Manufacturing Districts, report on the Vienna Exhibition published by The U.S. Department of State.

Walker, F.A. editor, 1877, International Exhibition 1876, United States Centennial Commission, Reports and Awards, Groups XXI-XXVII, J.B. Lippincott & Co., Philadelphia. The list of awards shows the Thurston's testing machine was cited for an award (Item 269, page 172).

Walker, F.A. editor, 1878, International Exhibition 1876, United States Centennial Commissioner Reports and Awards, Group XXVIII, J.B. Lippincott & Co., Philadelphia, 1878. This volume shows that President A.D. White was a judge in the Group on Education and Science and that the German Commissioner, General Reuleaux, assisted in the judging (pages 203, page vi).



Annotated References on Reuleaux in German

(From Professor Reinhard Braune

of the University of Hannover, Germany)

1. "Franz Reuleaux," Hans-Joachim Braun in Berlinische Lebensbilder: Band 6 Techniker, Wilhelm Treue and Wolfgang König, Editors, Colloquium Verlag, Berlin, 1990, pp. 279-292.

[Berlin Life Portraits: Engineers, is a rough translation. This article mentions correspondence about kinematics with (Robert) Henry Thurston of Sibley College, Ithaca (p. 289). There is also mention of Reuleaux's participation in the Philadelphia World Exhibition in 1876 as "Reichskommissar" (pp. 288, 290).]

2. "Ingenieurwissenschaft und Gesellschaftspolitik: Das Wirken von Franz Reuleaux" [Engineering Science and Corporate Politics: The Work of Franz Reuleaux.] by Hans Joachim Braun and Wolfhard Weber in Technik und Gesellschaft, Vol. 1, 1979, p. 285-300. [Contains 42 references. This article discusses Reuleaux's activities in the politics of engineering from World Exhibitions, patent questions, comparison of German and American industry in his "Letters from Philadelphia," and the relationship between the machine age and social questions. There is no mention of his kinematic models here.]

3. "Franz Reuleaux und die Grandlagen seiner Kinematik," Carl Weihe, Deutsches Museum, Abhandlungen und Berichte, VDI-Verlag Gmbh, Berlin, 14 Jahrgang, Heft 4, 1942.

[C. Wiehe was Reuleaux's last student. There is no mention of the Cornell collection, but at the end there appears to be suggestion that the kinematics section of the Deutschen Museum had a subset of the Reuleaux collection reproduced from the Technical Institute of Berlin.]

4. "The Kinematic (Reuleaux) Collection," Die Technische Hochschule 8(6) (1929) p. 158.

Article on the 100th anniversary of the birth of Reuleaux (1829-1905).

The Reuleaux Collection contains over 800 models and is the largest mechanism collection in the world. It has been copied in larger or smaller parts for other Technical Institutes in North America and Russia.

5. Monatsblätter des Berliner Bezirksvereins Deutscher Ingenieure, Nr S, Mai 1913. (Monthly Newsletter of the Berlin District Society of German Engineers.)

Page 10: outtake of article on Reuleaux mentions 800 models in Reuleaux collection (largest in the world, but still incomplete). Mentions a smaller collection in the Deutschen Museum in Münich.

6. Chronik der Königlichen Technischen Hochschule zu Berlin, 1799-1899, Berlin 1899. Lists table of collections on p. 33. Kinematische (Reuleaux) Sammlung - Prof. W. Hartmann, director of collection.


The author acknowledges the help of the following:

Cora Jackson, for cataloging and typing

Professor Dietmar Rempfer, Cornell University, for German translation

Professor Emeritus, Richard Phelan, Mechanical and Aerospace Engineering

Professor Reinhard Braune, Institut für Getriebetechnik, University of Hannover, Germany

John Reis for photography