THE MACHINES OF LEONARDO DA VINCI AND FRANZ REULEAUX

HISTORY OF MECHANISM AND MACHINE SCIENCEVolume 2

Series Editor

G.M.L. CECCARELLI

Aims and Scope of the Series

This book series aims to establish a well defined forum for Monographs and Pro-ceedings on the History of Mechanism and Machine Science (MMS). The seriespublishes works that give an overview of the historical developments, from the earli-est times up to and including the recent past, of MMS in all its technical aspects.

This technical approach is an essential characteristic of the series. By discussingtechnical details and formulations and even reformulating those in terms of modernformalisms the possibility is created not only to track the historical technical devel-opments but also to use past experiences in technical teaching and research today. Inorder to do so, the emphasis must be on technical aspects rather than a purely histor-ical focus, although the latter has its place too.

Furthermore, the series will consider the republication of out-of-print older workswith English translation and comments.

The book series is intended to collect technical views on historical developments ofthe broad field of MMS in a unique frame that can be seen in its totality as an En-cyclopaedia of the History of MMS but with the additional purpose of archiving andteaching the History of MMS. Therefore the book series is intended not only for re-searchers of the History of Engineering but also for professionals and students whoare interested in obtaining a clear perspective of the past for their future technicalworks. The books will be written in general by engineers but not only for engineers.

Prospective authors and editors can contact the Series Editor, Professor M. Ceccarelli,about future publications within the series at:

LARM: Laboratory of Robotics and MechatronicsDiMSAT – University of CassinoVia Di Biasio 43, 03043 Cassino (Fr)ItalyE-mail: ceccarelli@unicas.it

For a list of related mechanics titles, see final pages.

The Machines of Leonardo da Vinciand Franz Reuleaux

Kinematics of Machines from the Renaissanceto the 20th Century

By

FRANCIS C. MOON

Mechanical and Aerospace Engineering,Cornell University,Ithaca, New York, USA

A C.I.P. Catalogue record for this book is available from the Library of Congress.

ISBN 978-1-4020-5598-0 (HB)ISBN 978-1-4020-5599-7 (e-book)

Published by Springer,P.O. Box 17, 3300 AA Dordrecht, The Netherlands.

www.springer.com

Cover figures: Self portrait of Leonardo da Vinci, Royal Library Turin; Leonardo’s ratchetdrawing from Codex Madrid, National Library Madrid; Portrait of Franz Reuleaux and ratchetmechanism drawing from Kinematics of Machinery, Franz Reuleaux (1876)

Every effort has been made to contact the copyright holders of the figures which have beenreproduced from other sources. Anyone who has not been properly credited is requested tocontact the publishers, so that due acknowledgements may be made in subsequent editions.

Printed on acid-free paper

All Rights Reserved© 2007 SpringerNo part of this work may be reproduced, stored in a retrieval system, or transmittedin any form or by any means, electronic, mechanical, photocopying, microfilming, recordingor otherwise, without written permission from the Publisher, with the exceptionof any material supplied specifically for the purpose of being enteredand executed on a computer system, for exclusive use by the purchaser of the work.

To Lee, my helpmate in this six-year project; she is the onlyone I know who can read Reuleaux’s handwriting.

Contents

PART I

I Leonardo da Vinci and Franz Reuleaux: Machine Engineers . . 3I.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3I.2 Modern Applications of Kinematics: Leonardo in Your

Toothbrush . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15I.3 Deconstructing the Machine: Constructive Elements of Design 27I.4 Leonardo, ‘Ingenieur Ordinaire’ . . . . . . . . . . . . . . . . . . . . . . . . . 37I.5 Franz Reuleaux: Engineer-Scientist . . . . . . . . . . . . . . . . . . . . . . 47I.6 Influence of Leonardo da Vinci on 19th C. Machine Theorists 59I.7 Kinematics of Machines: The Geometry of Motion . . . . . . . . . 66I.8 Visual and Topological Thinking: Reuleaux’s Language of

Invention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76I.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

Preface by the Series Editor, Professor M. Ceccarelli . . . . . . . . . . . . . xi

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii

Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiii

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxiii

viii Contents

PART II

II Evolution of Design of Machines . . . . . . . . . . . . . . . . . . . . . . . . . . . 99II.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99II.2 Visual Kinematic Perception of Mechanisms . . . . . . . . . . . . . . 102II.3 Ancient Greek and Roman Machines . . . . . . . . . . . . . . . . . . . . . 107II.4 Machines in the Bible . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116II.5 Roger Bacon on Marvelous Machines in the 13th Century . . . 118II.6 Machines of the Middle Ages . . . . . . . . . . . . . . . . . . . . . . . . . . . 121II.7 Scientific and Technical Milieu in the Renaissance Machine

Age . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125II.8 Francesco di Giorgio Martini: The Leonardo of Siena . . . . . . . 135II.9 Theatre of Machines Books: Imitation or Invention? . . . . . . . . 146II.10 Mathematics, Mechanics and Design of Machines . . . . . . . . . . 160II.11 Art and the Machine Engineer . . . . . . . . . . . . . . . . . . . . . . . . . . . 175II.12 Concepts of Design and Invention by Leonardo and Reuleaux 188II.13 Models as the New ‘Theatre of Machines’ . . . . . . . . . . . . . . . . . 199II.14 James Watt and the Steam Engine: Pathways of Machine

Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212II.15 Machine Engineers and Inventors in the 19th Century . . . . . . . 223II.16 Berlin and the Machine Age of the 19th Century . . . . . . . . . . . 228II.17 Lost Knowledge from the Age of Machines: Mathematical

Kinematics and Rotary Engines . . . . . . . . . . . . . . . . . . . . . . . . . 239II.18 Prime Mover Machines: Thermodynamics, Kinematics and

Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248II.19 Flying Machines of Leonardo and Lilienthal . . . . . . . . . . . . . . . 255II.20 Kinematics of Animal and Human Motion . . . . . . . . . . . . . . . . 262II.21 Leonardo in a Robot: Automata, Clocks and Controlled

Machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276II.22 Leonardo and Reuleaux: A Summary . . . . . . . . . . . . . . . . . . . . . 289

293

PART III

III Comparison of the Kinematic Mechanisms of Leonardo andReuleaux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303

Color Plates

The Machines of Leonardo Da Vinci and Franz Reuleaux ix

PART IV

IV References, Bibliography & Appendices . . . . . . . . . . . . . . . . . . . . . 351Cited References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351Books on the Life of Leonardo da Vinci and as Machine Engineer . 364Books on the History of Machines in the Industrial Age . . . . . . . . . . 365Books on the History of the Renaissance in Europe . . . . . . . . . . . . . 366Books and Articles on Franz Reuleaux and the Kinematic Theory

of Machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366Books and Articles on Kinematics of Human and Animal Motion . 368History of Machines-related Books for a Teaching, Design Studio

Library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369Appendix I: A Summary of ‘Theatre of Machines’ Books

15th–18th Centuries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372Appendix II: On-Line Books and Papers at Cornell University

Library on The History of Machines and Mechanisms . . . . . . . 391Appendix III: Student Exercises in the History of Machines . . . . . . 394

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401

Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407

About the Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417

Preface by the Series Editor,Professor M. Ceccarelli

This book is part of a book series on the History of Mechanism and MachineScience (HMMS).

This series is novel in its concept of treating historical developments witha technical approach to illustrate the evolution of matters of Mechanical Engi-neering that are related specifically to mechanism and machine science. Thus,books in the series will describe historical developments by mainly lookingat technical details with the aim to give interpretations and insights of pastachievements. The attention to technical details is used not only to track thepast by giving credit to past efforts and solutions but mainly to learn from thepast approaches and procedures that can still be of current interest and useboth for teaching and research.

The intended re-interpretation and re-formulation of past studies on ma-chines and mechanisms requires technical expertise more than a merely his-torical perspective, therefore, the books of the series can be characterized bythis emphasis on technical information, although historical development willnot be overlooked.

Furthermore, the series will offer the possibility of publishing translationsof works not originally written in English, and of reprinting works of histori-cal interest that have gone out of print but are currently of interest again.

I believe that the works published in this series will be of interest to a widerange of readers from professionals to students, and from historians to tech-nical researchers. They will all obtain both satisfaction from and motivationfor their work by becoming aware of the historical framework which formsthe background of their research.

xii Preface by the Series Editor

I would like to take this opportunity to thank the authors and editors ofthese volumes very much for their efforts and the time they have spent inorder to share their accumulated information and understanding of the use ofpast techniques in the history of mechanism and machine science.

Cassino, April 2007Marco Ceccarelli (Chair of the Scientific Editorial Board)

Preface

Ah the Machine; both coveted and criticized, life sustaining and life destroy-ing yet always a symbol of human creativity and invention from the Renais-sance to robotics from the Wright brothers to the Wankel engine. There aremore than a billion mechanical machines in our world of six billion humans.These machines are the source of both marvel and mayhem in the life of ourplanet. This book is about the evolution of these machines and the inven-tors and engineers who created them from the early Renaissance to the early20th century. I have chosen two personalities who are icons of these twomachine ages, Leonardo da Vinci [1452–1519] and Franz Reuleaux [1829–1905], recognizing both the cadre of machine designers who influenced themas well as those who were influenced by the accomplishments of these twoengineers. A major thesis of this book is that the evolution of machine designmethodology, from the intuitive methods of the workshop to the math-based,engineering science analysis and synthesis of modern industrial design, wasof equal achievement as the creation of the marvelous machines themselves.

In the past two decades there has been increasing interest in rational meth-ods of design from topology and optimization theories to genetic algorithms.In the teaching of design at the novitiate level, the importance of design cy-cles and iteration is emphasized. Yet often the historical background for evo-lution of machine design is minimal or missing. With this book we provide anoverview of design evolution from the Renaissance period to the early 20thcentury.

Why another book on machine evolution? Certainly there have been along series of works that have both surveyed and analyzed machine evolutionas well as Leonardo’s drawings of machines such as Abbott P. Usher (1954),

Preface

Eugene Furguson (1968), Bertram Gille (1966), Charles Gibbs-Smith (1978)and Ladislao Reti (1974) and more recently G. Bassala (1988). In the pe-riod, 1960–80, there appeared many encyclopedic works such as Singer et al(1961), Emberto Eco (1966) and Joseph Needham (1965) as well as trans-

(1455) and Ramelli (1588). This book cannot hope to compete with the schol-arly nature of those books. However this group of scholars has largely steppedoff the stage of the history of technology. The mainstream of the history oftechnology has shifted its focus from scientific and technical issues, to social,cultural, economic and gender questions about technology, especially dealingwith the post machine age era of the 20th century. However, new questionsabout the complexity of modern technology cannot be entirely separated fromthe early history of machines, given the premise of the evolution of technol-ogy.

And why another book on Leonardo da Vinci? Surely there have beenhundreds written on this paragon of the Italian Renaissance and dozens aboutLeonardo as inventor and scientist. However many of these works were writ-ten before the discovery of Leonardo’s Codex Madrid in 1965. This previ-ously lost work reveals Leonardo’s interest in a theory of machines and ma-chine design, not simply clever inventions. Also recent work on the contribu-tions of Francesco di Giorgio (1439–1501) and other Tuscan artist-engineershave put some of Leonardo’s oft-cited inventions in a wider context of con-temporary Renaissance technology. This new status for Leonardo may dimin-ish his role as an inventor but raises his image as a precursor of the mathe-matics and science-based engineer that Franz Reuleaux and his generationrealized in the polytechnique schools of the 19th century.

And why study Franz Reuleaux? Most casual readers will not recognizethe name. However in the works of most of the important historians of ma-chines, such a Beck, Usher, Burstal, Eco, Furguson and Reti, Reuleaux’sname is cited as one of the greatest machine theorists of the 19th century.As the reader will discover in the text to follow, Reuleaux was known as the‘father of kinematics of machines’. During the height of his fame, the Ger-man engineer, of Belgium decent, was recognized around the world. Afterhis death in 1905, his reputation faded, only to be rediscovered in the pastdecade in many mathematical and engineering works. He was one of the firstproponents of a theory of machine invention and posited a series of princi-ples of design that were a century ahead of his time. Mathematicians nowcite his early work on so-called ‘curves of constant width’ and some highschool geometry classes teach about the ‘Reuleaux triangle’.

lations and facsimiles of classic ‘theatre of machines’ books such as Taccola

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The Machines of Leonardo Da Vinci and Franz Reuleaux

In writing this book, I have taken a chance that there is a new generationof readers like myself who missed this earlier era of the history of machinesin the 1960s and still respond with awe and wonder at the inventiveness ofhumankind in creating machines. Another reason for writing this book is tocontinue a theme put forward by the Leonardian scholar Ladislao Reti whenhe translated the rediscovered Codex Madrid in 1965. Reti posited the the-sis that Leonardo had planned a book on basic machine elements of design.In Reti’s thesis he compared Leonardo’s machine drawings with the basicconstructive elements proposed by Franz Reuleaux in his famous theory ofmachines published between 1854 and 1876. The Cornell University Libraryhas recently added over 50 rare books on the theory of machines on the webincluding Leonardo’s Codex Madrid I and translations of Reuleaux’s two im-portant works. This book will, I hope, serve as a guide to some of these worksthat the reader can now access without visiting a major library.

Lastly I have undertaken this work to showcase one of Reuleaux’s majorcontributions, the creation of a mechanical alphabet of over 800 models ofmachine mechanisms in Berlin. This mechanical alphabet went beyond theearlier 18th century work of Christopher Polhem of Sweden and the early19th century attempt of Charles Babbage to create a language of invention.The bulk of Reuleaux’s Berlin collection of models did not survive WWII.However a large subset of this collection (over 230 models) was reproducedand acquired by Cornell University in 1882. I have attempted to comparesome of the 19th century kinematic Reuleaux models with the 15th cen-tury designs of mechanisms of Leonardo da Vinci as a way of comparingthe methodology of machine design in the 15th and 19th centuries.

My own path to writing this unorthodox book has been rather circuitous.I spent the greater part of my career in academic research and teaching in thefield of theoretical and applied mechanics and dynamics, especially nonlin-ear dynamics and chaos theory mostly ignoring the subjects of machines andmachine design. During the decades of the 1960s thru the 1980s, the CornellKinematic Collection was in benign neglect and almost no one knew whoReuleaux was. However during travels to Germany in the late 1980s undera Humboldt Foundation award, several European colleagues brought my at-tention to the importance of the Collection. When a Berlin Museum tried topurchase the Cornell Collection during my tenure as Director of the SibleySchool of Mechanical and Aerospace Engineering, my curiosity was piquedand I started on a decade-long road of research and study about Reuleaux,the history of machines and inevitably to the question of Leonardo da Vinci’splace in the history of machines.

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Preface

Through my research on Reuleaux and the history of machines, I was sur-prised to learn of the major role that Cornell’s Sibley College of MechanicalEngineering played in the development of mechanical engineering in the 19thcentury. Cornell Professor Robert Thurston, originally from Stevens Institute,was the first president of the American Society of Mechanical Engineers andthree other Sibley faculty were presidents. Thurston met Reuleaux in 1873 inBerlin and Reuleaux translated one of Thurston’s books into German. Dur-ing this period Cornell not only acquired copies of a substantial part of theReuleaux model collection in Berlin, but also built an important library ofthe most significant European books on the theory of machines, a collectionI was fortunate to use for this book.

This book is also a supplement to a Cornell project to place theReuleaux Collection in a virtual museum on the web as part of the UnitedStates National Science Digital Library or NSDL. We have also digitizedmany of the famous books in the Cornell History of Science Library onthe history of machines from the 15th to the 19th century. This web-site called KMODDL, for Kinematic Models for Design Digital Library(http://kmoddl.library.cornell.edu), has had several hundred thousand visitorsin its short life thus far, and the reader of this book can find pictures andmovies of many of the machines and mechanisms on this website.

xvi

Acknowledgements

In writing this book I have been fortunate to have access to three majorresources; the Cornell Collection of Kinematic Models, the Archive of theDeutsches Museum in Munich and the Cornell University Library, Rare andManuscript Collection.

As faculty curator for the Cornell Collection of Kinematic Models, I havehad daily access to the 230 Reuleaux kinematic models made by Gustav Voigtof Berlin in 1882. This project began over a decade ago during a 1995 sab-batical leave visit to Germany, where colleagues told me of the importanceand fame of Franz Reuleaux and his kinematic model collection. In 2001 and2002 I returned to Germany to study the Reuleaux papers in Munich as wellas visit the Technical University of Berlin where he was professor and rector.

I am grateful to the Humboldt Stiftung of Germany for financial supportto visit and study the Reuleaux archives and collections of the Deutsches Mu-seum in Munich. This visit would not have been possible without the supportfrom my friend and colleague Professor Franz Kollmann formerly with TheTechnical University of Darmstadt. Of particular help at the Deutsches Mu-seum were Dr. Wilhelm Füssl, head of the Archiv, Karl Allwang, Curatorfor Mechanical Engineering, Manfred Spachtholz, Museum engineer and Mr.Sebastian Remberger.

Thanks are also due for support from the Cornell University Library staff,especially John Saylor, Director of the Engineering Library. Help is also ac-knowledged from Dr. David Corson, Head of the Rare and Manuscripts Col-lection and Dr. Elaine Engst, University Archivist. The Dibner Library at theSmithsonian Institution in Washington was a valuable resource as well as the

Acknowledgements

Library of Congress and the library of the American Philosophical Society inPhiladelphia of which Franz Reuleaux was a member.

In Germany I also had help from Professor Reinhard Braune of the Insti-tut für Getriebetechnik and the late Professor Karl Popp of the University ofHannover, Professor Friedrich Pfeiffer of the Technical University Munich,Professor Modler, and Professor Klaus Mauersberger, Technical Universityof Dresden. Thanks are also due to Professor Jörg Wauer of the UniversitätKarlsruhe for access to and for cataloging the Redtenbacher model collec-tion, Professor D. Severin, of the Technical University of Berlin, ProfessorDittrich and Profesor Burkhard Corves for access to the kinematic modelcollection in the Rhein.-Westf. Technische Hochschule Aachen. I fondly re-member my meeting in Berlin of the great grandson of Franz Reuleaux, Dr.Henning Reuleaux, who related some family stories about him.

In Italy I had help in retracing the paths of Leonardo da Vinci in Milan byRoberto Bragastini, a retired engineer and historian who arranged a visit tothe Biblioteca Ambrosiana and to the Leonardo machine models at the MuseoScienza in Milan. In Florence thanks are due to Dr. Paolo Brenni, FondazioneScienza e Tecnica/Istituto e Museo, Firenze.

A resurgence of interest in the history of machines has been sparked bythe History of Machines and Mechanisms Commission, of the InternationalFederation for the Theory of Machines and Mechanisms (IFToMM), headedby Professor Marco Ceccarelli, University of Cassino, Italy who kindly in-vited me to several important workshops of IFToMM in Cassino, Dresdenand Moscow. My thanks are also offered to Professor H-S. Yan of NationalChen Kung University, Taiwan, the current head of the HMM Commission.

In England I would like to thank Dr. Hugh Hunt, Engineering Department,Cambridge University for help in viewing the Robert Willis sketch book andthe Cambridge kinematic model collection. At the Science Museum LondonI was able to visit the storage and archives through help from curators Mr.Michael Wright and Ben Russel. They also gave me access to original photosof the 1876 Kensington Scientific Instrument Exhibition at which were 300models of Reuleaux. Special thanks also go to Gerald H.F. Seiflow (retiredengineer and Reuleaux relative) of Leicester England for information on theReuleaux family tree.

I was also privileged to have been given access to machine model collec-tions at the Technical University of Dresden, The University of Porto, Por-tugal, the Hauch Physike Cabinet in Sorø Denmark, the Rothschild PatentModel Museum in Cazenovia New York, and the Bauman Moscow StateTechnical University Kinematic Collection.

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The Machines of Leonardo Da Vinci and Franz Reuleaux

I also want to acknowledge help from the late Professor Werner Goldsmithof the University of California Berkeley, Dr. S. Shiroshita, Kyoto Univer-sity Museum, Jørgen F. Andersen of Sorø Academy, Denmark, ProfessorHanfreid Kerle, Braunschweig and Professor Paulo M.S. Tavares de Castro,Universidade do Porto and Professor Alexandre Golovin and Dr. ValentinTarabarin, Moscow. For help with the ASME historic designation for theCornell Reuleaux Collection, I thank Professor Robert Friedel, University ofMaryland, Diane Kaylor, ASME Heritage Committee, and Aaron J. Boltmanof the ASME Southern Tier Section.

This book was also inspired by a Cornell project to place the ReuleauxCollection in a virtual museum on the web called KMODDL or Kine-matic Models for Design Digital Library (http//:kmoddl.library.cornell.edu).KMODDL is a part of the United States National Science Digital Library(www.nsdl.edu). I have enjoyed the fruitful interaction with the KMODDLteam; Dr. Daina Taimina and Professor David Henderson of the MathematicsDepartment, Professor Hod Lipson of Mechanical and Aerospace Engineer-ing, John Saylor Principal Investigator of the KMODDL project and Engi-neering Librarian, and Dr. Kizer Walker, Digital Projects, University Library.The help of KMODDL webmaster Matt Arnstein is also acknowledged, aswell as graduate students David Caruso and Javier Lezaun of the Science andTechnology Studies Department. Special thanks are due to Professors Emer-iti Richard Phelan and Jack Booker who were the early custodians of theReuleaux Collection at Cornell.

Thanks also to those who gave me helpful feedback from an early editionof this book, especially Professor David Ollis, North Carolina State Univer-sity, Professor Emeriti Franz Kollman, Darmstadt Technische Hochschule,Dr. Klaus Mauersberger, Technischen Universität Dresden, Professor TeunKoetsier, Vrije Universiteit Amsterdam and Professor Marco Ceccarelli, Uni-versity of Cassino, Italy.

The author wishes to thank his editor at Springer, Nathalie Jacobs, andJolanda Karada (Karada Publishing Services) for their support and attentionto details in the production of this book.

Finally special thanks are due my wife Elizabeth E. Moon for transcrip-tions of the Reuleaux letter copy books in the Archiv of the Deutsches Mu-seum, for copy editing many of the references in the book and for continuousencouragement and patience for my obsession with this project.

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Acknowledgements

Photo credits

All photos in this book are by the author unless noted otherwise. Images from‘theatre of machines’ books courtesy Cornell University Library. Details ofmachines and mechanisms of Leonardo da Vinci from Codex Atlanticus or IlCodice Atlantico della Biblioteca Ambrosiana di Milano/Leonardo da Vinci,facsimile edition: published by Regis Accademia dei Lincei, 1894–1904. De-tails of machines and mechanisms from Codex Madrid or Tratado de Estaticay Mechanica en Italiano, 1493, facsimile edition: The Madrid Codices, Na-tional Library Madrid, No. 8937, McGraw-Hill Book Company, NY, 1974.Figure II.1 Greek Antikythera Mechanism (de Solla Price, 1959), courtesyScientific American, Figure II.43 Knee joint mechanism (Menschik, 1987),courtesy Springer Verlag, Berlin. Figure II.44, Chinese walking horse, cour-tesy Prof. H-S. Yan, Tainan University, Taiwan, Figure II.45, Passive walkingmachine, courtesy Prof. Andy Ruina, Cornell University.

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Notes

Note to the Reader

There are four parts to this book each of which may be of interest to dif-ferent readers. The author has written this book in the hope that it will findinterest in the engineering community, the history of technology communityas well as the lay reader. The first two parts are narrative and are written fornon-technical as well as technical readers. Part III is a catalog of machine el-ements and mechanisms of Leonardo and Reuleaux that may find interest inteaching engineering design. Part IV contains over 300 references as well asa comprehensive annotated list of the so-called ‘Theatre of Machines’ books.Part IV also contains a list of project and problems for students and classroomuse.

The author recognizes that each type of reader is used to a different styleof reference, be it footnotes, endnotes or a list of references at the end ofthe book. Coming from the academic engineering tradition, the author hasadopted the ‘Author (date)’ format for references with an alphabetical list atthe end of the book. Historical dates such as [birth–death] are listed in squarebrackets.

References to the work of Leonardo da Vinci follows traditional format ofciting the codex and the folio number:

Codex Atlanticus = CA; Folio number recto or versoCodex Madrid = CM; Folio number recto or versoInstitute of France Manuscripts = Ms A etc.

In the reference to early manuscripts, the letter ‘r’ is for recto and ‘v’ is forverso. There are several different facsimiles of Leonardo’s codices. The folionumber follows the more recent pagination. In the case of the Codex Atlanti-

Notes

cus the folios were renumbered in the last decades of the 20th century, I haveused the new folio numbers first with the old numbers cited second.

Note to the Teacher and Student

The author hopes that this book will be useful in the teaching of several disci-plines related to the history and design of machines. For this purpose a selec-tion of problems and projects are included in Part IV of this book. Some ofthese exercises have been used in a sophomore design synthesis course in me-chanical engineering at Cornell University. The Reuleaux models have alsobeen used in an introductory architectural drawing course as well as coursesin Computer Aided Design (CAD).

The material in this book can also be used for projects in the history ofscience and technology such as the comparative study of engineer-inventors,machine technology and sociological aspects of technology (see Part IV,Appendix II).

xxii

List of Figures

I.1 Portrait of Leonardo da Vinci [1452–1519] . . . . . . . . . . . . . . . . 5I.2 Portrait of Franz Reuleaux [1829–1905] . . . . . . . . . . . . . . . . . . 6I.3 Reuleaux’s six classes of kinematic mechanisms from

Kinematics of Machinery (1876) . . . . . . . . . . . . . . . . . . . . . . . . . 8I.4a Comparison of kinematic elements in machine design from

the books of Franz Reuleaux (on the left) and drawings ofLeonardo da Vinci from the Codex Madrid I (on the right).See also Table I.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

I.4b Comparison of kinematic elements in machine design fromthe books of Franz Reuleaux (on the left) and drawings ofLeonardo da Vinci from the Codex Madrid I (on the right).See also Table I.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

I.5 Selection of 350 kinematic models from Voigt Catalog ofReuleaux Models (c. 1900) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

I.6 The Angel of Machines: from Buch der ErfindungenGewerbe und Industrien, or Book of Inventions, Vol. 6,1887, F. Reuleaux, Editor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

I.7 Landing gear linkage for an Airbus jet. (Science Museum,London) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

I.8 Micro-electromechanical System [MEMS] gear train;Courtesy: Sandia National Laboratory . . . . . . . . . . . . . . . . . . . . 17

I.9 Modern robotic manipulator arm with end effector gripper . . . 20I.10a Sketch of the mechanisms in a modern electronic toothbrush:

Braun Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22I.10b Sketch of the mechanism in a motorized toothbrush: Colgate

Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23I.11a Four-link mechanism of Leonardo da Vinci (Codex Madrid I) 24

List of Figures

I.11b Slider-crank mechanism (Codex Madrid I) . . . . . . . . . . . . . . . . 24I.11c Gear and pinion (Codex Madrid I) . . . . . . . . . . . . . . . . . . . . . . . 24I.12 Top: toothbrush with crown wheel gear and pinion and

slider-crank mechanism. Middle: Crown wheel gear andlantern pinion of Leonardo da Vinci from the Codex MadridI. Bottom: Double slider-crank mechanism and worm geardrive of Leonardo da Vinci from the Codex Madrid I . . . . . . . . 25

I.13 First automobile of Carl Benz and the list of basic machineelements and mechanisms (c. 1885) (Courtesy of theDeutsches Museum, Munich) . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

I.14 Left: kinematic pairs; Right: (a) slider crank and (b) four-barkinematic chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

I.15 Sketch of kinematic elements in Leonardo’s textile spinningmachine (based on Codex Atlanticus, Folio 1090v) . . . . . . . . . . 35

I.16 Leonardo da Vinci: Exploded view of a ratchet winch (CodexAtlanticus, Folio 30v/8v.b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

I.17 Influence network of Leonardo da Vinci . . . . . . . . . . . . . . . . . . . 45I.18 Influence network of Franz Reuleaux in the 19th century

related to the kinematics theory of machines . . . . . . . . . . . . . . . 55I.19 Compilation of machine elements of Leonardo da Vinci by

Theodor Beck (1899) after Grothe (1874) . . . . . . . . . . . . . . . . . 64I.20 Table of kinematic motions from Lanz and Betancourt

(1809) after Hachette, Ecole Polytechnique . . . . . . . . . . . . . . . . 67I.21 Sketch of anti-friction ball bearing of Leonardo da Vinci

(Codex Madrid I, Folio 20v) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67I.22 Sketch of planetary gear mechanism of Leonardo da Vinci

(Codex Madrid I, Folio 13v) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68I.23 Sketch of helical screw mechanism, Leonardo da Vinci

(Codex Madrid I, Folio 57v) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69I.24 Kinematic chain for a four-bar mechanism (Reuleaux, 1876a) 72I.25 Centrodes or rolling curves for a four-bar mechanism

(Willson, 1898) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73I.26 Path points of motion of a Reuleaux triangle in a square

bearing (Reuleaux, 1876a, plate VIII, figure 1) . . . . . . . . . . . . . 73I.27a Inversions of the slider-crank mechanism (Reuleaux, 1876a) . 82I.27b Expansion of elements of the slider-crank mechanism (right)

into an eccentric mechanism (left). (Models from the CornellKinematic Mechanisms Collection: See models C-2, E-2, onthe KMODDL website) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

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The Machines of Leonardo Da Vinci and Franz Reuleaux

I.28 Sample symbol table for mechanisms from Reuleaux’sKinematics of Machinery (1876), for slider linkages androtary pump-engine mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . 86

I.29 Kinematic circuits and symbols based on Reuleaux,published by Francesco Masi (1883) . . . . . . . . . . . . . . . . . . . . . . 87

I.30 Six-bar compound mechanism with one degree of freedom90

I.31 Reuleaux straight-line mechanism with six links and seven

Kinematics Model Collection) . . . . . . . . . . . . . . . . . . . . . . . . . . 91I.32 Table of eight-bar linkages with one degree of freedom when

one bar is grounded (Grübler, 1917) . . . . . . . . . . . . . . . . . . . . . . 92I.33 Peaucellier exact straight-line mechanism with eight links

and ten revolute joints: one degree of freedom with one linkgrounded. (Reuleaux–Voigt Model S-35, Cornell KinematicMechanisms Collection; See also KMODDL website) . . . . . . . 93

I.34 Sketch of Leonardo’s ‘lazy tongs’ or ‘Nürnberg shears’mechanism of Leonardo da Vinci; six links and sevenrevolute joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

II.1 Partial reconstruction of Greek Antikythera Mechanismby D. de Solla Price. This multiple gear device is believedto have been used to calculate the motions of the planets.(Scientific American, 1959, with permission) . . . . . . . . . . . . . . 101

II.2 Moving point lights experiment in kinematic perception ofwalking humans. (Johansson, 1973, 1975) . . . . . . . . . . . . . . . . . 103

II.3 Six simple machines of antiquity . . . . . . . . . . . . . . . . . . . . . . . . . 108II.4 Wheeled chariot, Neo-Assyrian, 800 BC (Pergamon

Museum, Berlin) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109II.5 Lumber-cutting machine drawing by Francesco di Giorgio di

Martini (15th C.) after Villard de Honnecourt (c. 1225) . . . . . . 119II.6

University Library) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130II.7 Machine drawing hoist of Taccola (Mariano di Iacopo) . . . . . . 132II.8 Portrait of Madonna by Francesco di Georgio Martini

[1439–1501] in the Siena Pinacoteca Nazionale . . . . . . . . . . . . 136II.9 Drawing of water pumps with valves by Francesco di

Giorgio Martini (c. 1460) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

joints. (F = +1) Model S-32 in the Voigt catalog. (Cornell

(Reuleaux, 1876a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Leonardo’s drawing one of the Platonic solids for Fra LucaPacioli’s De Divina Proportione (1505). (Courtesy Cornell

xxv

List of Figures

II.10 Drawing of four-wheeled carts with steering mechanism byFrancesco di Giorgio Martini . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

II.11a Design for a log-cutting machine by Besson (1578) . . . . . . . . . 152II.11b Design for a log-cutting machine by Ramelli (1588) . . . . . . . . 152II.12a Log-cutting machine drawing of G.A. Böckler (1662) . . . . . . . 154II.12a Double-piston pump drawing of Vittorio Zonca [1568–1602] . 154II.13 Machine elements drawings (ratchets) of Jacob Leupold (1724)155II.14a Mechanism classification table from Borgnis (1818) . . . . . . . . 157II.14b Drawings of mechanisms from catalog of Henry Brown (1868) 158II.15 Leonardo’s quadrature of the cube using 6 tetrahedra. (Codex

Madrid II: Folio 70r) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163II.16 Path points of moving links; drawing of Leonardo da Vinci

(Codex Madrid I, Folio 63v) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166II.17 Architectural elements in steam engine design (Smithsonian

Institution, Washington DC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176II.18 Reuleaux’s designs for bearings pedestals in machines

(Courtesy Deutsches Museum Archive) . . . . . . . . . . . . . . . . . . . 177II.19 Kinetic sculpture with gears by contemporary artist Arthur

Ganson (MIT Museum) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179II.20 Engraving by Albrecht Dürer; ‘Triumphzug Kaiser

Maximilians’ (1515) (Scherer, 1907) . . . . . . . . . . . . . . . . . . . . . 182II.21 Engraving by Albrecht Dürer: ‘Triumphzug Kaiser

(Scherer, 1907). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184II.22a Print of Peter Bruegel [c. 1520–1569] of two post windmills.

(In Estampes de Peter Bruegel l’ancien, by R. van Bastelaer,1908) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

II.22b One of many studies for ‘The Drawbridge’ by Vincent vanGogh (c. 1888) with four-bar mechanisms. (In Vincent vanGogh; A Biographical Study, by J. Meier-Graefe, 1922,plate xxvii) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

II.23 Comparison of ‘globoid’ gear designs of Leonardo da Vinci(top) and Franz Reuleaux (bottom) . . . . . . . . . . . . . . . . . . . . . . . 192

II.24 A sampler of gear designs by Leonardo da Vinci (CodexMadrid I) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

II.25 Top: Leonardo da Vinci drawing of a wing in the ParisManuscripts; Ms. B Folio 88 verso. Bottom: Model of awing by Leonardo in the Museo Nazionale delle Scienza edella Tecnica Leonardo da Vinci, Milano . . . . . . . . . . . . . . . . . . 202

Maximillians’ (1515), showing two endless screw mechanisms

xxvi

The Machines of Leonardo Da Vinci and Franz Reuleaux

II.26 Rapid prototype models of historic machines (Lipson etal., 2005). Top: Worm gear and slider-crank mechanismof Leonardo da Vinci (Codex Madrid); Bottom: Rapidprototype ‘printed’ model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210

II.27 Sketch of steam engine components of James Watt, 1784 . . . . 214II.28 Reuleaux–Voigt model of a Watt straight-line mechanism

(Cornell University Collection of Kinematic Models) . . . . . . . 221II.29a Robert Willis p1800–1875] Professor, Cambridge University.

Forerunner of rational machine design. (Photo, RoyalSociety of London) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

II.29b Drawing of Willis of mechanism for Babbage’s DifferenceMachine calculator. (Courtesy, Cambridge Univ. EngineeringLibrary) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

II.30 Professor Ferdinand Redtenbacher [1809–1863], Teacher ofFranz Reuleaux, Eugen Langen and Karl Benz; KarlsruhePolytechnic School, Germany . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

II.31 The Technische Hochschule Charlottenburg, Berlin c. 1900 . . 230II.32 Top: Reuleaux Triangle model (Cornell Collection of

Kinematic Mechanisms); Bottom: Lunate drawing ofLeonardo da Vinci, with a curved triangle figure in the center(Paris Manuscript A, Folio 15v) . . . . . . . . . . . . . . . . . . . . . . . . . 240

II.33 Drawing of Thomas Arithmometer by Franz Reuleaux (1862) 242II.34 Reuleaux–Voigt Model S-35 of a Peaucellier straight-line

mechanism (Cornell Collection of Kinematic Mechanisms) . . 243II.35 Reuleaux rotary engine models (Cornell Collection of

Kinematic Mechanisms) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245II.36a Wankel engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246II.36b Wankel’s classification chart for rotary engines . . . . . . . . . . . . . 246II.37 Oliver’s Evans steam engine of 1803 (Thurston, 1878) . . . . . . 249II.38 Leonardo da Vinci sketch for an experiment to measure the

expansion of steam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250II.39 Ornithopter design of Leonardo da Vinci, Paris Manuscripts . 256II.40 Otto Lilienthal aircraft design sketch circa 1889 (Archives of

the Deutsches Museum, Munich) . . . . . . . . . . . . . . . . . . . . . . . . 260II.41 Left: Drawing of an arm by Leonardo da Vinci; Right:

Drawing of an arm by Reuleaux (1900) . . . . . . . . . . . . . . . . . . . 265II.42 Man in the machine; sketch from Borgnis (1818) . . . . . . . . . . . 269II.43 Four-bar mechanism replacement for a knee joint (Menschik,

1987) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272

xxvii

List of Figures

II.44 Chinese ‘walking horse’ design of H.-S. Yan (2005), TainanUniversity, Taiwan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

II.45 Passive walking machine, Professor Andy Ruina, CornellUniversity (see Collins et al., 2005) . . . . . . . . . . . . . . . . . . . . . . 274

II.46 Automaton cart and possible automaton pulley system ofLeonardo da Vinci (Codex Atlanticus; upper Folio 812r/folio296v.a; lower Folio 579r/folio 216v.b) . . . . . . . . . . . . . . . . . . . . 277

II.47 Modern Japanese Tea-serving Doll automaton (courtesy ofS. Shiroshita, Museum of Kyoto University) . . . . . . . . . . . . . . . 280

II.48 Clock and bell-ringing mechanism models of Reuleaux(Cornell Collection of Kinematic Mechanisms) . . . . . . . . . . . . 284

II.49 Chart of Influence of Renaissance Engineers after Reti (1963) 292

COLOR PLATES1 Close-up of positive displacement pump of Dart. Reuleaux–

Voigt Model I-7, Cornell University Collection of KinematicModels, nickel-plated brass and cast iron, Berlin, circa 1882(Photo, F.C. Moon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295

2 Clemen’s universal joint coupling. Reuleaux–Voigt ModelP-3, Cornell University Collection of Kinematic Models,nickel-plated brass and cast iron, Berlin, circa 1882 (Photo,F.C. Moon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295

3 Geneva-wheel intermittent mechanism for watches.Reuleaux–Voigt Model N-8, Cornell University Collectionof Kinematic Models, nickel-plated brass and cast iron,Berlin, circa 1882 (Photo, F.C. Moon) . . . . . . . . . . . . . . . . . . . . 296

4 Close-up of ratchet-wheel coupling. Reuleaux–Voigt ModelN-7, Cornell University Collection of Kinematic Models,nickel-plated brass and cast iron, Berlin, circa 1882 (Photo,F.C. Moon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296

5 Close-up of planetary gear train. Reuleaux–Voigt ModelG-3, Cornell University Collection of Kinematic Models,nickel-plated brass and cast iron, Berlin, circa 1882 (Photo,F.C. Moon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297

6 Positive-return cam with Reuleaux triangle. Reuleaux–VoigtModel L-6, Cornell University Collection of KinematicModels, nickel-plated brass and cast iron, Berlin, circa 1882(Photo, F.C. Moon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297

xxviii

The Machines of Leonardo Da Vinci and Franz Reuleaux

7 Spiral positive-displacement pump. Reuleaux–Voigt ModelI-4, Cornell University Collection of Kinematic Models,nickel-plated brass and cast iron, Berlin, circa 1882 (Photo,F.C. Moon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298

8 Worm gear and rack. Illinois Gear Corp. Model, CornellUniversity Collection of Kinematic Models, brass and castiron, Chicago, circa 1950 (Photo, F.C. Moon) . . . . . . . . . . . . . . 298

9 Close-up of cylinder escapement for a clock. Reuleaux–VoigtModel X-3, Cornell University Collection of KinematicModels, nickel-plated brass and cast iron, Berlin, circa 1882(Photo, F.C. Moon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299

10 Close-up of gear teeth for rack and pinion mechanism.Reuleaux–Voigt Model Q-1, Cornell University Collectionof Kinematic Models, nickel-plated brass and cast iron,Berlin, circa 1882 (Photo, F.C. Moon) . . . . . . . . . . . . . . . . . . . . 299

11 Planetary gear and four-bar linkage. Reuleaux–Voigt ModelO-1, Cornell University Collection of Kinematic Models,nickel-plated brass and cast iron, Berlin, circa 1882 (Photo,F.C. Moon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300

12 High and low pressure valve mechanism for a steam engine.Schröder Model, Cornell University Collection of KinematicModels, brass and cast iron, Darmstadt, Germany, circa1870–1880 (Photo, F.C. Moon) . . . . . . . . . . . . . . . . . . . . . . . . . . 300

III.1a Four-bar linkage: Codex Madrid I, Folio 1r . . . . . . . . . . . . . . . . 309III.1b Four-bar linkage: Reuleaux–Voigt Catalog, Model C-1

(Cornell Collection of Kinematic Mechanisms) . . . . . . . . . . . . 309III.2a Slider crank mechanism and worm drive: Codex Madrid I,

Folio 28v (see also Folio 30r or 2r) . . . . . . . . . . . . . . . . . . . . . . . 311III.2b Slider-crank mechanism: Reuleaux–Voigt Model, C-2

(Cornell Collection of Kinematic Mechanisms) . . . . . . . . . . . . 311III.3a Lazy tongs or Nürnberg shears: Codex Madrid I, Folio 24v . . . 313III.3b Lazy tongs – parallel mechanism: Reuleaux–Voigt Catalog,

Model T-2 (Cornell Collection of Kinematic Mechanisms) . . . 313III.4a Gimbals mechanism: Codex Madrid I, Folio 13v . . . . . . . . . . . 315III.4b Universal joint: Reuleaux–Voigt Catalog, Model P-1

(Cornell Collection of Kinematic Mechanisms) . . . . . . . . . . . . 315III.5a Belt and pulley mechanism: Codex Madrid I, Folio 23r . . . . . . 317III.5b Belt and pulley mechanism: Reuleaux Deutsches Museum

Model, DM 06/6275 (c. 1880) . . . . . . . . . . . . . . . . . . . . . . . . . . . 317

xxix

List of Figures

III.6a Endless screw or worm drive: Codex Madrid I, Folio 17v . . . . 319III.6b Endless screw or worm drive: Reuleaux–Voigt Catalog,

Model C-9 (Cornell Collection of Kinematic Mechanisms) . . . 319III.7a Screw jack: Codex Madrid I, Folio 26r . . . . . . . . . . . . . . . . . . . . 321III.7b

(Cornell Collection of Kinematic Mechanisms) . . . . . . . . . . . . 321III.8a Double helix reversing mechanism: Codex Madrid I, Folio 15r 323III.8b Double helix reversing mechanism: Reuleaux–Voigt Catalog,

Model M-6 (Cornell Collection of Kinematic Mechanisms) . . 323III.9a Pin-teeth rotary reversing mechanism: Codex Madrid I, Folio

17r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325III.9b Pin-teeth reversing mechanism: Reuleaux Model; Deutsches

Museum DM 06/62/78 (c. 1880) . . . . . . . . . . . . . . . . . . . . . . . . . 325III.10a Two intermittent mechanisms: Codex Madrid I, Folio 7r . . . . . 327III.10b Intermittent mechanism – Geneva Wheel: Reuleaux–Voigt

Catalog, Model N-8 (Cornell Collection of KinematicMechanisms) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

III.11a Ratchet and pawl mechanism: Codex Madrid I, Folio 117r . . . 329III.11b Ratchet and Pawl Mechanism: Reuleaux–Voigt Catalog,

Model N-17 (Cornell Collection of Kinematic Mechanisms) . . 329III.12a Verge clock escapement: Codex Madrid I, Folio 115v . . . . . . . 331III.12b Verge and balance wheel escapement: Reuleaux–Voigt

Catalog, Model X-1 (Cornell Collection of KinematicMechanisms) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331

III.13a Pinion and spur gear teeth: Codex Madrid I, Folio 5r . . . . . . . . 333III.13b Involute spur gear teeth: Reuleaux–Voigt Catalog, Model

Q-2 (Cornell Collection of Kinematic Mechanisms) . . . . . . . . . 333III.14a Single-sided rack and pinion: Codex Madrid I, Folio 35v . . . . 335III.14b Rack and pinion gear teeth: Reuleaux–Voigt Catalog, Model

Q-1 (Cornell Collection of Kinematic Models) . . . . . . . . . . . . . 335III.15a Planetary-epicyclic gear train: Codex Madrid I, Folio 13v . . . . 337III.15b Planetary-epicyclic gear train: Reuleaux–Voigt Catalog,

Model G-2 (Cornell Collection of Kinematic Mechanisms) . . . 337III.16a Bevel gears: Codex Madrid I, Folio 96r . . . . . . . . . . . . . . . . . . . 339III.16b Conical friction wheels: Reuleaux Model, Deutsches

Museum (c. 1880) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339III.17a Friction wheels: Codex Madrid I, Folio 113v . . . . . . . . . . . . . . 341

Screw pair: Reuleaux–Voigt Catalog, Model A-1

xxx

The Machines of Leonardo Da Vinci and Franz Reuleaux

III.17b Variable-ratio, friction wheel clutch: Reuleaux–VoigtCatalog, Model Y-10 (Cornell Collection of KinematicMechanisms) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341

III.18a Cam actuated lever: Codex Madrid I, Folio 6v . . . . . . . . . . . . . 343III.18b Positive-return cam with Reuleaux triangle: Reuleaux–Voigt

Catalog, Model L-2 (Cornell Collection of KinematicMechanisms) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343

III.19a Water wheel: Codex Madrid I, Folio 142r . . . . . . . . . . . . . . . . . 345III.19b Behrens–Dart pump and steam engine of 1867: Reuleaux–

Voigt Catalog, Model I-7 (Cornell Collection of KinematicMechanisms) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345

III.20a Flywheel designs: Codex Madrid I, Folio 114r . . . . . . . . . . . . . 347III.20b Flywheel or balance wheel: Reuleaux–Voigt Catalog, Model

N-27 (Cornell Collection of Kinematic Mechanisms) . . . . . . . . 347

IV.1 Theatre of Machines: Roberto Valturio (1472); Trebuchetsiege machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377

IV.2wheel driven bellows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379

IV.3shears and pendulum driven pump . . . . . . . . . . . . . . . . . . . . . . . 381

IV.4 Theatre of Machines: Jacobus de Strada (1617); Cover withimages of Archimedes and Vitruvius . . . . . . . . . . . . . . . . . . . . . 383

IV.5 Theatre of Machines: Vittorio Zonca (1607); Endless screwand winch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384

IV.6 Theatre of Machines: Georg Böckler (1661); Perpetualmotion machine design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386

IV.7 Theatre of Machines: Phillipe De le Hire (1695); Three-toothescapement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387

IV.8 Theatre of Machines: Jacob Leupold (1724); Windmill . . . . . . 388

Theatre of Machines: Jacques Besson (1578); Nürnberg

Theatre of Machines: Vannuccio Biringuccio (1540); Water

xxxi

List of Tables

I.1 Modern applications of kinematic mechanisms . . . . . . . . . . . . . 19I.1 20I.2 Classification of Leonardo’s machines by application . . . . . . . 34I.3 Reti’s comparison of Leonardo’s and Reuleaux’s basic

machine elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43I.4 Selection of machines cited in Franz Reuleaux’s The

51

II.1 Machine artifacts in Aristotle’s mechanical problems . . . . . . . . 109II.2 Comparison of Francesco di Giorgio’s and Reuleaux’s basic

machine elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139II.3 Comparison of Francesco di Giorgio’s and Reuleaux’s basic

kinematic chain mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140II.4 Theatre of machine books . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147II.5 Model collections of kinematic mechanisms . . . . . . . . . . . . . . . 204

III.1 Catalog of Reuleaux kinematic models, Gustav VoigtWerkstatt, Berlin (1907) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305

III.2 Comparison of Kinematic Mechanisms in Leonardo’s CodexMadrid with Reuleaux’s Kinematic Models (KMODDL) . . . . 306

III.3 Comparison of Machine Elements in Leonardo’s CodexMadrid I and in Reuleaux’s The Constructor, 4th edition(1893) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307

(Continued ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Constructor; 4th Edn (1893) . . . . . . . . . . . . . . . . . . . . . . . . . . . .