Proceedings of EUCOMES 08

Marco CeccarelliEditor

Proceedingsof EUCOMES 08

The Second European Conferenceon Mechanism Science

123

EditorProf. Marco CeccarelliLARM: Laboratory of Robotics and MechatronicsDiMSAT at University of CassinoVia Di Biasio 43, 03043 Cassino (Fr)Italyceccarelli@unicas.it

ISBN: 978-1-4020-8914-5 e-ISBN: 978-1-4020-8915-2

DOI 10.1007/978-1-4020-8915-2

Library of Congress Control Number: 2008934049

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Preface

The EUCOMES08, Second European Conference on Mechanism Science is thesecond event of a series that has been started in 2006 as a conference activity foran European community working in Mechanism Science. The first event was heldin Obergurgl, Austria in 2006. This year EUCOMES08 Conference has come toCassino in Italy taking place from 17 to 20 September 2008.

The aim of the EUCOMES Conference is to bring together European researchers,industry professionals and students from the broad ranges of disciplines referring toMechanism Science, in an intimate, collegial and stimulating environment.

In this second event we have received an increased attention to the initiative, ascan be seen by the fact that the EUCOMES08 Proceedings will contain contributionsby authors even from all around the world. This means also that there is a reallyinterest to have not only a conference frame but even a need of aggregation foran European Community well identified in Mechanism Science with the aim tostrengthen common views and collaboration activities among European researchersand institutions.

I believe that a reader will take advantage of the papers in these Proceedings withfurther satisfaction and motivation for her or his work. These papers cover the widefield of the Mechanism Science. The program of EUCOMES08 Conference hasincluded technical sessions with oral presentations, which, together with informalconversations during the social program, have enabled to offer wide opportunitiesto share experiences and discuss scientific achievements and current trends in theareas encompassed by the EUCOMES08 conference.

We received 80 papers, and after review 72 papers have been accepted both forpresentation and publication in the Proceedings. These papers cover several aspectsof the wide field of Mechanism Science. The contributions have been grouped insessions on Theoretical and Computational Kinematics, History of Mechanism Sci-ence, Design Algorithms, Mechanism Designs, Mechanical Transmissions, GearingSystems, Manipulators, Linkages, Mechanics of Robots, Experimental Mechanics,Dynamics of Multibody Systems, Industrial Applications, and Non Industrial Appli-cations. But they cover more subjects than those expressed in the above-mentionedsession titles.

We would like to express grateful thanks to the members of the InternationalSteering Committee for EUCOMES Conference for co-operating enthusiastically

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for the success of the EUCOMES08 event: Bob Bicker (Newcastle University,UK), Marco Ceccarelli (Univ. Cassino, Italy), Burkhard Corves (Univ. Aachen,Germany), Manfred Husty (Univ. Innsbruck, Austria), Jean-Pierre Merlet (INRIA,France), Doina Pisla (Tech. Univ. Cluj-Napoca, Romania), Fernando Viadero (Univ.Cantabria, Spain), Teresa Zielinska (Warsaw Tech. Univ., Poland).

We thank the authors who have contributed with very interesting papers in severalsubjects, covering many fields of Mechanism Science. We are grateful to the review-ers for the time and effort they spent evaluating the papers. I thank the Universityof Cassino for hosting the EUCOMES08 event. I would like to thank my colleaguesat the LARM, Laboratory of Robotics and Mechatronics of University of Cassinofor their help, namely Dr Chiara Lanni, Dr Erika Ottaviano, and particularly DrGiuseppe Carbone, who has served also as Secretary for EUCOMES08.

I am grateful to my wife Brunella, my daughters Elisa and Sofia, and my sonRaffaele. Without their patience and comprehension it would not have been possi-ble for me to organize EUCOMES08, Second European Conference on MechanismScience.

University of Cassino Marco CeccarelliJune 2008

Contents

Automatic Weapons of the Roman Empire . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Flavio Russo, Cesare Rossi and Ferruccio Russo

“DEUS-EX-MACHINA” in Phlius Theatre . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Argyris S. Papadogiannis, Marilena C. Tsakoumaki and Thomas G. Chondros

Archimedes and the Origins of Mechanisms Design . . . . . . . . . . . . . . . . . . . . 21Thomas G. Chondros

The Mirror Weapon in Archimedes Era . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29A.S. Papadogiannis, N.S. Papadogianni, A. Carabelas, S. Tsitomeneas,P. Kyraggelos and T.G. Chondros

The Creation of the Site About the Historical Part of Collection ofMechanisms Bauman MSTU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Theodor Vitiukov and Valentin Tarabarin

Using Computer Spreadsheets in Teaching Mechanisms . . . . . . . . . . . . . . . . 45Eres Söylemez

Hinged Frameworks with Unusual Geometrical Properties . . . . . . . . . . . . . . 55Mikhail Kovalev

A Comparison Between Line Geometries of Point and Line Displacements 61Chintien Huang

A Kinematic Approach to Calculate Protein Motion Paths . . . . . . . . . . . . . . 69Mikel Diez, Vı́ctor Petuya, Mónica Urı́zar and Alfonso Hernández

Solutions of the Equation of Meshing for Planar Gear Profiles . . . . . . . . . . . 77Giovanni Bonandrini, Giovanni Mimmi and Carlo Rottenbacher

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A Numerical Method for the Second-Order Mobility Analysis ofMechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87Igor Fernández de Bustos, Josu Agirrebeitia and Rafael Avilés

Mathematical Models of Mechanisms with Essentially Elastic Links . . . . . 95G. Ualiyev and Assylbek Jomartov

Design and Simulation of a New Hybrid Mobile Robot for OverpassingObstacles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101Gianni Castelli and Erika Ottaviano

Evolving Four-Bars for Optimal Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Hans-Peter Schröcker, Bert Jüttler and Martin Aigner

A New Family of Overconstrained 6R-Mechanisms . . . . . . . . . . . . . . . . . . . . . 117Martin Pfurner

Development of a Spherical Linkage Mechanism with the Aid of theDynamic Spatial Geometry Program “GECKO” . . . . . . . . . . . . . . . . . . . . . . . 125G. Lonij, Mathias Husing, S.W. Choi and Burkhard Corves

Elastic and Safety Clutch with Radial Disposed Elastic Lamellas . . . . . . . . 133Ioan Stroe

Computational Multi-Objective Optimization to Design Service Robots . . 139Cristina Castejón, Giuseppe Carbone, Juan Carlos Garcı́a Pradaand Marco Ceccarelli

An Optimal Design for a New Underactuated Finger Mechanism . . . . . . . . 149Shuangji Yao, Marco Ceccarelli, Giuseppe Carbone and Zhen Lu

Synthesis of a Spatial Five-Link Mechanism with Two Degrees ofFreedom According to the Given Laws of Motion . . . . . . . . . . . . . . . . . . . . . . 159Nodar Davitashvili and Otar Gelashvili

Synthesis of Mechanisms with Evolutionary Techniques . . . . . . . . . . . . . . . . 167J.A. Cabrera, J.J. Castillo, F. Nadal, A. Ortiz and A. Simón

Optimal Synthesis of Steering Mechanisms Including TransmissionAngles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175Ana de-Juan, Ramon Sancibrian and Fernando Viadero

Workspace Fitting and Control for a Serial-Robot Motion Simulator . . . . . 183Andrés Kecskeméthy, Ismar Masic and Martin Tändl

Contents ix

Operation Features of Milli-CaTraSys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191Eusebio Hernandez-Martinez, Giuseppe Carbone and Carlos Lopez-Cajun

Design of an Actuation System for a Fatigue Test RIG . . . . . . . . . . . . . . . . . . 201Luca Pugi, Andrea Rindi, Benedetto Allotta and Giuseppe Gori

The Influence of Motion Mode and Friction on the Dynamics of aParallel Robot Used for Orientation Applications . . . . . . . . . . . . . . . . . . . . . . 209Doina Pisla and Tiberiu Itul

Elastohydrodynamic Models for Predicting Friction in Point ContactsLubricated with Polyalphaolefins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219J. Echávarri Otero, P. Lafont Morgado, J.B. Sánchez-Peñuela, J.L. MuñozSanz, J.M. Munoz-Guijosa, A. Dı́az Lantada and H. Lorenzo Yustos

An Integrated Differentiation-Projection Approach for the KinematicData Consistency of Biomechanical Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 229F.J. Alonso, J. Cuadrado and P. Pintado

Design of Simple Humanoid Dedicated to the Research on the GaitSynthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237Teresa Zielinska, Krzysztof Mianowski and Przemyslaw Kryczka

A Comparison of Algorithms for Path Planning of Industrial Robots . . . . . 247Francisco Rubio, Francisco Valero, Josep Lluı́s Suñer and Vicente Mata

Stiffness Analysis of Parallel Manipulator Using Matrix StructuralAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255Rogério Sales Gonçalves and João Carlos Mendes Carvalho

Modelling of Robot’s Motion by Use of Vibration of Internal Masses . . . . . 263Jatsun Sergey, Dyshenko Vyacheslav, Yatsun Andreyand Malchikov Andrey

Mechanical Design of a 3-dof Parallel Robot Actuated by Smart Wires . . . 271Terenziano Raparelli, Pierluigi Beomonte Zobel and Francesco Durante

A Multicriteria Approach for Optimal Trajectories in DynamicParameter Identification of Parallel Robots . . . . . . . . . . . . . . . . . . . . . . . . . . . 279Xabier Iriarte, Miguel Dı́az-Rodrı́guez and Vicente Mata

Reinforcement Neural Network for the Stabilization of a FurutaPendulum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287Benedetto Allotta, Luca Pugi and Fabio Bartolini

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A Technique for Vibration Suppression of a 2 DOF CompliantManipulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295Giovanni Incerti

Investigation on the Baumgarte Stabilization Method for DynamicAnalysis of Constrained Multibody Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 305Paulo Flores, Rui Pereira, Margarida Machado and Eurico Seabra

Cornering Stability and Dynamic Analysis of a Four Steering WheelsVehicle Driven by “In Wheel” Engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313Massimo Callegari, Andrea Gabrielli and Matteo-Claudio Palpacelli

Dynamic Modelling of a Single – Link Flexible Arm to be Used as aSensing Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321Javier Guerra Fernández, Vicente Feliu Batlleand Miguel Ángel Caminero Torija

Method of Dynamic Analysis of Mechanisms of Variable Structure . . . . . . . 329Assylbek Jomartov and Z.G. Ualiyev

A Contribution to the Synthesis of a Trihedral Conjugate Cam . . . . . . . . . . 337Miroslav Václavı́k and Zdeněk Koloc

Experimental and Theoretical Research of Cams Wearing of CamsMechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343Alexander Golovin, Alexey Lafitsky and Alexey Simuskhin

Dynamic Features of Speed Increasers from Mechatronic Wind andHydro Systems. Part I: Structure Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . 351C. Jaliu, D.V. Diaconescu, M. Neagoe and R. Săulescu

Dynamic Features of Speed Increasers from Mechatronic Wind andHydro Systems. Part II: Dynamic Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361C. Jaliu, D.V. Diaconescu, M. Neagoe and R. Săulescu

A Computer Aided Method for Cam Profile Design . . . . . . . . . . . . . . . . . . . . 369A. Petropoulou, S. Dimopoulos, D. Mourtzis and T.G. Chondros

On the Power Transmission and Running Quality of Micro-Mechanisms . 377Hanfried Kerle

Probable Simulating Models of Wear for Open Gearing withHigh-Ratio Gear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387Alexander Golovin and Tamara Milevskaya

Contents xi

Alternative in Harmonic Train Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397Valentin Tarabarin and Zinaida Tarabarina

On the Position of the Single Pair Tooth Segment Relative to the PitchPoint, for Internal Gears, with Effect on Contact Stress Calculus . . . . . . . . 405Radu Velicu, Gheorghe Moldovean and Cristina A. Bozan

Gears and Belt Drives for Non-Uniform Transmission . . . . . . . . . . . . . . . . . . 415Hellmuth Stachel

Fulleroid-Like Linkages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423Gökhan Kiper

On the Classification of Compliant Mechanisms . . . . . . . . . . . . . . . . . . . . . . . 431Lena Zentner and Valter Böhm

Comparative Kinematics of Mobile Transversal Coupling, as MultibodySystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439Cornel Cătălin Gavrilă

The Synthesis of a Linkage with Linear Actuator for Solar Trackingwith Large Angular Stroke . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447Ion Visa, Dorin Diaconescu, Valentina Popa, Bogdan Burduhosand Radu Saulescu

Dynamics of Heel Strike in Bipedal Systems with Circular Feet . . . . . . . . . . 455Josep Maria Font and József Kövecses

Parallel Manipulators with Simple Geometrical Structure . . . . . . . . . . . . . . 463Adolf Karger

Analysis of Wire Elasticity for Wire-driven Parallel Robots . . . . . . . . . . . . . 471Jean-Pierre Merlet

Kinematic Analysis of a Compliant, Parallel and Three-DimensionalMeso-Manipulator Generated from a Planar Structure . . . . . . . . . . . . . . . . . 479Cinzia Amici, Alberto Borboni, Pier Luigi Magnani and Diego Pomi

Dynamic Analysis of a Compliant, Parallel and Three-DimensionalMeso-Manipulator Generated from a Planar Structure . . . . . . . . . . . . . . . . . 487Cinzia Amici, Alberto Borboni, Pier Luigi Magnani and Diego Pomi

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Modelling of the Orientation Error of a 3-DOF Translational ParallelManipulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495Zouhaier Affi and Lotfi Romdhane

Sensitivity Analysis of Degenerate and Non-Degenerate Planar ParallelManipulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505Nicolas Binaud, Stéphane Caro and Philippe Wenger

3D Object Reconstruction Using a Robot Arm . . . . . . . . . . . . . . . . . . . . . . . . . 513Cesare Rossi, Sergio Savino and Salvatore Strano

Considerations on Process Performance in Incremental Forming byInducing High Frequency Vibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523D. Mundo, G. Gatti, G. Ambrogio, L. Filice and G. A. Danieli

Scheduling and Verification of Micro Assembly Processes . . . . . . . . . . . . . . . 531Kerstin Schöttler, Arne Burisch, Annika Raatz and Jürgen Hesselbach

Cambio – A Miniaturized Tool Changer for Desktop Factory Application . 541Arne Burisch, Christian Loechte, Annika Raatz and Adriano Fabrizi

Tensegrity Concept – From Natural Systems to Robots . . . . . . . . . . . . . . . . . 549Simona-Mariana Cretu

Laser-Based Structuring of Piezoceramics for Mobile Microrobots . . . . . . . 559Christoph Edeler and Daniel Jasper

Evaluation of Spatial Vibrations Using a Platform with 6 Degrees ofFreedom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567Jiri Blekta, Josef Mevald and Iva Petrikova

Mechanical Design and Optimization of a Microsurgical Robot . . . . . . . . . . 575M. Miroir, J. Szewczyk, Y. Nguyen, S. Mazalaigue, A. Bozorg Grayeliand O. Sterkers

Multy Mirror Adjustable Space Reflector as the Mechanism with ManyDegrees of Freedom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585Vicktor I. Bujakas

Dynamic Modeling of a Parallel Robot Used in Minimally InvasiveSurgery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595N. Plitea, D. Pisla, C. Vaida, B. Gherman and A. Pisla

Contents xiii

Controlling the Traditional Rigid Endoscopic Instrumentation Motion . . . 603D. Moschella and G.A. Danieli

Use of Substitute of Mechanisms for Tolerance Investigation of GuidanceMechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613Mathias Husing and Burkhard Corves

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623

Contributors

Zouhaier Affi Laboratoire de Génie Mécanique, Ecole Nationale d’Ingénieurs deMonastir, e-mail: zouhaier.affi@enim.rnu.tn

Josu Agirrebeitia Departamento de Ingenierı́a Mecánica, Escuela Superior deIngenieros de Bilbao, Alda. de Urquijo s/n 48013 Bilbao (Vizcaya), Spain

Martin Aigner Institute of Applied Geometry, University of Linz, Linz, Austria

Benedetto Allotta Sezione di Meccanica Applicata alle Macchine, Dipartimento diEnergetica “Sergio Stecco”, Università di Firenze, Via Santa Marta 3, 50100 Firenze(FI), Italy, e-mail: ben@mapp1.de.unifi.it, web page: http://mapp1.de.unifi.it

F.J. Alonso Departamento de Ingenierı́a Mecánica, Energética y de los Materiales,Universidad de Extremadura, Avda. de Elvas s/n, 06071 Badajoz, Spain, e-mail:fjas@unex.es

G. Ambrogio Dipartimento di Meccanica, Università della Calabria, Via P. Bucci,87036, Arcavacata di Rende (Cs), Italy

Cinzia Amici Dipartimento di Ingegneria Meccanica e Industriale (DIMI),Università degli Studi di Brescia, Via Branze 38, 25123 Brescia (BS), Italy, e-mail:cinzia.amici@ing.unibs.it

Malchikov Andrey Mechatronical Departmnent, Kursk State TechnicalUniversity, Kursk, Russia

Yatsun Andrey Mechatronical Departmnent, Kursk State Technical University,Kursk, Russia

Rafael Avilés Departamento de Ingenierı́a Mecánica, Escuela Superior deIngenieros de Bilbao, Alda. de Urquijo s/n 48013 Bilbao (Vizcaya), Spain

Fabio Bartolini Sezione di Meccanica Applicata alle Macchine, Dipartimento diEnergetica “Sergio Stecco”, Università di Firenze, Via Santa Marta 3, 50100 Firenze(FI), Italy, e-mail: bartolini@mapp1.de.unfi.it, web page: http://mapp1.de.unifi.itTM

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xvi Contributors

Vicente Feliu Batlle Departamento de Ingenierı́a Eléctrica, Electrónica yAutomática, ETS Ing. Industriales, Universidad de Castilla – La Mancha Avda.Camilo José Cela, s/n 13071 Ciudad Real, Spain

Nicolas Binaud Institut de Recherche en Communications et Cybernétique deNantes, UMR CNRS no 6597, 1 rue de la Noë, 44321 Nantes, e-mail: France,binaud@irccyn.ec-nantes.fr

Jiri Blekta Department of Applied Mechanics, Technical University of Liberec,Studentská 2, 46117 Liberec, Czech Republic

Valter Böhm Fakultät für Maschinenbau, Technische Universität Ilmenau, PF100565, 98684 Ilmenau, Germany

Giovanni Bonandrini Dipartimento di Meccanica Strutturale, Università di Pavia,Via Ferrata 1, I-27100 Pavia, Italy

Alberto Borboni Dipartimento di Ingegneria Meccanica e Industriale (DIMI),Università degli Studi di Brescia, Via Branze 38, 25123 Brescia (BS), Italy

Cristina A. Bozan Department of Product Design and Robotics, TransilvaniaUniversity of Braşov, Bdul Eroilor 27, 500036 Braşov, Romania, e-mail:crissy ro@yahoo.com

A. Bozorg Grayeli Inserm, Unit-M 867, Paris; AP-HP Hôpital Beaujon, Serviced’ORL, Clichy; Université Denis-Diderot, France

V.I. Bujakas P.N. Lebedev Physical Institute, Russian Academy of Science,Moscow, Russia, e-mail: bujakas@yandex.ru.

Bogdan Burduhos Department of Product Design and Robotics, TransilvaniaUniversity of Brasov, Eroilor Boulevard 29, 500036 Brasov, Romania, e-mail:bogdan.burduhos@unitbv.ro

Arne Burisch Institute of Machine Tools and Production Technology; Institut fürWerkzeugmaschinen und Fertigungstechnik, Technische Universität Braunschweig,Langer Kamp 19 B, 38106 Braunschweig, Germany, e-mail: a.burisch@tu-bs.de

J.A. Cabrera Department of Mechanical Engineering, University of Málaga,Campus El Ejido, 29013 Málaga, Spain

Massimo Callegari Dipartimento di Meccanica, Università Politecnicadelle Marchem, Via Brecce Bianche s/n, 60131 Ancona, Italy, e-mail:m.callegari@univpm.it

Miguel Ángel Caminero Torija Departamento de Ingenierı́a Eléctrica, Electrónicay Automática, ETS Ing. Industriales, Universidad de Castilla – La Mancha Avda,Camilo José Cela, s/n 13071 Ciudad Real, Spain

A. Carabelas University of Patras, Department of Mechanical Eng & Aeronautics,265 00 Patras, Greece

Contributors xvii

Giuseppe Carbone LARM: Laboratory of Robotics and Mechatronics, DiMSAT,University of Cassino, Via Di Biasio 43, 03043 Cassino (Fr), Italy, e-mail:carbone@unicas.it

Stéphane Caro Institut de Recherche en Communications et Cybernétiquede Nantes, UMR CNRS no 6597, 1 rue de la Noë, 44321 Nantes, France,caro@irccyn.ec-nantes.fr

C. Castejón MAQLAB Group, Mechanical Dept. Carlos III University, Av. De laUniverisidad 30, 28911 Madrid, Spain, e-mail: castejon@ing.uc3m.es

G. Castelli LARM: Laboratory of Robotics and Mechatronics, DiMSAT,University of Cassino, Via G. Di Biasio 43, 03043 Cassino, Italy, e-mail:g.castelli@unicas.it

J.J. Castillo Department of Mechanical Engineering, University of Málaga,Campus El Ejido, 29013 Málaga, Spain

Marco Ceccarelli LARM: Laboratory of Robotics and Mechatronics,DiMSAT, University of Cassino, Via Di Biasio 43, 03043 Cassino (Fr), Italy,ceccarelli@unicas.it, cecca@unicas.it

S.W. Choi Department of Mechanism Theory and Dynamics of Machines,RWTH-Aachen University, Aachen, 52056 Germany

Thomas G. Chondros University of Patras, Department of Mechanical Eng. &Aeronautics, 265 00 Patras, Greece, e-mail: chondros@mech.upatras.gr

B. Corves Department of Mechanism Theory and Dynamics of Machines,RWTH-Aachen University, Aachen, 52056 Germany

J. Cuadrado Departamento de Ingenierı́a Industrial II, Universidad de La Coruña,Mendizábal s/n, 15403 Ferrol, Spain, e-mail: javicuad@cdf.udc.es

G.A. Danieli Dipartimento di Meccanica, Università della Calabria, Via P. Bucci,87036, Arcavacata di Rende (Cs), Italy, e-mail: d.mundo@unical.it

Nodar Davitashvili Georgian Technical University, 77, M. Kostava Str., 0175,Tbilisi, GA, e-mail: nodav@geo.net.ge

Ana de-Juan Department of Structural and Mechanical Engineering, Universityof Cantabria, ETSIIT, Avda. De los Castros s/n. Santander (Spain), e-mail:dejuanam@unican.es, url: http://personales.unican.es/sancibrr

Dorin V. Diaconescu Department of Product Design and Robotics, TransilvaniaUniversity of Brasov, Eroilor Boulevard 29, 500036 Brasov, Romania, e-mail:dvdiaconescu@unitbv.ro

A. Dı́az Lantada División de Ingenierı́a de Máquinas, Universidad Politécnica deMadrid, José Gutiérrez Abascal 2, 28006 Madrid, Spain

Miguel Dı́az-Rodrı́guez Departamento de Tecnologı́a y Diseño, Universidad deLos Andes, Merida, Venezuela, e-mail: dmiguel@ula.ve

xviii Contributors

Mikel Diez Department of Mechanical Engineering, University of the BasqueCountry, Bilbao, 48013, Spain, e-mail: mikel.diez@ehu.es

S. Dimopoulos University of Patras, Department of Mechanical Engineering &Aeronautics, 265 00 Patras, Greece

Francesco Durante Dipartimento di Ingegneria Meccanica, Energetica eGestionale – DIMEG, Università dell’Aquila, Roio Poggio, L’Aquila, Italy

J. Echávarri Otero División de Ingenierı́a de Máquinas, UniversidadPolitécnica de Madrid, José Gutiérrez Abascal 2, 28006 Madrid, Spain, e-mail:jechavarri@etsii.upm.es

Christoph Edeler Division Microrobotics and Control Engineering, Uni-versity of Oldenburg, Uhlhornsweg 84, 26111 Oldenburg, Germany, e-mail:christoph.edeler@kisum.uni-oldenburg.de

Adriano Fabrizi Laboratory of Robotics and Mechatronics at DiMSAT, Universityof Cassino, Cassino, Via Di Biasio 43, 03043 Cassino (Fr), Italy

Javier Guerra Fernández Departamento de Ingenierı́a Eléctrica, Electrónica yAutomática, ETS Ing. Industriales, Universidad de Castilla – La Mancha Avda.Camilo José Cela, s/n 13071 Ciudad Real, Spain, e-mail: Javier.Guerra@uclm.es

Igor Fernández de Bustos Departamento de Ingenierı́a Mecánica, EscuelaSuperior de Ingenieros de Bilbao, Alda. de Urquijo s/n 48013 Bilbao (Vizcaya),Spain, e-mail: igor.fernandezdebustos@ehu.es

L. Filice Dipartimento di Meccanica, Università della Calabria, Via P. Bucci,87036, Arcavacata di Rende (Cs), Italy

Paulo Flores Departamento de Engenharia Mecânica, Universidade doMinho, Campus de Azurém, 4800-058 Guimarães, Portugal, e-mail: pflo-res@dem.uminho.pt

Josep Maria Font Department of Mechanical Engineering, Centre for IntelligentMachines, McGill University, 817 Sherbrooke Street West, H3A 2K6 Montréal,Québec, Canada, e-mail: josep.font@mcgill.ca

Andrea Gabrielli Dipartimento di Meccanica, Università Politecnicadelle Marchem, Via Brecce Bianche s/n, 60131 Ancona, Italy, e-mail:andrea.gabrielli@univpm.it

G. Gatti Dipartimento di Meccanica, Università della Calabria, Via P. Bucci,87036, Arcavacata di Rende (Cs), Italy

Cornel Cătălin Gavrilă Product Design and Robotics Department, TransilvaniaUniversity of Brasov, Eroilor 29, 500036 Braşov, România, cgavrila@unitbv.ro

Otar Gelashvili Georgian Technical University, 77, M. Kostava Str., 0175, Tbilisi,GA

Contributors xix

A. Gherman Technical University of Cluj-Napoca, Constantin Daicoviciu 15,RO-400020 Cluj-Napoca, Romania

Alexander Golovin Department of Theory Mechanisms & Machines, BaumanMoscow State Technical University, 2nd Baumanskaya Str., 5, 105005 Moscow,Russia, e-mail: aalgol@rambler.ru

Rogério Sales Gonçalves School of Mechanical Engineering, Federal Universityof Uberlândia, Campus Santa Mônica, CEP 38400-902, Uberlândia, MG, Brasil,e-mail: ufursgoncalves@yahoo.com.br

Giuseppe Gori Servindustria SRL Pistoia, Italy

Alfonso Hernández Department of Mechanical Engineering, University of theBasque Country, Bilbao, 48013, Spain

E. Hernandez-Martinez Facultad de Ingenierı́a, Universidad Autónoma deQuerétaro, Qro, México, e-mail: e.hernandez@unicas.it

Jürgen Hesselbach Institute of Machine Tools and Production Technology,Technische Universität Braunschweig, Langer Kamp 19 B, 38106 Braunschweig,Germany

Chintien Huang Department of Mechanical Engineering, National ChengKung University, No. 1, University Road, Tainan 701, Taiwan, e-mail:chuang@mail.ncku.edu.tw

M. Husing Department of Mechanism Theory and Dynamics of Machines,Eilfschornestreinstr. 18, RWTH-Aachen University, Aachen, 52056 Germany,e-mail: huesing@igm.rwth-aachen.de

Giovanni Incerti Dipartimento di Ingegneria Meccanica e Industriale,Università di Brescia, Via Branze 38, 25123 Brescia, Italy, e-mail: gio-vanni.incerti@ing.unibs.it

Xabier Iriarte Departamento de Ingenierı́a Mecánica, Energética y deMateriales, Universidad Pública de Navarra, 31006, Pamplona, España, e-mail:xabier.iriarte@unavarra.es

Tiberiu Itul Technical University of Cluj-Napoca, Constantin Daicoviciu 15,RO-400020 Cluj-Napoca, Romania

C. Jaliu Department of Product Design and Robotics, Transilvania University ofBrasov, Bdul Eroilor 29, 500036 Brasov, Romania, e-mail: cjaliu@unitbv.ro

Daniel Jasper Division Microrobotics and Control Engineering, University ofOldenburg, Uhlhornsweg 84, 26111 Oldenburg, Germany

A.A. Jomartov Institute of Mechanics and Machine Sciences, Valikhanov st. 106,050010 Almaty, Republic Kazakhstan, e-mail: legsert@mail.ru

Bert Jüttler Institute of Applied Geometry, University of Linz, Linz, Austria

xx Contributors

Adolf Karger Charles University Praha, Faculty of Mathematics and Physics,Czech Republic, e-mail: Adolf.Karger@mff.cuni.cz

Andrés Kecskeméthy Chair of Mechanics, University Duisburg-Essen,Lotharstraße 1, 47057 Duisburg, Germany, e-mail: andres.kecskemethy@uni-due.de

Hanfried Kerle Institut für Werkzeugmaschinen und Fertigungstechnik,Technische Universität Braunschweig, Langer Kamp 19b, D-38106 Braunschweig,Germany, e-mail: h.kerle@t-online.de

Gökhan Kiper Mechanical Engineering Department, Middle East TechnicalUniversity, İnönü Bulvarı, 06531 Ankara, Turkey, e-mail: kiper@metu.edu.tr

Zdeněk Koloc, Ph.D. Research Institute of Textile Machines Liberec, Plc., U Jezu525/4, 46119 Liberec, Czech Republic

Mikhail Kovalev Bauman Moscow State University, 105005, Moscow, 2-yaBaumanskaya, 5, Russia, e-mail: mdkovalev@mtu-net.ru

József Kövecses Department of Mechanical Engineering, Centre for IntelligentMachines, McGill University, 817 Sherbrooke Street West, H3A 2K6 Montréal,Québec, Canada, e-mail: jozsef.kovecses@mcgill.ca

Przemyslaw Kryczka Faculty of Power and Aeronautical Engineering,ul.Nowowiejska 24, Warsaw University of Technology, 00-665 Warsaw, Poland

P. Kyraggelos University of Patras, Department of Mechanical Eng. &Aeronautics, 265 00 Patras, Greece

Alexey Lafitsky Mechanical-Technological Department, Bauman Moscow StateTechnical University, 2nd Baumanskaya Str., 5, 105005 Moscow, Russia, e-mail:lexxx 13.87@mail.ru

Christian Loechte Institut für Werkzeugmaschinen und Fertigungstechnik,Technische Universität Braunschweig, Langer Kamp 19 b, 38106 Braunschweig,Germany

G. Lonij Department of Mechanism Theory and Dynamics of Machines, RWTH-Aachen University, Aachen, 52056 Germany, e-mail: lonij@igm.rwth-aachen.de

C. Lopez-Cajun Facultad de Ingenierı́a, Universidad Autónoma de Querétaro,Qro, México, e-mail: cajun@uaq.mx

Zhen Lu School of Automation Science and Electrical Engineering, BeihangUniversity, Beijing P.R., China

Margarida Machado Departamento de Engenharia Mecânica, Universidadedo Minho, Campus de Azurém, 4800-058 Guimarães, Portugal, e-mail:margarida@dem.uminho.pt

Pier Luigi Magnani Dipartimento di Ingegneria Meccanica e Industriale (DIMI),Università degli Studi di Brescia, Via Branze 38, 25123 Brescia (BS), Italy

Contributors xxi

Ismar Masic Chair of Mechanics, University Duisburg-Essen, Lotharstraße 1,47057 Duisburg, Germany, e-mail: ismar.masic@uni-due.de

Vicente Mata Departamento de Mecánica y Materiales, UniversidadPolitécnica de Valencia, Camino de Vera, 46020, Valencia, España, e-mail:vmata@mcm.upvnet.upv.es

S. Mazalaigue Collin SA, Bagneux, France

João Carlos Mendes Carvalho School of Mechanical Engineering, FederalUniversity of Uberlândia, Campus Santa Mônica, CEP 38400-902, Uberlândia,MG, Brasil, e-mail: jcmendes@mecanica.ufu.br

Jean-Pierre Merlet COPRIN project-team, INRIA Sophia Antipolis, France,e-mail: Jean-Pierre.Merlet@sophia.inria.fr

Josef Mevald Department of Applied Mechanics, Technical University of Liberec,Studentská 2, 46117 Liberec, Czech Republic

Krzysztof Mianowski Faculty of Power and Aeronautical Engineering,ul.Nowowiejska 24, Warsaw University of Technology, 00-665 Warsaw, Poland

Tamara Milevskaya Mechanical-Technological Department, Bauman MoscowState Technical University, 2nd Baumanskaya Str., 5, 105005 Moscow, Russia,e-mail: cherryjoy@yandex.ru

Giovanni Mimmi Dipartimento di Meccanica Strutturale, Università di Pavia, ViaFerrata 1, I-27100 Pavia, Italy, e-mail: giovanni.mimmi@unipv.it

M. Miroir Université Pierre et Marie Curie-Paris 6, FRE-2507, Institut desSystèmes Intelligents et Robotique (ISIR), Paris, France; Collin SA, Bagneux,France, e-mail: miroir@isir.fr

Gheorghe Moldovean Department of Product Design and Robotics, TransilvaniaUniversity of Braşov, Bdul Eroilor 27, 500036 Braşov, Romania, e-mail:ghmoldovean@unitbv.ro

P. Lafont Morgado División de Ingenierı́a de Máquinas, Universidad Politécnicade Madrid, José Gutiérrez Abascal 2, 28006 Madrid, Spain

D. Moschella Dipartimento di Meccanica, Università della Calabria, Via P. Bucci,87036, Arcavacata di Rende (Cs), Italy, e-mail: d.mundo@unical.it

D. Mourtzis University of Patras, Department of Mechanical Engineering &Aeronautics, 265 00 Patras, Greece

D. Mundo Dipartimento di Meccanica, Università della Calabria, Via P. Bucci,87036, Arcavacata di Rende (Cs), Italy, e-mail: d.mundo@unical.it

J.L. Muñoz Sanz División de Ingenierı́a de Máquinas, Universidad Politécnica deMadrid, José Gutiérrez Abascal 2, 28006 Madrid, Spain

xxii Contributors

J.M. Munoz-Guijosa División de Ingenierı́a de Máquinas, UniversidadPolitécnica de Madrid, José Gutiérrez Abascal 2, 28006 Madrid, Spain

F. Nadal Department of Mechanical Engineering, University of Málaga, CampusEl Ejido, 29013 Málaga, Spain

M. Neagoe Department of Product Design and Robotics, Transilvania Universityof Brasov, Bdul Eroilor 29, 500036 Brasov, Romania

Y. Nguyen Inserm, Unit-M 867, Paris; AP-HP Hôpital Beaujon, Service d’ORL,Clichy; Université Denis-Diderot, France

A. Ortiz Department of Mechanical Engineering. University of Málaga, CampusEl Ejido, 29013 Málaga. Spain

E. Ottaviano LARM: Laboratory of Robotics and Mechatronics, DiMSAT,University of Cassino, Via G. Di Biasio 43, 03043 Cassino, Italy, e-mail:ottaviano@unicas.it

Matteo-Claudio Palpacelli Dipartimento di Meccanica, Università Politec-nica delle Marchem, Via Brecce Bianche s/n, 60131 Ancona, Italy, e-mail:m.palpacelli@univpm.it

N.S. Papadogianni University of Patras, Department of Mechanical Eng. &Aeronautics, 265 00 Patras, Greece

Argyris S. Papadogiannis University of Patras, Department of Mechanical Eng.& Aeronautics, 265 00 Patras, Greece, e-mail: papadog@mech.upatras.gr

Rui Pereira Departamento de Matemática, Universidade do Minho, Campus deAzurém, 4800-058 Guimarães, Portugal, e-mail: rmp@mct.uminho.pt

Iva Petrikova Department of Applied Mechanics, Technical University of Liberec,Studentská 2, 46117 Liberec, Czech Republic, e-mail: iva.petrikova@tul.cz

Petropoulou A. University of Patras, Department of Mechanical Engineering &Aeronautics, 265 00 Patras, Greece

Vı́ctor Petuya Department of Mechanical Engineering, University of the BasqueCountry, Bilbao, 48013, Spain

Martin Pfurner Unit Geometry and CAD, Technikersrt. 13, University ofInnsbruck, 6020 Innsbruck, Austria, email: martin.pfurner@uibk.ac.at

P. Pintado Departamento de Mecánica Aplicada, Universidad de CastillaLa Mancha, Camilo J Cela s/n, 13071 Ciudad Real, Spain, e-mail:Publio.Pintado@uclm.es

A. Pisla Technical University of Cluj-Napoca, Constantin Daicoviciu 15,RO-400020 Cluj-Napoca, Romania

Doina Pisla Technical University of Cluj-Napoca, Constantin Daicoviciu 15,RO-400020 Cluj-Napoca, Romania, e-mail: Doina.Pisla@mep.utcluj.ro

Contributors xxiii

N. Plitea Technical University of Cluj-Napoca, Constantin Daicoviciu 15,RO-400020 Cluj-Napoca, Romania

Diego Pomi Dipartimento di Ingegneria Meccanica e Industriale (DIMI),Università degli Studi di Brescia, Via Branze 38, 25123 Brescia (BS), Italy

Valentina Popa Department of Product Design and Robotics, TransilvaniaUniversity of Brasov, Eroilor Boulevard 29, 500036 Brasov, Romania, e-mail:valentina.popa@unitbv.ro

J.C. Garcı́a Prada MAQLAB Group, Mechanical Dept. Carlos III University, Av.De la Univerisidad 30, 28911 Madrid, Spain, e-mail: jcgprada@ing.uc3m.es

Luca Pugi Sez., Meccanica Applicata Dip. Energetica Sergio Stecco, Università diFirenze, Via Santa Marta 3, 50100 Firenze (FI), Italy; Corso di laurea in Ingegneriadei Trasporti, Università di Firenze, Via Santa Marta 3, 50100 Firenze (FI), Italy,e-mail: luca@mapp1.de.unfi.it

Dominik Raab Chair of Mechanics, University Duisburg-Essen, Lotharstraße 1,47057 Duisburg, Germany, dominik.raab@uni-due.de

Annika Raatz Institute of Machine Tools and Production Technology; Institut fürWerkzeugmaschinen und Fertigungstechnik, Technische Universität Braunschweig,Langer Kamp 19 B, 38106 Braunschweig, Germany

Terenziano Raparelli Dipartimento di Meccanica, Politecnico di Torino, CorsoDuca degli Abruzzi 24, Torino, Italy

Andrea Rindi Sez., Meccanica Applicata Dip. Energetica Sergio Stecco,Università di Firenze, Via Santa Marta 3, 50100 Firenze (FI), Italy

Lotfi Romdhane Laboratoire de Génie Mécanique, Ecole Nationale d’Ingénieursde Sousse, Sousse, Tunisia, e-mail: lotfi.romdhane@enim.rnu.tn

Cesare Rossi University of Napoli “Federico II”, via Claudio, 21 – 80125 NapoliItaly, e-mail: cesare.rossi@unina.it

Carlo Rottenbacher Dipartimento di Meccanica Strutturale, Università di Pavia,Via Ferrata 1, I-27100 Pavia, Italy

Francisco Rubio Dpt. of Mechanical Engineering, Politechnic University ofValencia, Camino de Vera s/n Valencia 46023, Spain, e-mail: frubio@mcm.upv.es

Ferruccio Russo Free Lance Journalist, Napoli, Italy

Flavio Russo USSME Historical Bureau HQ Italian Army, Napoli, Italy

J.B. Sánchez-Peñuela División de Ingenierı́a de Máquinas, UniversidadPolitécnica de Madrid, José Gutiérrez Abascal 2, 28006 Madrid, Spain

Ramon Sancibrian Department of Structural and Mechanical Engineering,University of Cantabria, ETSIIT, Avda. De los Castros s/n. Santander, (Spain), url:http://personales.unican.es/sancibrr

xxiv Contributors

Radu Săulescu Department of Product Design and Robotics, TransilvaniaUniversity of Brasov, Eroilor Boulevard 29, 500036 Brasov, Romania, e-mail:rsaulescu@unitbv.ro

Sergio Savino University of Napoli “Federico II”, via Claudio, 21 – 80125 Napoli,Italy

Kerstin Schöttler Institute of Machine Tools and Production Technology,Technische Universität Braunschweig, Langer Kamp 19 B, 38106 Braunschweig,Germany, e-mail: k.schoettler@tu-bs.de

Hans-Peter Schröcker Unit Geometry and CAD, Technikersrt. 13, UniversityInnsbruck, 6020 Innsbruck, Austria

Eurico Seabra Departamento de Engenharia Mecânica, Universidadedo Minho, Campus de Azurém, 4800-058 Guimarães, Portugal, e-mail:eseabra@dem.uminho.pt

Jatsun Sergey Mechatronical Departmnent, Kursk State Technical University,Kursk, Russia, e-mail: jatsun@kursknet.ru

A. Simón Department of Mechanical Engineering, University of Málaga, CampusEl Ejido, 29013 Málaga, Spain

Alexey Simuskhin Mechanical-Technological Department, Bauman MoscowState Technical University, 2nd Baumanskaya Str., 5, 105005 Moscow, Russia,e-mail: simuskhin@mail.ru

Eres Söylemez Mechanical Engineering Department, Middle East TechnicalUniversity, İnönü Bulvarı, 06531 Ankara, Turkey, e-mail: eres@metu.edu.tr

Hellmuth Stachel Institute of Discrete Mathematics and Geometry, ViennaUniversity of Technology, Wiedner Hauptstr. 8-10/104, A 1040 Wien, Austria,e-mail: stachel@dmg.tuwien.ac.at

O. Sterkers Inserm, Unit-M 867, Paris; AP-HP Hôpital Beaujon, Service d’ORL,Clichy; Université Denis-Diderot, France

Salvatore Strano University of Napoli “Federico II”, via Claudio, 21 – 80125Napoli, Italy

Ioan Stroe Department Design of Products and Robotics, Faculty of TechnologicEngineering University, “Transylvania” of Brasov, B-dul. Eroilor nr. 29, 500036Brasov, Romania, e-mail: stroei@unitbv.ro

Josep Lluı́s Suñer Departamento de Mećanica y Materials, UniversidadPolitécnica de Valencia, Camino de Vera, 46020, Valencia, España

J. Szewczyk Université Pierre et Marie Curie-Paris 6, FRE-2507, Institut desSystèmes Intelligents et Robotique (ISIR), Paris, France

Martin Tändl Chair of Mechanics, University Duisburg-Essen, Lotharstraße 1,47057 Duisburg, Germany, e-mail: martin.taendl@uni-due.de

Contributors xxv

Valentin Tarabarin The “Theory of Machines and Mechanisms” Department, TheBauman Moscow State Technical University, 2nd Baumanskaya Str., 5, 105005,Moscow, Russia, e-mail: vtarabarin@gmail.com

Zinaida Tarabarina The “Theory of Machines and Mechanisms” Department,The Bauman Moscow State Technical University, 2nd Baumanskaya Str., 5,105005, Moscow, Russia

Marilena C. Tsakoumaki University of Patras, Department of Mechanical Eng.& Aeronautics, 265 00 Patras, Greece

S. Tsitomeneas University of Patras, Department of Mechanical Eng. &Aeronautics, 265 00 Patras, Greece

G. Ualiyev Institute of Mechanics and Machine Sciences, Valikhanov St. 106,050010 Almaty, Republic Kazakhstan, e-mail: legsert@mail.ru

Z.G. Ualiyev Institute of Mechanics and Machine Sciences, Valikhanov St. 106,050010 Almaty, Republic Kazakhstan, e-mail: legsert@mail.ru

Mónica Urı́zar Department of Mechanical Engineering, University of the BasqueCountry, Bilbao, 48013, Spain

Prof. Miroslav Václavı́k, Ph.D., Research Institute of Textile MachinesLiberec, Plc., U Jezu 525/4, 46119 Liberec, Czech Republic, e-mail:miroslav.vaclavik@vuts.cz

C. Vaida Technical University of Cluj-Napoca, Constantin Daicoviciu 15,RO-400020 Cluj-Napoca, Romania

Francisco Valero Departamento de Mećanica y Materials, Universidad Politécnicade Valencia, Camino de Vera, 46020, Valencia, España

Radu Velicu Department of Product Design and Robotics, Transilvania Universityof Braşov, Bdul Eroilor 27, 500036 Braşov, Romania, e-mail: rvelicu@unitbv.ro

Fernando Viadero Department of Structural and Mechanical Engineering,University of Cantabria, ETSIIT, Avda. De los Castros s/n., Santander (Spain), url:http://personales.unican.es/sancibrr

Ion Visa Department of Product Design and Robotics, Transilvania University ofBrasov, Eroilor Boulevard 29, 500036 Brasov, Romania, e-mail: visaion@unitbv.ro

Theodor Vitiukov Student, Dept. Theory Machines and Mechanisms, BaumanMoscow State Technical University, Moscow, Russia, e-mail: vietfed7@gmail.com

Dyshenko Vyacheslav Mechatronical Departmnent, Kursk State TechnicalUniversity, Kursk, Russia

Philippe Wenger Institut de Recherche en Communications et Cybernétique deNantes, UMR CNRS no 6597, 1 rue de la Noë, 44321 Nantes, France, e-mail:wenger@irccyn.ec-nantes.fr

xxvi Contributors

Shuangji Yao School of Automation Science and Electrical Engineering, BeihangUniversity, Beijing P.R., China, e-mail: buaayaoshuangji@163.com

H. Lorenzo Yustos División de Ingenierı́a de Máquinas, Universidad Politécnicade Madrid, José Gutiérrez Abascal 2, 28006 Madrid, Spain

Lena Zentner Fakultät für Maschinenbau, Technische Universität Ilmenau, PF100565, 98684 Ilmenau, Germany, e-mail: lena.zentner@tu-ilmenau.de

Teresa Zielinska Faculty of Power and Aeronautical Engineering, ul.Nowowiejska24, Warsaw University of Technology, 00-665 Warsaw, Poland, e-mail:teresaz@meil.pw.edu.pl

Pierluigi Beomonte Zobel Dipartimento di Ingegneria Meccanica, Energetica eGestionale – DIMEG, Università dell’Aquila, Roio Poggio, L’Aquila, Italy, e-mail:zobel@ing.univaq.it

Automatic Weapons of the Roman Empire

Flavio Russo, Cesare Rossi and Ferruccio Russo

Abstract In the present paper the mechanics and the mechanisms that were used insome military weapons of the Roman Army are presented. In particular it is shownthat both automatic weapons and pneumatic weapons were invented and used at thatages.

These military devices and in particular the design and construction of their com-ponents can show us that mechanical knowledge were much more advanced thanone can commonly think.

Keywords Kinematics · Mechanism design · Manipulators

Introduction

Certainly the Roman Empire was conquered and hold not only by the army itselfbut also by the Roman technology and modernity. This modernity was not only inthe field of the Right and Literature but also (and perhaps mostly) in the field ofEngineering and Science.

The Engineering, in particular was more advanced than one can commonly think;this is certainly true in the field of architectural works but probably even more truein the field of Hydraulics and Mechanics. This last field is probably less known thanthe other because the archaeological finds are less evident, smaller and sometimesunrecognised.

The weapons of the Roman Army presented in this paper contribute to showthat the Mechanics and Mechanisms Science were very advanced and also thesurprising modernity of some mechanical constructions and conceptions ofthose ages.

C. Rossi (B)University of Napoli “Federico II”, via Claudio, 21–80125 Napoli Italye-mail: cesare.rossi@unina.it

M. Ceccarelli (ed.), Proceedings of EUCOMES 08,DOI 10.1007/978-1-4020-8915-2 1, C© Springer Science+Business Media B.V. 2009

1

2 F. Russo et al.

The Repeating Catapult

The word catapult comes from the Greek (���� = through and ����� = shield).During the Roman Empire this word was used for a machine that throws darts, whilethe word ballista (that also comes from the Greek word ��� = to throw) wasused for a machine that throws balls. During the Middle Age the words were usedwith the opposite meaning: ballista for a dart throwing machine and catapult for aball throwing one.

The Roman catapult was one of the most important weapons of the light artilleryof the Roman Army. It is similar to a large crossbow and throws darts. In his concep-tion the ballista is considered the most complex and scientifically evolved weaponbefore the industrial revolution. Few centuries after the fall of the Roman Empire itwas no more built as it was very expensive and difficult to built.

The Working Principles of a Catapult

To describe the working principle of a “normal” catapult, we must start from themotor. This last term, in the Hellenistic Age, was adopted to indicate the reason of akinematic event. The ballistae where moved by two different kinds of elastic motors:the flexion motor and the torsion motor. The first one was used in the crossbows andsmall ballistae and was made first by a combination of wood, horns and sinews andlater by steel or bronze leaves. For larger and more powerful catapults (and also forother launching machines) it was necessary a small and powerful motor: the torsionmotor. According to sources, this last appeared around the middle of the 4th centuryBC in the same period torsion artillery appeared on the scene and replaced flexionartillery in just a few decades.

In Fig. 1 the torsion motor of a catapult is shown.How it can be seen, a torsion motor consisted of a strong square wooden frame,

reinforced by iron straps, divided into three separate sections. The central sectionwas used to insert the frame of the weapons, while the sides were for the two coilsof twisted rope. Inside were the arms to which the rope was affixed, like the ends ofan archery bow.

The coils were made of twisted bovine sinews, horsehair or women’s hair. Ker-atinous formations were preferred for their superior resistance, excellent for elasticmotors that worked by repeated cycles of torsion and immediate return. Since the ki-netic power of a weapon depended on the diameter of the coils, the diameter becamethe dimensional module, just like the calibre in modern artillery.

Preparation for firing consisted of applying an initial torsion to the coils by meansof special levers, almost up to the yield point. By effecting an additional rotation ofapproximately 50◦/60◦ using the arms of the weapon rather than the levers, rotatingthem by pulling the cord with the crank, a tremendous amount of potential elasticenergy was stored. When the restraint was released and the weapon fired, the coilwould rotate rapidly in the opposite direction, pulling the arms to fire or hurl theprojectile.

Automatic Weapons of the Roman Empire 3

Fig. 1 Torsion motor of a catapult

The dart was about 450 mm and weighted about 200 g or 850 mm long and itsweighted about 250 g; the range was up to 550 m.

The Repeating Catapult Working Principle

A pictorial drawing and an orthogonal technical drawing of our reconstruction of therepeating catapult is shown in Fig. 2; it is possible to observe the arrow magazine,the chain and the crank handles.

The repeating catapult is described by Philon of Byzantium [3, 4] and can beconsidered as a futuristic automatic weapon that throws 481 mm long darts. Thismachine was attributed to Dionysius of Alexandria and, apparently, it was usedaround the 1st century BC; it was as a part of the arsenal of Rhodes that maybe considered as a concentration of the most advanced mechanical kinematic andautomatic systems of the time, many of which are still widely used [5].

Essentially, it consisted of a container holding within it a number of arrows, acylinder feeding device and movement chain.

The description left to us by Philon, as is easily understandable, was not writtento eliminate all doubt, as it lacks a technical glossary and an analytic style. In Fig. 3some details of the mechanism are shown.

According to Philon, the arrows were located in a vertical feeder (see Fig. 4) andwere transferred one at a time into the firing groove by means of a rotating drumactivated alternatively by a guided cam, in turn activated by a slide. A simple rota-tion of the crank was sufficient to move the drum, the slide, the coupling mechanismand the release mechanism. The cycle repeated automatically without interruption

4 F. Russo et al.

Fig. 2 Reconstruction of the repeating catapult

or inverting the rotation of the sprocket until the charger was empty, a charger thatcould be re-loaded without suspending firing.

It is interesting to note that the motion from the crank shaft to the other partsoccurred by means of two flat link chains pulled by pentagonal sprockets, as shownalso in Fig. 4. These, similar to modern electrical saws, had interior teeth that wereinserted into the spaces of the pentagonal motor sprocket and the return sprocket,preventing them from exiting. Similar types of chains, called Galle, are attributed toLeonardo da Vinci and transmit motion in bicycles and motorcycles.

One of the longer interior teeth (see Fig. 4) pulled the slide which in turn pulledthe cord, loading the coils of the motor. When in motion, an attached cam causeda 180◦ rotation in the direction of the loaded cylinder, drawing an arrow from theloader and placing it in the channel in front of the rope (see Fig. 6). When the slidereached the rear of the weapon, the cog released it, while another opened the releasemechanisms. An instant later, upon completion of sprocket rotation, the same cogcoupled with the slide from underneath, pulling in the opposite direction. Near thetop of the weapon, the second device closed the hook after it had retrieved the cord,while the feeder picked up another arrow from the feeder. A half rotation in thesprocket and the cycle was repeated. In Fig. 4 is also shown the feed mechanismcompared with the one of the Gatling machine gun; this last is considered as thefirst (1862 U.S. patent) machine gun and it’s working principle is still used for actualaircraft automatic weapons.

From a ballistic perspective, the rate of fire must have been about of five strokeper minute: very little when compared to our automatic weapons, but certainly im-pressive for the era. Paradoxically, this very reason made it useless as it concentrated

Automatic Weapons of the Roman Empire 5

Fig. 3 Details of the mechanism

all the arrows in the same location in such a short period of time that it continued tostrike the same target.

An unquestionable demonstration of its potential was confirmed in the early1900s, when a life size reproduction was made in Germany: during the testingperformed in front of the Kaiser, one of its arrows split a another arrow exactlyin two!

The Pneumatic Ballista

The only and not insignificant drawback of torsion motors was the strongly hygro-scopic nature of the coils, which were weakened when they came into contact withwater or a humid environment. Rain or even a prolonged exposure to humidity orfog drastically decreased its potential. When they wanted to use torsion artillery inNordic climates or in naval contexts, the motors had to be carefully protected in

6 F. Russo et al.

A B C

Fig. 4 Chain and trigger mechanism (A); repeating catapult (B) and Gatling machine gunfeedingmechanisms (C)

hermetically sealed housings. These solutions were not completely satisfying, so anew invention in this field was made in the same ages.

During the Hellenistic Age, many scientists and engineer invented a number ofdevices that make use of pneumatics, so the knowledge of this academic disciplineshould have been very advanced. In particular, Philon of Byzantium was perfectly(2nd century BC) described a weapon in his work Belopoica, that he defined as anair spring ballista. In this weapon he makes only minimum modifications to theusual (already at that ages) cylinder-piston device.

A pictorial reconstruction of this device is shown in Fig. 5 and some particularsin the lower part of the figure.

The ballista is essentially made up by two cylinder-piston devices that substitutethe usual torsion motor. The pistons are fixed to the catapult’s frame while the pis-tons are linked to a rack and pinion system; the catapult’s arms are moved by thepinions; these last are obviously confined to a sector gear.

In Fig. 6 an orthogonal design is reported.Although even one cylinder would have been sufficient, in order to reach the

correct volume it would have required a larger diameter and stroke; this was difficultto achieve at the time with any degree of precision.

In his description Philon stated that the cylinders were first hammered externallyto increase their resistance, bored internally with a drill and then polished. As forthe pistons, he mentions the geometric precision of the lathe enhanced by polishing.Since even the smallest tolerances cannot prevent loss of compression, recourse togaskets is inevitable: Philon mentions two, one at the mouth of the cylinders and the