Computer-Aided Analysis of Rigid and Flexible Mechanical Systems

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Series E: Applied Sciences - Vol. 268

Computer-Aided Analysis of Rigid and Flexible Mechanical Systems

ediled by

Manuel F.O. Seabra Pereira and

Jorge A.C. Ambr6sio lnstituto de Engenharia Mecânica, Insli tulo Superior Tecnico, Lisboa, Portugal

Springer Science+Business Media, a.v.

Proceedings of the NATO Advanced Study Institute on Computer-Aided Analysis of Rigid and Flexible Mechanical Systems Tr6ia, Portugal June 27-July 9, 1993

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

ISBN 978-94-010-4508-7 ISBN 978-94-011-1166-9 (eBook)

DOI 10.1007/978-94-011-1166-9

Printed on acid-free paper

AII Rights Reserved © 1994 Springer Science+Business Media Dordrecht

Originally published by Kluwer Academic Publishers in 1994 Softcover reprint ofthe hardcover lst edition 1994 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photo­copying, recording or by any information storage and retrieval system, without written permission from the copyright owner.

NA TO·ADV ANCED STUDY INSTITUTE COMPUTER AIDED ANALYSIS OF RIGID AND FLEXIBLE MECHANICAL SYSTEMS

TROIA, PORTUGAL 27 JUNE· 9 JULY, 1993

MAIN SPONSORS:

NATO: U.S. Army T ARDEC: NSF:

OTHER SPONSORS

JNICT:

FLAD: IDMEC: CEMUL:

DIRECTOR

North Atlantic Treaty Organization United States Army, TARDEC National Science Foundation

Junta Nacional de Investigar;ao Cientffica e Tecnologica Fundar;ao Luso Americana para 0 Desenvolvimento Instituto de Engenharia Meciinica Centro de Mecanica e Materiais da Universidade Tecnica de Lisboa

Manuel F.O. Seabra Pereira, IDMEC-Instituto Superior Tecnico, Portugal

SCIENTIFIC COMMITTEE:

Michel Geradin, Universite de Liege, Belgium Edward J. Haug, University of Iowa, USA Manfred Hiller, University of Duisburg,Gemlany Parviz Nikravesh, University of Arizona, USA

CONTENTS

List of Participants ix

Preface xv

PART I - Methods in Rigid Multibody Dynamics 1

Constrained Multibody Dynamics R. A Wehag,?, M.J. Belczynski 3

Construction of the Equations of Motion for Multibody Dynamics Using Point and Joint Coordinates

P. A Nikravesh, H. E. Affifi 31

Dynamics of Multibody Systems with Minimal Coordinates M. Hiller, A Kecskemethy 61

Symbolic Computations in Multibody Systems W. Schiehlen 101

On-Line Dynamic Analysis of Mechanical Systems T. R. Kane 137

Topological Description of Articulated Systems J. Wittenburg 159

PART n - Dynamics of Flexible Mechanical Systems 197

Flexibility in Multibody Dynamics With Applications to Crash worthiness J.AC. Ambr6sio, M. S. Pereira 199

Finite Element Modelling Concepts in Multibody Dynamics M. Geradin, A Cardona, D.B. Doan, J. Duysens 233

Kinematic and Dynamic Simulation of Rigid and Flexible Systems With Fully Cartesian Coordinates

J. Garcia de Jalon, J. Cuadrado, A Avello, J.M. Jimenez 285

Computer Implementation of Flexible Multibody Equations A A Shabana 325

Flexibility Effects in Multibody Systems R. L. Huston, Y. Wang 351

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PART HI " Kinematic Aspects of Multibody Systems 377

On Twist and Wrench Generators and Annihilators J. Angeles 379

Application of Computer Aided Kinematics to Modelling of Contacts in Robotic Manipulation

J. de Schutter, H. Bruyninckx, S. Dutre 413

PART IV "Computational Issues and Numerical Methods 445

Reduction of Multibody Simulation Time by Appropriate Fonnulation of Dynamical System Equations

R. Schwertassek 447

Computational Challenges in Mechanical Systems Simulation L. R. Petzold 483

Numerical Integration of Second Order Differential-Algebraic Systems in Flexible Mechanism Dynamics

A. Cardona, M. Geradin 501

PART V " ManlMachine Interaction and Virtual Prototyping 531

Dynamic Simulation for Vehicle Virtual Prototyping J. S. ,Freeman,E.J. Haug,J. G. Kuhl,F.F. Tsai 533

Man/Machine Interaction Dynamics and Perfonnance Analysis, Biomechanics and NDISCOS Multibody Equations

R~~~ ill

INDEX 609

LIST OF PARTICIPANTS

Lecturers:

Jorge AmbrOsio IDMEC - P610 do I.S.T., Av. Rovisco Pais, 1096 Lisboa, Portugal

Jorge Angeles McGill University, 817 Sherbrooke Street West, Montreal, Quebec H3A 2K6, Canada

Alberto Cardona INTEC, Giiemes 3450, 3000 Santa Fe, Argentina

Jeffrey S. Freeman Center for Computer Aided Design, Coli. of Engineering, University of Iowa, Iowa City, Iowa 525242, USA

Harold P. Frisch Robotics Branch, Code 714.1, Goddard Space Center, Greenbelt, Maryland 20771, USA

Michel Geradin LTAS - Universite de Liege, Rue Ernest Solvay 21, 4000 Liege, Belgium

Manfred Hiller Fachgebiet Mechanik, Universitat Duisburg, Lotharstr. 1,4100 Duisburg, Germany

Ronald L. Huston Dept. of Mech. and Industrial Eng., Univ. of Cincinatti, Cincinatti, Ohio 45221-0072, USA

J. Garcia de Jalon CElT, po Manuel de LardiZlibal 15,20009 San Sebastian, Guipuzcoa, Spain

Thomas R. Kane Division of Applied Mechanics, Durand Bldg, Stanford Univ., Stanford, CA 94305, USA

Parviz Nikravesh Dept. of Aerospace and Mech. Engng., University of Arizona, Tucson, AZ 85721, USA

Manuel S. Pereira IDMEC - P610 do I.S.T., Av. Rovisco Pais, 1096 Lisboa, Portugal

Linda Petzold Comp.Scie.Depl.(4-192 EE/CS Big), 200 Union Street SE, Univ.of Minnesota, Minneapolis MN55455, USA

W. Schiehlen Institut B fur Mechanik, Pfaffenwaldring 9, Univ. Stuttgart, D-7ooo Stuttgart 80, Germany

J. De Schutter K.U.L., Afdel. Mech. Konst. en Prod., Celestijnenlaan 300 B, B-3OO1 Hevcrlee, Belgium

Richard Schwertassek Inst. fur Dynamik der Flugsystem, DLR Oberpfaffenhoffen, D-8031 Wessling, Germany

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x

Abmed Sbabana University of Illinois at Chicago, Dept. of Mech. Engng.(M/C 251), 2039 Engineering Research Facility, 842 West Taylor Street, Chicago, Illinois 6OfIJ7-7022, USA

Roger Webage System Simulation & Tech. Division, AMSTA-RY, U.S. Army T ARDEC, Warren MI 48397-5000, USA

J. Wittenburg Institut fur Technische Mechanik, Universitat Karlsruhe, D-76139 Karlsruhe, Germany

Participants:

Joao Abrantes Laborat6rio Biomeciinica, Faculdade de Motricidade Humana, 1499 Lisboa, Portugal

Venkatesb Agaram L.O.M., Dept. Mecanique, Swiss Federal Inst. of Techn., CH-1015 Lausanne, Switzerland

Sunil Agrawal Ohio University, Dept. Mech. Engng., Athens, OH 45701, USA

Claudia Oitaven Alves Instituto Gulbenkian de Ciencia, Centro de Biologia, R. Quinta Grande, Apanado 14,2781 Oeiras , Portugal

Martin Anantbaraman Universitat Duisburg, FB 7 FG 16, Lotharstraf3e 1,47057 Duisburg, Germany

Kurt S. Anderson Institut fur Mechanik, TH Darmstadt, Hochschulstrasse 1, D-6100 Darmstadt, Germany

Daniel Bach Institut fur Mechanik, HG F38.1, ETH Zentrum, CH-8092 Zurich, Switzerland

Behnam Bahr Wichita State Univ., Mech. Eng. Dept., 1845 N. Fairmount, Wichita, KS67260-0035, USA

J. Infante Barbosa ENIDH - Escola Nautica, Av. Bonneville Franco, Parro d'Arcos 2780 Oeiras, Portugal

Eduardo Bayo University of California, Dept. of Mech. Engng., Santa Barbara, CA 93106, USA

M. Belczynski System Simulation & Tech. Division, U.S. Army TACOM, (AMSTA-RY), Warren, MI 48397-5000, USA

F. Bennis Laboratoire d'Automatique de Nantes, Ecole Centrale Nantes, URA CNRS 823, 1 Rue de la Noe, 44072 Nantes Cedex 03, France

Roman Bogacz Inst. of Fundamental Tech. Res., Polish Academy of Sciences, ul. Swietokrzyska 21, 00-049 Warsaw, Poland

Marco Borri Dipart. di Ingegn. Aerospaziale, Politecnico di Milano, via Golgi 40, 20133 Milano, Italy

Hans Brauchli Institut fur Mechanik, HG F38.1, ETH Zentrum, CH-8092 Zurich, Switzerland

Pasquale Campanile C. Ricerche FIAT, Ente Veicoli/Calcoli, Strada Torino 50, 10043 Orbassano (TO), Italy

Marco Ceccarelli Dept Industrial Engng., Univ. of Cassino, Via Zamosch 43, 03043 Cassino (FR), Italy

J.Choi Dept. Mech. Eng (M/C 251)-2039 ERF, Univ. of Illinois at Chicago, Box 4348, Chicago, IL 60680, USA

Kenneth Clark Mathematical Sc. Div., U.S. Army Res. Office, Research Triangle Park, NC 27709, USA

Jose Sa da Costa I.S .T.- DEM, Av. Rovisco Pais, 1096 Lisboa, Portugal

M. A. Crisfield Imperial Coll1ege, Dept. Aero., Prince Consort Road, London SW7 2BY, United Kingdom

J. Cuadrado University of Navarra, Manuel de Lardizabal 15,20009 San Sebastian, Spain

Joiio P. Dias Instituto Superior Tecnico, Dept. Eng. Meciinica, A v. Rovisco Pais, 1096 Lisboa, Portugal

D.B.Doan L.T.A.S., Universite de Liege, Rue Ernest Solvay 21,4000 Liege, Belgium

Robert Dombroski U.S.Army Ardec, SMCAR-FSA-F Bldg 61N, Picatinny Arsenal- NJ 07806-5000, USA

J. Duysens L.T.A.S ., University of Liege, 21, Rue Ernest Solvay 21, B-4000 Liege, Belgium

Haluk Erol Istanbul Technical University, Faculty of Mech. Engng., Gumussuyu, Istanbul, Turkey

Yanis Erotokritos Inst. of Sound & Vibration Research, Univ. of Southampton, S09 5NH, United Kingdom

Christian Goualou Ecole Centrale de Paris, L.R.S.A. - Res. Lab. for Auto. Safety, Grande Voie des Vignes, 92295 Chatenay-Malabry, France

Simon Guest Univ Cambridge, Dept.of Eng.,Trumpington Street, Cambridge CB2 IPZ,United Kingdom

John Hansen Technical University of Denmark, Dept. of Solid Mechanics, Building 421,2800 Lyngby, Denmark

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Michael Hansen Technical University of Denmark, Dept. of Solid Mechanics, Building 404, 2800 Lyngby, Denmark

Christian Hardell Lulea Univ. of Technology, Division of Computer Aided Design, S-95187 Lulea, Sweden

S. G.Hutton Univ. of British Columbia, Dept. of Mech. Engng, 2324 Main Mall, Vancouver, BC ,V6T lZ4, Canada

How-Young Hwang 1100 Arthur St., Apt. I-I, Iowa City, IA 52240, USA

J. M. Jimenez University of Navarra, Manuel de Lardizabal 15, 20009 San Sebastian, Spain

Andres Kecskemethy Fachgebiet Mechatronik, Universitat Duisburg, Lotharstr. 1,47057 Duisburg, Germany

Albrecht Keil Inst. fur Mechatronik, Reichenhainer Str. 88, P.O. Box 408, 0-9022 Chemnitz, Germany

Willy Koppens TNO Road-Vehicles Research Institute, P.O. Box 6033, 2600 JA Delft, Netherlands

Hamid Lankarani Wichita State University, Mech. Engng. Dept., Wichita, KS 67260-0035, USA

Dirk Lefeber Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium

Tomasz Lekszycki lost. Fund. Tech. Research, Swietokrzyska 21, 00-049 Warszawa, Poland

Bill Lipsett Dept. of Mechanical Engng., University of Alberta, Edmonton Alberta T6G 2G8, Canada

Jean·Pierre Mariot Lab. de Mecanique Prod. et Mat., FacuIte des Sciences - B.P. 535,72017 Le Mans, France

J. P. Meijaard Lab. Eng. Mechanics, Delft Univ. of Tech., Mekelweg 2, NL-2628 CD Delft, Netherlands

Frank Melzer Inst. B of Mechanics, Univ. Stuttgart, Pfaffenwaldring 9,0-70550 Stuttgart, Germany

Arkadiusz Mezyk Silesian Tech. Univ. Gliwice, Eng. Mech. Dept., Konarskiego 18a, 44-100 Gliwice, Poland

Fran~ois Minne Laboratoire de Genie Mecanique, Le MonLHouy - B.P. 311, 59304 Valenciennes, France

Carlos A. Mota Soares IDMEC - P6lo do I.S.T., Av. Rovisco Pais, 1096 Lisboa, Portugal

John McPhee University of Waterloo, Systems Des.Eng., Ontario, N2L 3G 1, Canada

Alvaro Costa Neto Universidade de Si'io Paulo, Esc. de Eng. de Si'io Carlos, Av. Dr. Carlos Botelho 1465, C.P. 359, CEP 13560-250, Si'io Carlos - SP, Brasil

Juana Mayo Nunez

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Escuela Sup. de Ing. Indust., Dept. de Ing. Mec. y Materiales, Av. Reina Mercedes sin, 41012 Sevilla, Spain

Jose Luis H. Oliver Univ. Politecnica Valencia, Dept. Ingenieria Mecanica, 46022 Valencia, Spain

Verlinden Olivier Faculte Poly technique de Mons, 31 Boulevard Dolez, 7000 Mons, Belgium

Martin Otter Insti. for Robotics and Syst. Dynam., DLR Oberpfaffenhofen, D-8031 Wessling, Germany

TugrulOzel Dokuz Eylul University, Dept. Mech. Engng., Bornova 35100, Izmir, Turkey

Ettore Pennestri Univ. di Roma "Tor Vergata", Dip. Ingegneria Meccanica, Via Della Ricerca Scientifica, 00133 Roma, Italy

Vincent Pesch Univ. of Illinois at Urbana-Champaign, 1206 W. Green Street, Urbana, 1161801, USA

Jean-Marc Pini Dassault Aviation - Centre Spatial, 17 Av. Didier Daurat, B.P. 23, 3 I 70 I Blagnac, France

Enrico Pisino C. Ricerche FIAT, Ente Veicoli/Calcoli, Strada Torino 50,10043 Orbassano (TO), Italy

Marco Quadrelli Comput. Modelling Center, Georgia Institute of Tech. Atlanta, GA 30332-0356, USA

Udo Rein Inst. A fur Mechanik, Univ. Stuttgart, Pfaffenwaldring 9, D-70550 Stuttgart, Germany

David Russell Clarkson University, Dept. of Mech. and Aeron. Engng., Old Main, Potsdam, New York 13699-5725, USA

Ernst Dieter Sach Deutsche Aerospace AG., Dept. RTT22, Poslfach 801169, 8000 Munich 80, Germany

DelfSachau DLR - lost. fur Robotik und Syst Dyn., Oberpfaffenhofen, D-8031 - Wessling, Germany

Jean-Claude Samin Univ. Calholique de Louvain, Place du Levant 2, B-1348 Louvain-la-Neuve, Belgium

Saide Sarigul Dokuz Eylul University, Dept. Mech. Engng., Bornova 35100, Izmir, Turkey

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Ole Ivar Sivertsen Dept. of Machine Design, Norwegian Institute of Tech., N-7034 Trondheim, Norway

Miguel Sofer Institut fur Mechanik, HG F38.1, ETH Zentrum, CH-8092 Zurich, Switzerland

Annika Stensson Lulea Univ. of Technology, Division of Computer Aided Design, S-95187 Lulea, Sweden

Tahsin Sumer ArCelik A.S., Research Dept., Cayirova 41460, Istanbul, Turkey

G. Tzvetkova Bulgarian Academy of Sciences, G. Bonchev str., Blok 4, 1113 Sofia, Bulgaria

Ken Willmert Clarkson University, Dept. of Mech. and Aeron. Engng., Old Main, Potsdam, New York 13699-5725, USA

Harry Yae University of Iowa, Dept. of Mech. Engng., Iowa City, Iowa 52242, USA

YungM. Yoo Korea Automotive Tech. Inst., 1638-3 Seocho Dong, Seocho Ku - Seoul, Korea

E. V. Zakhariev Bulgarian Acad of Sciences, Inst.of Mech. & Biomechanics, G.Bontchev Street B14, 1113 Sofia, Bulgaria

PREFACE

This book contains the edited version of the lectures presented at the NATO ADVANCED STUDY INSTITUTE on "COMPUTER AIDED ANALYSIS OF RIGID AND FLEXIBLE MECHANICAL SYSTEMS". held in Troia. Portugal. from the 27 June to 9 July. 1993. and organized by the Instituto de Engenharia Mecanica. Instituto Superior Tecnico. This ASI addressed the state-of-art in the field of multibody dynamics. which is now a well developed subject with a great variety of formalisms. methods and principles. Ninety five participants. from twenty countries. representing academia. industry. government and research institutions attended this Institute. This contributed greatly to the success of the Institute since it encouraged the interchange of experiences between leading scientists and young scholars and promoted discussions that helped to generate new ideas and to defme directions of research and future developments.

The full program of the Institute included also contributed presentations made by participants where different topics have been explored. Such topics include: formulations and numerical aspects in rigid and flexible mechanical systems; object-oriented paradigms; optimal design and synthesis; robotics; kinematics; path planning; control; impact dynamics; and several application oriented developments in weapon systems. vehicles and crash worthiness. These papers have been revised and will be published by Kluwer in a special issue of the Journal of Nonlinear Dynamics and in a forthcoming companion book.

This book brings together. in a tutorial and review manner. a comprehensive summary of current work and is therefore suitable for a wide range of interests. ranging from the advanced student to the researchers and implementators concerned with advanced theoretical issues in multibody dynamics. The applicational aspects will help the readers to apprise the different approaches available today and their use and suitability as efficient design tools. This book is organized into five parts. each one addressing the state­of-art techniques and methods in the principal areas of study of the Institute:

Part I Part II Part III Part IV Part V

Formulations and Methods in Rigid Multibody Systems Dynamics of Flexible Multibody Systems Kinematics Aspects of Multibody Systems Computational Techniques and Numerical Methods Man/Machine Interaction and Virtual Prototyping

Different techniques that may be used to obtain efficient and general computer based dynamics modeling and simulation algorithms of rigid multibody systems are presented in Part I. The adequate choice of coordinates to represent the dynamics of multibody systems it is still a central issue in multibody dynamics. It is shown here that both recursive and absolute methods have their merits in the response to the growing complexity of mechanical systems. The use of augmented Lagrangian and penalty methods are still popular as a result of their conceptual simplicity and of permitting. with a minimum effort. the calculation of forces associated with the constraints. Projection methods. singular value decomposition and Gaussian triangularization techniques are also used. Here a set of independent coordinates are selected as a sub-set of the dependent ones. Formulations based on independent coordinates present. as main advantage. the reduction of the number of equations to be integrated. improving in the process the numerical stability of the problem. The integration of constraints. generally associated with cut-joints. is still possible. It is also shown that these methodologies are generally very efficient. leading to faster running programs. General graph theoretic approaches are also referred in this part of the book. Paths may be identified to define spanning trees of kinematic and dynamic computational sequences that are used to create efficient algorithms. The degree of parallelism of the equations is identified allowing an efficient implementation in multiprocessor computer platforms.

Finally special emphasis has been given to the automatic generation of the equations of motion of multibody systems. in close form. by means of symbolic manipulators. The computer time needed for the analysis of specific problems is greatly reduced with this approach. Specialized software such as NEWEUL and ROBOTRAN or general programs like MAPLE and MA THEMA TICA can be used for this purpose. Extension of this philosophy of development are computer codes included within the framework of Object Oriented Programming. Yet involving a high level of abstraction, they are easy to maintain. comparing to more conventional practices of code developmenl Regarding implementation and use of tools for modeling. generation. simulation and visualization of multibody systems. the problem of integration of CAD interfaces with current formalisms is also addressed by using of parametric multibody system databases.

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Part II includes different formulations and methodologies to incorporate the elastodynamic effects which are treated either using a finite element modeling concept or a moving frame approach. Aexible members are treated in a fully nonlinear manner including geometric stiffening and other second order effects, often encountered in fast speed operations. The more conventional linearized forms of substructuring and modal approaches, which are used to reduce the size of the problem, are reviewed. Nonlinear material behavior issues are also addressed as applied to crashworthiness of vehicles. The scope of application is extended to satellite antenna deployment problems, lightweight robots and vehicle dynamics.

Of special importance to the dynamics of multibody systems are kinematic considerations. Part III is devoted to kinematic issues of particular interest to the general dynamics problem of multibody systems. The concepts of twist and wrench generators and annihilators are developed, which can find extensive applications in the mechanics of grasping and provide a better understanding of problems associated with force and motion control of manipulators. In this part, new approaches to the modeling and motion specification of robotics manipulation tasks involving complex time varying motion constraints are presented, enhancing the state-of-art in complex applications in this area

Part IV is devoted to the computational challenges in mechanical systems analysis concerned with the reduction of multibody dynamics simulation time. Related developments and applications in solution methods in the fields of numerical methods, new algorithms and emerging new powerful parallel computer platforms are presented and analyzed. Recent contributions to time integration methods applicable to differential algebraic equations and problems related to time integration of flexible systems with high frequency content are thoroughly discussed here. The efficiency and robustness of numerical integration schemes in the modeling of multibody systems are also extensively discussed. New stable formulations for second order integration schemes are discussed as applied to constrained multibody systems. Computational challenges for efficient and reliable numerical methods are underlined. Some contributions on the aspects of stability, conditioning, accuracy and time step control are also included. Finally, ideas to combine the methods available in computer sciences and numerical mathematics are explored with the objective of taking advantage of interdisciplinary approaches in order to achieve, with acceptable accuracy levels, computer execution times beyond the present limits.

Virtual prototyping and human/machine interaction are fundamentally new capabilities that are now becoming available to address human factor based design issues. Part V includes contributions that address the key requirements and recent developments in operator-in-the-loop virtual prototyping capabilities. The objective is to access, in real-time, the behavior of mechanical systems with high level of fidelity in order to ensure valid human-machine interaction prediction. These emerging methodologies provide the framework for vehicle and other kinds of man operated machinery simulators. Biomechanical aspects, including muscleskeleton, and traditional multibody dynamics are pointed out to establish interdisciplinary lines of communication on human behavior analyses and mechanical systems design capabilities with the focus on human performance, ergonomics and cumulative injury potential.

Without the sponsorship and financial support of the Scientific Affairs Division of NATO, the U.S. Army - T ARDEC and the National Science Foundation, this ASI and book would not have been possible. The financial support of the Junta Nacional de Investiga~ao Cientifica e Tecnol6gica, the Funda~ao Luso­Americana para 0 Desenvolvimento and the Centro de Mecanica e Materiais da Universidade Tecnica de Lisboa is also gratefully acknowledged.

The Institute Director wishes to express his gratitude to Prof. Jorge A.C. Ambrosio for his help and cooperation in organizing the AS!. The editors are indebted to the members of the Organizing Committee, Prof. M. Geradin, Prof. E. Haug, Prof. M. Hiller and Prof. P. Nikravesh and also to Prof. C. Mota Soares for their help, advise and support in organizing the AS!. We would like to thank all lecturers and participants in the Institute for their active participation in the discussions and contributed presentations. The smooth running of the AS! is also a result of the competent work of Ms. Gloria Ramos, Miss Alexandra Andrade, and Mr. Amandio Rebelo from Centro de Mecanica e Materiais da Universidade Tecnica de Lisboa.

Lisbon, February 1994

Manuel F.O. Seabra Pereira

Jorge A.C. Ambrosio