Abstract
This chapter includes the main components necessary to formulate the dynamics of planar multibody systems. In this process, the fundamental issues associated with embryogenesis of multibody systems are presented. The main types of coordinates utilized in the formulations of general planar multibody systems are described. In addition, the fundamental characteristics of some relevant constraint equations are also presented in this chapter. Then, the key aspects related to the dynamic analysis of planar multibody mechanical systems are discussed. The formulation of multibody system dynamics adopted here uses the generalized absolute coordinates to derive the multibody system equations of motion. This formulation results in the establishment of a mixed set of ordinary differential and algebraic equations, which are numerically solved in order to predict the dynamic behavior of multibody systems.
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References
Alonso M, Finn EJ (1981) FÃsica: um curso universitário. Vol I—Mecânica, Editora Edgard Blücher Ltda, São Paulo, Brasil
Ambrósio J, VerÃssimo P (2009) Sensitivity of a vehicle ride to the suspension bushing characteristics. J Mech Sci Technol 23:1075–1082
Ambrósio JAC, Neto MA, Leal RP (2007) Optimization of a complex flexible multibody systems with composite materials. Multibody Syst Dyn 18:117–144
Anand DK, Cunniff PF (1973) Engineering mechanics dynamics. Houghton Mifflin Company, Boston
Arnold VI (1987) Métodos matemáticas da mecânica clássica. Editora Mir Moscow, Soviet Union
Burton P (1979) Kinematics and dynamics of planar machinery. Prentice-Hall, Englewood Cliffs, New Jersey
Ceccarelli M (1998) Mechanism schemes in teaching: a historical overview. J Mech Des 120:533–541
Ceccarelli M, Cigola M (2001) Trends in the drawing of mechanisms since the early Middle Ages. Proc Inst Mech Eng Part C J Mech Eng Sci 215:269–289
Chace MA (1967) Analysis of the time-dependence of multi-freedom mechanical systems in relative coordinates. J Eng Ind 89:119–125
Chapra SC, Canale RP (1989) Numerical methods for engineers. 2nd ed. McGraw-Hill
Eich-Soellner E, Führer C (1998) Numerical methods in multibody dynamics. Teubner-Verlag Stuttgart, Germany
Flores P (2015) Concepts and formulations for spatial multibody dynamics. Springer, Berlin
Flores P, Claro JCP (2007) Cinemática de mecanismos. Almedina, Portugal
Flores P, Ambrósio J, Claro JCP, Lankarani HM (2008) Kinematics and dynamics of multibody systems with imperfect joints: models and case studies. In lecture notes in applied and computational mechanics, vol 34. Springer, Berlin, Heidelberg, New-York
Galileo G (1638) Dialogues concerning two new sciences (trans: Crew H, de Salvio A, 1914, reprinted in 1956). Macmillan, New York
Hartog JP (1948) Mechanics. Dover Publications, New York
Haug EJ (1989) Computer-aided kinematics and dynamics of mechanical systems—volume I: basic methods. Allyn and Bacon, Boston, Massachusetts
Huston RL (1990) Multibody dynamics. Butterworth-Heinemann, Boston, Massachusetts
Jálon JG (2007) Twenty-five years of natural coordinates. Multibody Syst Dyn 18:15–33
Jálon JG, Bayo E (1994) Kinematic and dynamic simulations of multibody systems: the real-time challenge. Springer, New York
Levinson L (1970) Fundamentals of engineering mechanics. Mir Publishers, Moscow
Meireles F (2007) Kinematics and dynamics of biomechanical models using multibody systems methodologies: a computational and experimental study of human gait. M.Sc. Dissertation, University of Minho, Guimarães, Portugal
Müller A (2009) Generic mobility of rigid body mechanisms. Mech Mach Theory 44(6):1240–1255
Newton I (1687) Philosophiae Naturalis Principia Mathematica. London
Nikravesh PE (1988) Computer-aided analysis of mechanical systems. Prentice Hall, Englewood Cliffs
Nikravesh PE (2007) Initial condition correction in multibody dynamics. Multibody Syst Dyn 18:107–115
Nikravesh PE (2008) Planar multibody dynamics: formulation, programming, and applications. CRC Press, London
Orlandea N, Chace MA, Calahan DA (1977) A sparsity oriented approach to the dynamic analysis and design of mechanical systems—part 1 and 2. J Eng Ind 99:773–784
Paul B, Krajcinovic D (1970) Computer analysis of machines with planar motion, part 1—kinematics, part 2—dynamics. J Appl Mech 37:697–712
Pombo J, Ambrósio J (2008) Application of a wheel-rail contact model to railway dynamics in small radius curved tracks. Multibody Syst Dyn 19:91–114
Rahnejat H (2000) Multi-body dynamics: historical evolution and application. Proc Inst Mech Eng Part C J Mech Eng Sci 214:149–173
Reuleaux F (1963) The kinematics of machinery. Dover, New York
Schiehlen W (1990) Multibody systems handbook. Springer, Berlin
Seabra E, Flores P, Silva JF (2007) Theoretical and experimental analysis of an industrial cutting file machine using multibody systems methodology. In: Bottasso CL, Masarati P, Trainelli L (eds) Proceedings of ECCOMAS thematic conference multibody dynamics 2007. Milan, Italy, 25–28 June, 12 p
Shabana AA (1989) Dynamics of multibody systems. Wiley, New York
Sheth PN, Uicker JJ (1971) IMP (Integrated Mechanism Program): a computer-aided design analysis system for mechanisms and linkages. J Eng Ind 94(2):454–464
Shigley JE, Uicker JJ (1995) Theory of machines and mechanisms. McGraw Hill, New York
Silva M, (2003) Human motion analysis using multibody dynamics and optimization tools. Ph.D. Dissertation, Technical University of Lisbon, Portugal
Silva MPT, Ambrósio JAC (2002) Kinematic data consistency in the inverse dynamic analysis of biomechanical systems. Multibody Syst Dyn 8:219–239
Späth H (1995) One dimensional spline interpolation algorithms. AK Peters, Wellesley
Targ S (1976) Curso Técnico-prático de Mecânica. Lopes da Silva Editora, Rio de Janeiro
Wehage RA, Haug EJ (1982) Generalized coordinate partitioning for dimension reduction in analysis of constrained systems. J Mech Des 104:247–255
Zhu W-H, Piedboeuf J-C, Gonthier Y (2006) A dynamics formulation of general constrained robots. Multibody Syst Dyn 16:37–54
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Flores, P., Lankarani, H.M. (2016). Multibody Systems Formulation. In: Contact Force Models for Multibody Dynamics. Solid Mechanics and Its Applications, vol 226. Springer, Cham. https://doi.org/10.1007/978-3-319-30897-5_4
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DOI: https://doi.org/10.1007/978-3-319-30897-5_4
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