Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-19T09:02:53.341Z Has data issue: false hasContentIssue false
  • English
  • Français

Computational efficiency of multi-body systems dynamic models

Published online by Cambridge University Press:  16 June 2021

Cs. Antonya Open the ORCID record for Cs. Antonya [Opens in a new window]  and
R. G. Boboc Open the ORCID record for R. G. Boboc [Opens in a new window]
Cs. Antonya
Affiliation:
Transilvania University of Brasov, 29 Eroilor, 500036 Brasov, Romania
R. G. Boboc*
Affiliation:
Transilvania University of Brasov, 29 Eroilor, 500036 Brasov, Romania
*
*Corresponding author. Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

For several decades, simulation and analysis of mechanisms have been performed with dedicated computer-aided engineering software that implements general dynamic formulations, known in the literature as multi-body systems (MBS) formulations. The MBS name is related to the structure of the mechanism, which is often considered to be a collection of bodies interconnected by mechanical joints (pairs). Nevertheless, only a few formulations are really based on a true multi-body mechanical model, while many others instantiate mathematically quite different mechanical concepts. This paper aims to identify and discuss the mechanical models that fundament the main multi-body mathematical formulations known in the literature. The main features of each model are outlined, based on a detailed presentation of the structure and equations of motion, together with their link with the kinematic and dynamic formulations. A comparative study related to computational efficiency is then presented for the identified main models, based on a test mechanism. Comparative advantages and disadvantages are discussed at the end, considering the identified mechanical models.

Keywords

multi-body systemsmulti-particle systemsdynamicscomputational efficiency
Type
Article
Information
Robotica , Volume 39 , Issue 12 , December 2021 , pp. 2333 - 2348
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Paraskevopoulos, E. and Natsiavas, S., “A new look into the kinematics and dynamics of finite rigid body rotations using Lie group theory,” Int. J. Solids Struct. 50(1), 57–72 (2013).CrossRefGoogle Scholar
Haug, E. J., “Elements and Methods of Computational Dynamics,” In: Computer Aided Analysis and Optimization of Mechanical System Dynamics (Springer, Berlin, Heidelberg, 1984) pp. 3–38.CrossRefGoogle Scholar
Haug, E., Computer-Aided Kinematics and Dynamics of Mechanical Systems, (vol. I, Allyn & Bacon, Inc., MA, USA, 1989).Google Scholar
Shabana, A. A., Dynamics of Multibody Systems (Cambridge University Press, Cambridge, 2013).CrossRefGoogle Scholar
García de Jalón, J. and Bayo, E., Kinematic and Dynamic Simulation of Multibody Systems: the Real Time Challenge (Springer, Berlin, 1994).CrossRefGoogle Scholar
Schiehlen, W. O. and Kreuzer, E. J., “Symbolic Computerized Derivation of Equations of Motion,” In: Dynamics of Multibody Systems (K. Magnus ed.) (Springer-Verlag, Berlin, Heidelberg, New York, 1978), pp. 290–305.10.1007/978-3-642-86461-2_24CrossRefGoogle Scholar
Schiehlen, W. O., Multi-body Systems Handbook (Springer-Verlag, Berlin, Heidelberg, 1990).CrossRefGoogle Scholar
Attia, H. A., “Computational dynamics of three-dimensional closed-chains of rigid bodies,” Appl. Math. Comput. 172(1), 286–304 (2006).Google Scholar
Talabã, D., “A Particle Model for Mechanical Systems Simulation: A Model Based Overview of Multi-Body Systems Formulations,” In: Virtual Nonlinear Multi-body Systems (NATO Advanced Study Institute, Prague, 2000) pp. 189–195.Google Scholar
Talabã, D. and Antonya, C., “The Multi-Particle System (MPS) Model as a Tool for Simulation of Mechanisms with Rigid and Elastic Bodies,” Proceedings of the 3th International Symposium on Multi-Body Dynamics: Monitoring and Simulation Techniques (Loughborough, 2004) pp. 111–119.Google Scholar
Attia, H. A., “Equations of motion of planar mechanical systems based on particle dynamics and a recursive algorithm,” Proc. Inst. Mech. Eng. K-J. Multi-Body Dyn. 218, 31–38 (2004).Google Scholar
Talabã, D. and Antonya, C., “Dynamic Models in Multi-Body Systems,” In: Product Engineering: Eco-Design, Technologies and Green Energy (D. Talaba and T. Roche, eds.) (Springer, Netherlands, 2005) pp. 227–252.Google Scholar
Orlandea, N., Chace, M. A. and Calahan, D. A., “A sparsity-oriented approach to the dynamic analysis and design of mechanical system—Part 1,” J. Eng. Ind. Aug, 99(3), 773–779 (1977).CrossRefGoogle Scholar
Nikravesh, P. E. and Chung, I. S., “Application of euler parameters to the dynamic analysis of three-dimensional constrained mechanical systems,” J. Mech. Des. 104(4), 785–791 (1981).Google Scholar
Wittenburg, J., Dynamics of Systems of Rigid Bodies (Teubner, Stuttgart, 1977).10.1007/978-3-322-90942-8CrossRefGoogle Scholar
De Jalón, J. G., Unda, J. and Avello, A., “Natural coordinates for the computer analysis of multibody systems,” Comput. Methods Appl. Mech. Eng. 56(3), 309–327 (1986).CrossRefGoogle Scholar
Saura, M., Segado, P. and Dopico, D., “Computational kinematics of multibody systems: Two formulations for a modular approach based on natural coordinates,” Mech. Mach. Theory 142(2019), 103602 (2019).CrossRefGoogle Scholar
Nikravesh, P. E., Formulation, Programming with MATLAB§, and Applications (Taylor & Francis, CRC Press, Boca Raton, 2018).Google Scholar
Nikravesh, P., Computer-Aided Analysis of Mechanical Systems (Prentice Hall, Inc., River, NJ, USA, 1988).Google Scholar
Flores, P. and Lankarani, H. M., Contact Force Models for Multibody Dynamics (Springer International Publishing, Cham, 2016) pp. 53–91.10.1007/978-3-319-30897-5_4CrossRefGoogle Scholar
Müller, A., “Generic mobility of rigid body mechanisms,” Mech. Mach. Theory 44(6), 1240–1255 (2009).CrossRefGoogle Scholar
Roberson, R. E. and Schwertassek, R., Dynamics of Multi-Body Systems (Springer Verlag, Berlin, 1988).CrossRefGoogle Scholar
Huang, T., Yang, S., Wang, M., Sun, T. and Chetwynd, D., “An approach to determining the unknown twist/wrench subspaces of lower mobility serial kinematic chains,” J. Mech. Rob. 7(3), 031003 (2015).CrossRefGoogle Scholar
Talabã, D., “Mechanical models and the mobility of robots and mechanisms,” Robotica 33(1), 1–13 (2014).Google Scholar
Gebel, E. S., “Mathematical modeling of dynamics of multi-lever linkages,” Procedia Eng. 100(2015), 1562–1571 (2015).CrossRefGoogle Scholar
de Jalón, J. G., “Twenty-five years of natural coordinates,” Multibody Syst. Dyn. 18(1), 15–33 (2007).10.1007/s11044-007-9068-0CrossRefGoogle Scholar
Pappalardo, C. M., “A natural absolute coordinate formulation for the kinematic and dynamic analysis of rigid multibody systems,” Nonlinear Dyn. 81(4), 1841–1869 (2015).CrossRefGoogle Scholar
Flores, P., Machado, M., Seabra, E. and Tavares da Silva, M., “A parametric study on the Baumgarte stabilization method for forward dynamics of constrained multibody systems,” J. Comput. Nonlinear Dyn. 6(1), 011019 (2011).CrossRefGoogle Scholar
Marques, F., Souto, A. P. and Flores, P., “On the constraints violation in forward dynamics of multibody systems,” Multibody Syst. Dyn. 39(4), 385–419 (2017).CrossRefGoogle Scholar
Lin, S. and Huang, J. N., “Stabilization of Baumgarte’s method using the Runge-Kutta approach,” J. Mech. Des. 124(4), 633–641 (2002).CrossRefGoogle Scholar
M. S. C. ADAMS/ View help – Adams 2014.Google Scholar
Yang, L., Xue, S. and Yao, W., “Application of Gauss principle of least constraint in multibody systems with redundant constraints,” Proc. Inst. Mech. Eng. Part K J. Multi-body Dyn. (2020). doi: http://dx.doi.org/10.1177/1464419320975301CrossRefGoogle Scholar
Flores, P., and Nikravesh, P. E., “Comparison of Different Methods to Control Constraints Violation in Forward Multibody Dynamics,” International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, vol. 55966 (American Society of Mechanical Engineers, 2013) p. V07AT10A028.Google Scholar