Abstract
A new index reduction approach is developed for the inverse dynamics simulation of underactuated mechanical systems. The underlying equations of motion contain both holonomic and servo constraints. The proposed method is applied to a very general and versatile formulation of cranes. The numerical results demonstrate the functional efficiency of the method.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Kirgetov VI (1967) The motion of controlled mechanical systems with prescribed constraints (servoconstraints). J Appl Math Mech 31(3):465–477
Blajer W (1997) Dynamics and control of mechanical systems in partly specified motion. J Franklin Inst 334B(3):407–426
Lam SH (1998) On Lagrangian dynamics and its control formulations. Appl Math Comput 91:259–284
Uhlar S, Betsch P (2009) A rotationless formulation of multibody dynamics: Modeling of screw joints and incorporation of control constraints. Multibody Syst Dyn 22(1):69–95
Blajer W, Seifried R, Kołodziejczyk K (2013) Diversity of servo-constraint problems for underactuated mechanical systems: a case study illustration. Solid State Phenom 198:473–482
Seifried R, Blajer W (2013) Analysis of servo-constraint problems for underactuated multibody systems. Mech Sci 4(1):113–129
Blajer W (2014) The use of servo-constraints in the inverse dynamics analysis of underactuated multibody systems. J Comput Nonlinear Dynam 9(4):041008/1-11
Kunkel P, Mehrmann V (2004) Index reduction for differential-algebraic equations by minimal extension. Z Angew Math Mech (ZAMM) 84(9):579–597
Altmann R, Betsch P, Yang Y (2015) Index reduction by minimal extension for the inverse dynamics simulation of cranes. Accepted for Publication in Multibody System Dynamics. doi:10.1007/s11044-015-9471-x
Blajer W, Kołodziejczyk K (2004) A geometric approach to solving problems of control constraints: theory and a DAE framework. Multibody Syst Dynam 11(4):343–364
Kiss B, Lévine J, Müllhaupt P (1999) Modelling, flatness and simulation of a class of cranes. Electr Eng 43(3):215–225
Ascher UM, Petzold LR (1998) Computer methods for ordinary differential equations and differential-algebraic equations. SIAM, Philadelphia
Blajer W, Kołodziejczyk K (2011) Improved DAE formulation for inverse dynamics simulation of cranes. Multibody Syst Dynam 25(2):131–143
Blajer W, Kołodziejczyk K (2005) A computational framework for control design of rotary cranes. In: Goicolea JM, Cuadrado J, Garcia Orden JC (ed) Proceedings of ECCOMAS thematic conference on advances in computational multibody dynamics (CD-ROM), Madrid, June 21–24
Acknowledgments
The second author was supported by the ERC Advanced Grant ‘Modeling, Simulation and Control of Multi-Physics Systems’ MODSIMCONMP. The third author was supported by the Deutsche Forschungsgemeinschaft (DFG) under Grant BE 2285/12-1. This support is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Betsch, P., Altmann, R., Yang, Y. (2016). Numerical Integration of Underactuated Mechanical Systems Subjected to Mixed Holonomic and Servo Constraints. In: Font-Llagunes, J. (eds) Multibody Dynamics. Computational Methods in Applied Sciences, vol 42. Springer, Cham. https://doi.org/10.1007/978-3-319-30614-8_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-30614-8_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-30612-4
Online ISBN: 978-3-319-30614-8
eBook Packages: EngineeringEngineering (R0)