Abstract
Manipulator dynamics tells us how the manipulator responds to joint torques and external forces. Each joint is normally equipped with an actuator which generates either linear forces or torques in the direction or around a fixed axis. The relatively simple joint torques and forces applied at each joint result in a complex overall motion of the robotic manipulator. One of the most important questions in robotics is thus how to find the joint torques that give the desired robot motion.
In this chapter we present the dynamic equations of a robotic manipulator in a well-defined but simple way. The chapter can be used in an introductory course to robotics and will give the reader a good understanding of how to model manipulator arms. Furthermore, as the formulation is based on the mathematically rigid formulations presented in the previous chapters, this chapter may also be interesting for readers already familiar with robotics and would like a mathematically more robust treatment than the one normally found in textbooks on robotics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Arnold, V. I. (1989). Mathematical methods of classical mechanics. Berlin: Springer.
Duindam, V. (2006). Port-based modeling and control for efficient bipedal walking robots. Ph.D. thesis, University of Twente.
Duindam, V., & Stramigioli, S. (2008). Singularity-free dynamic equations of open-chain mechanisms with general holonomic and nonholonomic joints. IEEE Transactions on Robotics, 24(3), 517–526.
Fossen, T. I. (2002). Marine control systems. Trondheim: Marine Cybernetics AS. 3rd printing.
From, P. J. (2012a). An explicit formulation of singularity-free dynamic equations of mechanical systems in Lagrangian form—part one: single rigid bodies. Modeling, Identification and Control, 33(2), 45–60.
From, P. J. (2012b). An explicit formulation of singularity-free dynamic equations of mechanical systems in Lagrangian form—part two: multibody systems. Modeling, Identification and Control, 33(2), 61–68.
From, P. J., Duindam, V., & Stramigioli, S. (2012). Corrections to “Singularity-free dynamic equations of open-chain mechanisms with general holonomic and nonholonomic joints”. IEEE Transactions on Robotics, 28(6), 1431–1432.
Lagrange, J.-L. (1788). In Mécanique analytique. Chez la Veuve Desaint.
Marsden, J. E., & Ratiu, T. S. (1999). Texts in applied mathematics. Introduction to mechanics and symmetry (2nd ed.). New York: Springer.
Murray, R. M., Li, Z., & Sastry, S. S. (1994). A mathematical introduction to robotic manipulation. Boca Raton: CRC Press.
Siciliano, B., Sciavicco, L., Villani, L., & Oriolo, G. (2011). Advanced textbooks in control and signal processing. Robotics: modelling, planning and control. Berlin: Springer.
Zefran, M., & Bullo, F. (2004). Robotics and automation handbook. Lagrangian dynamics. Boca Raton: CRC Press.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag London
About this chapter
Cite this chapter
From, P.J., Gravdahl, J.T., Pettersen, K.Y. (2014). Dynamics of Manipulators on a Fixed Base. In: Vehicle-Manipulator Systems. Advances in Industrial Control. Springer, London. https://doi.org/10.1007/978-1-4471-5463-1_7
Download citation
DOI: https://doi.org/10.1007/978-1-4471-5463-1_7
Publisher Name: Springer, London
Print ISBN: 978-1-4471-5462-4
Online ISBN: 978-1-4471-5463-1
eBook Packages: EngineeringEngineering (R0)