Summary
This paper focuses on investigating systematically the phenomenon of the bouncing motion when a robotic manipulator slides on a rough surface. From the viewpoint of rigid body dynamics, this phenomenon is related to the dynamical properties of a multi-rigid-body system subject to unilateral constraints with friction. Applying the LCP (Linear Complementary Problem) theory, we can classify the bouncing motion into two cases: one that is due to the action of inertia of system; the other that is due to the singularities of rigid-body model induced by friction forces. As an example of a planar multibody system with single unilateral constraint, the admissible set for a two-link manipulator is studied in detail. Meanwhile, The numerical results show that the paradoxes in rigid body model can occur even if the value of coefficient of friction is very small.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Brogliato B (1999) Nonsmooth Mechanics, 2nd edition. Springer, London, 1999.
Ivanov A P (2003) Singularities in the dynamics of systems with non-ideal constraints, J. Appl. Math. Mech 67(2): 185–192
Brach R M (1997) Impact Coefficients and Tangential Impacts Trans. ASME. J of App Mech 64: 1014–1016.1997
Pfeiffer F, Glocker CH (1998) Unilateral multibody contact. Netherlands: Kluwer Academic Publishers
Payr M, Glocker C (2005) Oblique Frictional Impact of a Bar: Analysis and Comparison of Different Impact Laws, Nonlinear Dynamics 41: 361–383
David E. Stewart (2000) Rigid-Body Dynamics with Friction and Impact, SIAM 42(1): 3–39
Gái]enot F, Brogliato B. (1999) New results on Painlevé paradoxes. European Journal of Mechanics A/Solids 18:653–677
Moreau J J, Jean M (1996) Numerical treatment of contact and friction: The contact dynamicsmethods, Engineering and System Design Analysis 4: 201–208
Lotstedt P (1981) Coulomb friction in two-dimensional rigid-body systems. ZAMM, 61: 605–615
R.I. Leine, B. Brogliato, H. Nijmeijer (2002) Periodic motion and bifurcations induced by the Painlevé paradox, European Journal of Mechanics A/Solids 21:869–896
Yu W, Mason M T (1992) Two-dimensional rigid-body collisions with friction, J Appl Mech 59: 635–642
Lecornu L (1905) Sur la loi de Coulomb. Comptes Rendu des Séances de l’Academie des Sciences 140(6):847–848
Baraff D (1991) Coping with Friction for Non-penetrating Rigid Body Simulation, Computer Graphics 25(4): 31–40
Zhao Zhen, Chen Bin, Caishan Liu and Jin Hai (2004) Impact Model Resolution On Painlevé’s Paradox. ACTA Mechanica Sinica 20(6):659–660
Peng S, Kraus P, Kumar V, Dupont P (2001) Analysis of rigid-body dynamic models for simulation of systems with frictional contacts, Journal of Applied Mechanics 68: 118–128
Ivanov A P (1997) The problem of constrainted Impact, J Appl Maths Mechs 61(3):341–253
B. Brogliato (2003) Some Perspectives on the Analysis and Control of Complementarity Systems, IEEE Transaction on automatic control 48(6): 918–935
Nijmeijer H, van der Shaft A J (1990) Nonlinear Dynamical Control Systems, New York: Springer-Verlag
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer
About this paper
Cite this paper
Liu, C., Zhen, Z., Chen, B. (2007). The Admissible Set for a Robotic System with Unilateral Constraint. In: Eberhard, P. (eds) IUTAM Symposium on Multiscale Problems in Multibody System Contacts. IUTAM Bookseries, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-5981-0_13
Download citation
DOI: https://doi.org/10.1007/978-1-4020-5981-0_13
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-5980-3
Online ISBN: 978-1-4020-5981-0
eBook Packages: EngineeringEngineering (R0)