Analysis of frictional impact in a multibody mechanical system requires a friction model capable of correct detection of all possible impact modes such as sliding, sticking, and reverse sliding. Conventional methods for frictional impact analysis have either shown energy gain or not developed for jointed mechanical system, and especially not for closed-chain multibody systems. This paper presents a general formulation for the analysis of impact problems with friction in both open- and closed-loop multibody mechanical systems. Poisson’s hypothesis is used for the definition of the coefficient of restitution, and thus the energy gains inherent with the use of Newton’s hypothesis are avoided. A canonical form of the system equations of motion using Cartesian coordinates and Cartesian momenta is utilized. The canonical momentum-balance equations are formulated and solved for the change in the system Cartesian momenta using an extension of Routh’s graphical method for the normal and tangential impulses. The velocity jumps are calculated by balancing the accumulated system momenta during the contact period. The formulation is shown to recognize all modes of impact; i.e., sliding, sticking, and reverse sliding. The impact problems are classified into seven types, and based on the pre-impact system configuration and velocities, expressions for the normal and tangential impulses are derived for each impact type. Examples including the tip of a double pendulum impacting the ground with some experimental verification, and the impact of the rear wheel and suspension system of an automobile executing a very stiff bump are analyzed with the developed formulation. [S1050-0472(00)02304-7]

Issue Section:
Technical Papers
Keywords:
impact (mechanical), mechanical contact, sliding friction, stiction, pendulums
Topics:
Closed kinematic chains, Equations of motion, Friction, Impulse (Physics), Pendulums, Suspension systems, Momentum, Multibody systems, Wheels
1.
Khulief, Y. A., Haug, E. J., and Shabana, A. A., 1983, “Dynamic Analysis of Large Scale Mechanical Systems with Intermittent Motion,” Tech. Report No. 83-10, University of Iowa, College of Engineering.
2.
Hunt
,
K. H.
, and
Grossley
,
F. R. E.
,
1975
, “
Coefficient of Restitution Interpreted as Damping in Vibroimpact
,”
ASME J. Appl. Mech.
,
42
, pp.
440
–
445
.
3.
Wittenburg, J., 1977, Dynamics of Systems of Rigid Bodies, Teubner, Suttgart.
4.
Wehage, R. A., 1980, “Generalized Coordinate Partitioning in Dynamic Analysis of Mechanical Systems,” Ph.D. dissertation, University of Iowa.
5.
Haug
,
E. J.
,
Wu
,
S. C.
, and
Yang
,
S. M.
,
1986
, “
Dynamics of Mechanical Systems with Coulomb Friction, Stiction, Impact and Constraint Addition and Deletion-I
,”
Mech. Mach. Theory
,
21
, No.
5
, pp.
401
–
406
.
6.
Lankarani, M. H., and Nikravesh, P. E., 1988, “Application of the Canonical Equations of Motion in Problems of Constrained Multibody Systems with Intermittent Motion,” Advances in Design Automation, DE-Vol. 14, pp. 417–423.
7.
Wittaker, E. T., 1937, Analytical Dynamics, 4th ed., Cambridge University Press, London.
8.
Keller
,
J. B.
,
1986
, “
Impact with Friction
,”
ASME J. Appl. Mech.
,
53
, pp.
1
–
4
.
9.
Han, I., and Gilmore, B. J., 1990, “Multibody Impact Motion with Friction-Analysis, Simulation, and Experimental Validation,” Proc. R. Soc. London, Ser. A, Chicago, Sept. 16–19.
10.
Kane, T. R., 1984, “A Dynamics Puzzle,” Stanford Mechanics Alumni Club Newsletter, p. 6.
11.
Brach
,
R. M.
,
1989
, “
Rigid Body Collision
,”
ASME J. Appl. Mech.
,
56
, pp.
133
–
138
.
12.
Routh, E. J., 1891, Dynamics of a System of Rigid Bodies, Fifth edition, MacMillan and Co., London.
13.
Wang
,
Y.
, and
Mason
,
M. T.
,
1992
, “
Two-Dimensional Rigid-Body Collisions with Friction
,”
ASME J. Appl. Mech.
,
59
, pp.
635
–
642
.
14.
Pereira, M. S., and Nikravesh, P. E., 1994, “Impact Dynamics of Multibody Systems with Frictional Contact using Joint Coordinates and Canonical Equations of Motion.” Proc. R. Soc. London, Ser. A, Proc. of NATO Advanced Science Institute on Computer-Aided Analysis of Rigid and Flexible Mechanical System, Troia, Portugal.
15.
Glocker, C., Pfeiffer, F., 1994, “Multiple Impacts With Friction in Rigid Multibody Systems.” Proc. R. Soc. London, Ser. A, Proc. Fifth Conf. On Non-linear Vibrations, Stability, and Dynamics of Structures and Machines, VPI State University, Blacksburg, VA.
16.
Cataldo, E., and Sampio, R., 1998, “Collision Between Rigid Bodies: Comparing Some Models.” Proc. Int. Symp. On Impact and Friction of Solids and Machines, Ottawa, Canada, pp. 172–182.
17.
Maguitu, D., and Hurmuzlu, I. 1994, “Spatial Collision of Kinematic Chains with Multiple Contact Points,” ASME DSL-Vol. 55-2, Dynamic Systems and Control.
18.
Ahmed
,
S.
,
Lankarani
,
H. M.
, and
Perreira
,
M. F. O. S.
,
1999
, “
Frictional Impact Analysis in Open-Loop Multibody Mechanical System.
”
ASME J. Mech. Des.
,
121
, pp.
119
–
127
.
19.
Shivaswamy
,
S.
, and
Lankarani
,
H. M.
,
1997
, “
Impact Analysis of Plates Using a Quasi-static Approach
,”
ASME J. Mech. Des.
,
119
, pp.
376
–
381
.
Copyright © 2000
 by ASME
You do not currently have access to this content.