A three-dimensional single-point impact solution has been developed based on the original work of Keller. The formulation involves an integrated form of Keller’s equations and leads to a different numerical procedure to solve for the after-impact velocities. In this integral formulation, the kinetic and static friction coefficients are differentiated and any of the three hypotheses of the coefficient of restitution can be employed. Furthermore, a singularity problem that may occur in Keller’s solution is avoided with the integral formulation. Numerical examples are given to illustrate the features of the integral formulation and the differences between the two formulations.

1.
Routh
,
E. J.
, 1877,
An Elementary Treatise on the Dynamics of a System of Rigid Bodies
,
3rd ed.
,
Macmillan
,
London
.
2.
Keller
,
J. B.
, 1986, “
Impact With Friction
,”
ASME J. Appl. Mech.
0021-8936,
53
, pp.
1
4
.
3.
Batlle
,
J. A.
, and
Condomines
,
A. B.
, 1991, “
Rough Collisions in Multibody Systems
,”
Mech. Mach. Theory
0094-114X,
26
, pp.
565
577
.
4.
Bhatt
,
V.
, and
Koechling
,
J.
, 1995, “
Three-Dimensional Frictional Rigid-Body Impact
,”
ASME J. Appl. Mech.
0021-8936,
62
, pp.
893
898
.
5.
Stronge
,
W. J.
, 1994, “
Swerve During 3-Dimensional Impact of Rough Rigid Bodies
,”
ASME J. Appl. Mech.
0021-8936
61
, pp.
605
611
.
6.
Wang
,
Y.
, and
Mason
,
M. T.
, 1992, “
2-Dimensional Rigid-Body Collisions With Friction
,”
ASME J. Appl. Mech.
0021-8936,
59
, pp.
635
642
.
7.
Han
,
I.
, and
Gilmore
,
B. J.
, 1993, “
Multi-Body Impact Motion With Friction: Analysis, Simulation, and Experimental Validation
,”
ASME J. Mech. Des.
0161-8458,
115
, pp.
412
422
.
8.
Stoimenov
,
L. G.
, 1992, “
The Problem of Glancing Collision Between Solids. Experimental and Theoretical Investigation of Collision Between Rough Solids
,”
Int. Appl. Mech.
1063-7095,
28
, pp.
842
848
.
9.
Shen
,
H.
, and
Townsend
,
M. A.
, 1998, “
Collisions of Constrained Rigid Body Systems With Friction
,”
Shock Vib.
1070-9622,
5
, pp.
141
151
.
10.
Haessig
,
D.
, and
Friedland
,
B.
, 1991, “
On the Modeling and Simulation of Friction
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
113
, pp.
354
362
.
You do not currently have access to this content.