The aim of this paper is to find out a computational procedure for the kinematic and dynamic analysis of a mechanism with multiple loops having motion spaces of a Lie algebra or Lie algebras. The basis of a motion space of the loop is determined such that it consists of passive joints axes in a loop, and a basis of a wrench space is determined to be its dual basis. The analysis of a closed loop mechanism can be done by selecting loop-cut-joints and computing values of wrenches acting on these joints from the condition that virtual works of passive joints are zero. By expressing these wrenches in the coordinate vectors on the dual bases, the concise analysis procedure can be obtained. Because a formulation for the analysis is developed based on the bases consisting of passive joint axes and their dual bases, the computational procedure can be applied to a mechanism with any Lie algebras.

Issue Section:
Technical Papers
Keywords:
kinematics, dynamics, Lie algebras, closed loop systems, mechanical engineering computing
Topics:
Dynamic analysis, Kinematics, Space, Lie algebras
1.
Stramigioli, S., Mascheke, B., and Bidard, C., 2000 “A Hamiltonian Formulation of the Dynamics of Spatial Mechanisms Using Lie Groups and Screw Theory,” Proceedings of a Symposium Commemorating the Legacy, Work and Life of Sir R. S. Ball(in CD ROM), July, University of Cambridge, Trinity College.
2.
Sugimoto, K., 2000, “Synthesis of Connecting Chains for Parallel Manipulators Based on Lie Algebra,” Workshop W6, ICRA 2000.
3.
Sugimoto
,
K.
,
2001
, “
Kinematic Analysis and Derivation of Equations of Motion for Mechanisms With Loops of Different Motion Spaces
,”
JSME Int. J. Ser. C
,
44
(
3
), pp.
610
–
617
.
4.
Featherstone, R., 1987, Robot Dynamics Algorithms, Kluwer Academic Publishers.
5.
Featherstone, R., and Orin, D., 2000, “Robot Dynamcs: Equations and Algorithms,” Proceedings of the 2000 IEEE, ICRA, April.
6.
Sugimoto, K., 2000, “Matrix Representation of Kinematic and Dynamic Analysis of Mechanisms,” Proceedings of a Symposium Commemorating the Legacy, Work and Life of Sir R. S. Ball(in CD ROM), July, University of Cambridge, Trinity College.
7.
Davies
,
T. H.
,
1983
, “
Mechanical Networks-2:Formulas for the Degrees of Mobility and Redundancy
,”
Mech. Mach. Theory
,
18
(
2
), pp.
103
–
106
.
8.
Nakamure
,
Y.
, and
Ghodoussi
,
M.
,
1989
, “
Dynamic Computation of Closed-Link Robot Mechanisms With Nonredundant and Redundant Actuators
,”
IEEE Trans. Rob. Autom.
,
5
(
3
), pp.
294
–
302
.
9.
Sugimoto
,
K.
,
1989
, “
Computational Scheme for Dynamic Analysis of Parallel Manipulators
,”
ASME J. Mech., Transm., Autom. Des.
,
111
, March, pp.
29
–
33
.
10.
Ball, R. S., 1900, A Treatise on the Theory of Screws, Cambridge University Press.
11.
Kane
,
T. R.
, and
Levinson
,
D. A.
,
1983
, “
The Use of Kane’s Dynamical Equations in Robotics
,”
Int. J. Robot. Res.
,
2
(
3
), pp.
3
–
21
.
12.
Uicker
,
J. J.
,
1967
, “
Dynamic Force Analysis of Spatial Lonkages
,”
ASME J. Appl. Mech.
,
34
, pp.
418
–
424
.
13.
Walker
,
M. W.
, and
Orin
,
D. E.
,
1982
, “
Efficient Dynamic Computer Simulation of Robotic Mechanisms
,”
ASME J. Dyn. Syst., Meas., Control
,
104
, pp.
205
–
211
.
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