Abstract

A new approach to the synthesis of planar linkage mechanisms with approximate velocity constraints is proposed. The paper presents the first closed-form complex-number dyad solution to the ground pivot specification problem for two precision positions with velocity specified at one of the positions. The solution is then manipulated in order to add approximate velocity constraints to design methods for two exact positions and an unlimited number of approximate positions. The approximate position and velocity constraints facilitate more realistic representation of design objectives. Solution spaces are presented using two-dimensional ground-pivot maps. Computer implementation of the proposed methodologies would allow designers with little or no knowledge of the synthesis techniques to interactively explore maps of solutions for four-bar motion generation.

Issue Section:
Technical Papers
Keywords:
design engineering, kinematics, velocity
Topics:
Design
1.
Holte
,
J. E.
,
Chase
,
T. R.
, and
Erdman
,
A. G.
,
2000
, “
Mixed Exact-Approximate Position Synthesis of Planar Mechanisms
,”
ASME J. Mech. Des.
,
122
, No.
3
, pp.
287
–
293
.
2.
Ahn, S., 1993, “Optimization Enhanced Synthesis of Planar Four-Bar Motion Generation Linkages,” University of Minnesota, Ph.D. Thesis.
3.
Johnson, L. G., 1995, “Complex-Number Based Multiply Separated Precision Position Synthesis of Planar Linkages,” M. S. Thesis, University of Minnesota.
4.
Tesar
,
D.
,
1968
, “
The Generalized Concept of Four Multiply Separated Positions in Coplanar Motion
,”
J. Mec.
,
3
, No.
21
, pp.
11
–
23
.
5.
Tesar
,
D.
, and
Eschenbach
,
P. W.
,
1967
, “
Four Multiply Separated Positions in Coplanar Motion
,”
ASME J. Eng. Ind.
,
89
, Series B, No.
2
, pp.
231
–
234
.
6.
Loerch, R. J., Erdman, A. G., Sandor, G. N., and Midha, A., 1975, “Synthesis of Four-Bar Linkages With Specified Ground Pivots,” Proceedings of the 4th Applied Mechanisms Conference, Chicago, November 1975, Stillwater, Oklahoma: Oklahoma State University, pp. 10.1–10.6.
7.
James
,
P. A.
, and
Roth
,
B.
,
1994
, “
A Unified Theory for Kinematic Synthesis
,”
ASME J. Mech. Des.
,
116
, No.
1
, pp.
144
–
154
.
8.
Tesar
,
D.
,
1967
, “
The Generalized Concept of Three Multiply Separated Positions in Coplanar Motion
,”
J. Mec.
,
2
, pp.
461
–
474
.
9.
Schaefer
,
R. S.
, and
Kramer
,
S. N.
,
1979
, “
Selective Precision Synthesis of Planar Mechanisms Satisfying Position and Velocity Constraints
,”
Mech. Mach. Theory
,
14
, No.
3
, pp.
161
–
170
.
10.
Chidambaran, C., and Erdman, A. G., 1999, “LINCAGES 2000 Mechanism Design Software,” Proceedings of the Applied Mechanisms and Robotics Conference, Cincinnati, OH, December 13–15, 1999.
11.
Erdman, A. G., and Sandor, G. N., 1997, Mechanism Design Analysis and Synthesis, Volume, 1, Third Edition, Prentice Hall, Englewood Cliffs, NJ, p. 539.
12.
Holte, J. E., 1996, “Two Precision Position Synthesis of Planar Mechanisms with Approximate Position and Velocity Constraints,” Ph.D. Thesis, University of Minnesota.
Copyright © 2001
 by ASME
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