This paper presents the results of a detailed study of the singular configurations of 3-DOF planar parallel mechanisms with three identical legs. Only prismatic and revolute joints are considered. From the point of view of singularity analysis, there are ten different architectures. All of them are examined in a compact and systematic manner using planar screw theory. The nature of each possible singular configuration is discussed and the singularity loci for a constant orientation of the mobile platform are obtained. For some architectures, simplified designs with easy to determine singularities are identified.

Issue Section:
Technical Papers
Keywords:
manipulator kinematics, geometry, singular value decomposition
Topics:
Screws
1.
Merlet, J.-P., 1996, “Direct Kinematics of Planar Parallel Manipulators,” Proc. IEEE Int. Conf. on Robotics & Automation, Minneapolis, MN, April, pp. 3744–3749.
2.
Hayes, M. J. D., 1999, “Kinematics of General Planar Stewart-Gough Platforms,” Ph.D. thesis, McGill University, Montreal, QC, Canada, September.
3.
Daniali
,
H. R. Mohammadi
,
Zsombor-Murray
,
P. J.
, and
Angeles
,
J.
,
1995
, “
Singularity Analysis of Planar Parallel Manipulators
,”
Mech. Mach. Theory
,
30
(
5
), pp.
665
–
678
.
4.
Sefrioui
,
J.
, and
Gosselin
,
C. M.
,
1995
, “
On the Quadratic Nature of the Singularity Curves of Planar Three-Degree-Of-Freedom Parallel Manipulators
,”
Mech. Mach. Theory
,
30
(
4
), pp.
533
–
551
.
5.
Bonev, I. A., and Gosselin, C. M., 2001, “Singularity Loci of Planar Parallel Manipulators with Revolute Joints,” Proc. 2nd Workshop on Computational Kinematics, Seoul, South Korea, pp. 291–299, May, (http://www.parallemic.org/Reviews/Review001.html).
6.
Mohammed
,
M. G.
, and
Duffy
,
J.
,
1985
, “
A Direct Determination of the Instantaneous Kinematics of Fully Parallel Robot Manipulators
,”
ASME J. Trans. Autom. Mech. Des.
,
107
(
2
), pp.
226
–
229
.
7.
Kumar
,
V. R.
,
1992
, “
Instantaneous Kinematics of Parallel-Chain Robotic Mechanisms
,”
ASME J. Mech. Des.
,
114
(
3
), pp.
349
–
358
.
8.
Tsai, L.-W., 1999, Robot Analysis: the Mechanics of Serial and Parallel Manipulators, John Wiley & Sons.
9.
Zlatanov, D., Fenton, R. G., and Benhabib, B., 1994, “Analysis of the Instantaneous Kinematics and Singular Configurations of Hybrid-Chain Manipulators,” Proc. ASME 23rd Biennial Mechanisms Conference, DE-Vol. 72, Minneapolis, MN, September, pp. 467–476.
10.
Joshi
,
S. A.
, and
Tsai
,
L.-W.
,
2002
, “
Jacobian Analysis of Limited-DOF Parallel Manipulators
,”
ASME J. Mech. Des.
,
124
, June, pp.
254
–
258
.
11.
Hunt, K. H., 2000, “Don’t Cross-Thread the Screw,” Proc. Symposium Commemorating Sir R. S. Ball, Cambridge, UK, July.
12.
Hunt, K. H., 1978, Kinematic Geometry of Mechanisms, Oxford University Press.
13.
Gosselin
,
C. M.
, and
Angeles
,
J.
,
1990
, “
Singularity Analysis of Closed-Loop Kinematic Chains
,”
IEEE Trans. Rob. Autom.
,
6
(
3
), pp.
281
–
290
.
14.
Zlatanov, D., Fenton, R. G., and Benhabib, B., 1994, “Singularity Analysis of Mechanisms and Robots via a Motion-Space Model of the Instantaneous Kinematics,” Proc. IEEE Int. Conf. on Robotics & Automation. San Diego, CA, May, pp. 980–985.
15.
Karger, A., and Husty, M., 1996, “On Self-Motions of a Class of Parallel Manipulators,” Recent Advances in Robot Kinematics, J. Lenarcic and V. Parenti-Castelli, eds., Kluwer Academic Publishers, pp. 339–348.
16.
Ma, O., and Angeles, J., 1992, “Architecture Singularities of Platform Manipulators,” Proc. IEEE Int. Conf. on Robotics & Automation, Sacramento, CA, April, pp. 1542–1547.
17.
Bonev, I. A., 2002, “Geometric Analysis of Parallel Mechanisms,” Ph.D. Thesis, Laval University, Quebec, QC, Canada, October.
18.
Chablat, D., and Wenger, P., 1998, “Working Modes and Aspects in Fully Parallel Manipulators,” Proc. IEEE Int. Conf. on Robotics & Automation, Leuven, Belgium, May, pp. 1994–1969.
19.
Gosselin, C. M., Lemieux, S., and Merlet, J.-P., 1996, “A New Architecture of Planar Three-Degree-Of-Freedom Parallel Manipulator,” Proc. IEEE Int. Conf. on Robotics & Automation, Minneapolis, MN, April, pp. 3738–3743.
20.
Daniali, H. R. M., Zsombor-Murray, P. J., and Angeles, J., 1993, “The Kinematics of 3-DOF Planar and Spherical Double-Triangular Parallel Manipulators,” Computational Kinematics, J. Angeles et al., eds., Kluwer Academic Publishers, pp. 153–164.
21.
HEPHAIST Alignment Stage NAF3, HEPHAIST SEIKO Co., Ltd. (http://www.hephaist.co.jp).
22.
Chung, Y.-H., Choo, J.-H., and Lee, J.-W., 2001, “SenSation: A New 2 DOF Parallel Mechanism for Haptic Device,” Proc. 2nd Workshop on Computational Kinematics, Seoul, South Korea, May 20–22, pp. 45–56,
Copyright © 2003
 by ASME
You do not currently have access to this content.