This paper presents a methodology for the Jacobian analysis of limited degrees-of-freedom (DOF) parallel manipulators. A limited-DOF parallel manipulator is a spatial parallel manipulator which has less than six degrees-of-freedom. It is shown that a 6×6 Jacobian matrix, which provides information about both architecture and constraint singularities, can be derived by making use of the theory of reciprocal screws. The 3-UPU and 3-RPS parallel manipulators are used as examples to demonstrate the methodology.

Issue Section:
Technical Papers
Keywords:
manipulators, matrix algebra, Jacobian matrices, machine theory, constraint theory
Topics:
Manipulators, Jacobian matrices, Reactor protection systems, Screws
1.
Clavel, R., 1988, “A Fast Robot with Parallel Geometry,” 18th International Symposium on Industrial Robots, Sydney, Australia, pp. 91–100.
2.
Di Gregorio, R., and Parenti-Castelli, V., 1998, “A Translational 3-DOF Parallel Manipulator,” Advances in Robot Kinematics: Analysis and Control, J. Lenarcic and M. L. Husty (eds.), Kluwer Academic Publishers, pp. 49–58.
3.
Di Gregorio, R., and Parenti-Castelli, V., 1999, “Mobility Analysis of the 3-UPU Parallel Mechanism Assembled for a Pure Translational Motion,” Proceedings of the IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Atlanta, GA, September 19–23, pp. 520–525.
4.
Gosselin
,
C.
, and
Angeles
,
J.
,
1989
, “
The Optimum Kinematic Design of a Spherical Three-Degree-of-Freedom Parallel Manipulator
,”
ASME J. Mech. Des.
,
111
, pp.
437
–
445
.
5.
Gosselin, C., and Hamel, J., 1994, “The Agile Eye: A High-Performance Three-Degree-of-Freedom Camera-Orienting Device,” Proceedings of the IEEE International Conference on Robotics and Automation, San Diego, CA, pp. 781–786.
6.
Herve´, J. M., 1995, “Design of Parallel Manipulators Via the Displacement Group,” 9th World Congress on the Theory of Machines and Mechanisms, Milan, August 30–September 2, pp. 2079–2082.
7.
Joshi, S. A., and Tsai, L. W., 2001, “A Comparison Study of Two 3-DOF Parallel Manipulators: One with Three and the Other with Four Supporting Limbs,” Accepted for Publication to the IEEE J. Rob. Autom.
8.
Karouia, M., and Herve´, J. M., 2000, “A Three-DOF Tripod For Generating Spherical Rotation,” Advances in Robot Kinematics, J. Lenarcic and M. M. Stanisic (eds.), Kluwer Academic Publishers, pp. 395–402.
9.
Lee, K., and Shah, D. K., 1987, “Kinematic Analysis of a Three Degrees of Freedom In-Parallel Actuated Manipulator,” Proceedings of the IEEE International Conference on Robotics and Automation, Raleigh, NC, March 31–April 3, 1, pp. 345–350.
10.
Tsai, L. W., 1996, “Kinematics of a Three-DOF Platform With Three Extensible Limbs,” Recent Advances in Robot Kinematics, J. Lenarcic and V. Parenti-Castelli (eds.), Kluwer Academic Publishers, pp. 401–410.
11.
Tsai, L. W., 1999, “The Enumeration of a Class of Three-DOF Parallel Manipulators,” 10th World Congress on the Theory of Machine and Mechanisms, Olulu, Finland, June 20–24, 3, pp. 1121–1126.
12.
Tsai
,
L. W.
, and
Joshi
,
S. A.
,
2000
, “
Kinematics and Optimization of a Spatial 3-UPU Parallel Manipulator
,”
ASME J. Mech. Des.
,
122
, No.
4
, pp.
439
–
446
.
13.
Tsai, L. W., and Joshi, S. A., 2001, “Comparison Study of Architectures of Four 3 Degree-of-Freedom Translational Parallel Manipulators,” Proceedings of 2001 IEEE International Conference on Robotics and Automation, May 2001, Seoul, Korea, paper No. 10320.
14.
Tsai, L. W., and Stamper, R., 1996, “A Parallel Manipulator with Only Translational Degrees of Freedom,” CD-ROM Proceedings, 1996 ASME Design Engineering Technical Conferences, Irvine, CA, 96-DETC/MECH-1152.
15.
Tsai, L. W., Walsh, G. C., and Stamper, R., 1996, “Kinematics of a Novel Three DOF Translational Platform,” Proceedings of the IEEE International Conference on Robotics and Automation, Minneapolis, MN, pp. 3446–3451.
16.
Yang, P. H., Waldron, K. J., and Orin, D. E., 1996, “Kinematics of a Three Degree-of-Freedom Motion Platform for a Low-Cost Driving Simulator,” in Advances in Robot Kinematics, J. Lenarcic and V. Parenti-Castelli (eds.), Kluwer Academic Publishers, pp. 89–98.
17.
Zlatanov, D., Bonev, I., and Gosselin, C., 2001, “Constraint Singularities,” NewsLetter on: http://www.parallemic.org, July.
18.
Zlatanov, D., Fenton, R. G., and Benhabib, B., 1994, “Singularity Analysis of Mechanism and Robots Via a Velocity-Equation Model of the Instantaneous Kinematics,” Proceedings of the IEEE International Conference on Robotics and Automation, San Diego, CA, pp. 986–991.
19.
Park
,
F. C.
, and
Kim
,
J. W.
,
1999
, “
Singularity Analysis of Closed Kinematic Chains
,”
ASME J. Mech. Des.
,
121
, No.
1
, pp.
32
–
38
.
20.
Mohamed
,
M. G.
, and
Duffy
,
J.
,
1985
, “
A Direct Determination of the Instantaneous Kinematics of Fully Parallel Robot Manipulators
,”
ASME J. Mech., Transm., Autom. Des.
,
107
, pp.
226
–
229
.
21.
Tsai, L. W., 1999, Robot Analysis: The Mechanics of Serial and Parallel Manipulators, John Wiley & Sons, New York, NY.
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