This paper presents an algorithm for generating trajectories for multi-degree of freedom spatial linkages, termed constrained parallel manipulators. These articulated systems are formed by supporting a workpiece, or end-effector, with a set of serial chains, each of which imposes a constraint on the end-effector. Our goal is to plan trajectories for systems that have workspaces ranging from two through five degrees-of-freedom. This is done by specifying a goal trajectory and finding the system trajectory that comes closest to it using a dual quaternion metric. We enumerate these parallel mechanisms and formulate a general numerical approach for their analysis and trajectory planning. Examples are provided to illustrate the results.
Issue Section:
Technical Papers
1.
Collins
, C. L.
, McCarthy
, J. M.
, Perez
, A.
, and Su
, H.-J.
, 2002
, “The Structure of an Extensible Java Applet for Spatial Linkage Synthesis
,” ASME J. Comput. Inf. Sci. Eng.
, 2
(1
), pp. 45
–49
.2.
McCarthy, J. M., 2000, Geometric Design of Linkages, Springer-Verlag, New York, NY.
3.
McCarthy, J. M., 2000, “Mechanisms Synthesis Theory and the Design of Robots,” Proc. Int. Conf. Robotics and Automation, San Francisco, CA, April 24–28.
4.
Lee
, E.
, and Mavroidis
, C.
, 2002
, “Solving the Geometric Design Problem of Spatial 3R Robot Manipulators Using Polynomial Continuation
,” ASME J. Mech. Des.
, 124
(4
), pp. 652
–661
.5.
Perez, A., and McCarthy, J. M., 2002, “Dual Quaternion Synthesis of a 2-TPR Constrained Parallel Robot,” Proc. of the WORKSHOP on Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators, Clement M. Gosselin and Imme Ebert-Uphoff eds., Quebec City, Quebec, Canada, Oct. 3–4.
6.
Rubel
, A. J.
, and Kaufman
, R.
, 1977
, “KINSYN III: A New Human-Engineered System for Interactive Computer-Aided Design of Planar Linkages
,” ASME J. Eng. Ind.
, 99B
(2
), pp. 440
–448
.7.
Erdman, A., and Gustafson, J., 1977, “LINCAGES: Linkage INteractive Computer Analysis and Graphically Enhanced Synthesis Packages,” Technical Report 77-DET-5, American Society of Mechanical Engineers.
8.
Waldron, K. J., and Song, S. M., 1981, “Theoretical and Numerical Improvements to Interactively Linkage Design Program, RECSYN,” Proc. of the Seventh Applied Mechanisms Conference, Kansas City, MO.
9.
Ruth, D. A., and McCarthy, J. M., 1997, “SphinxPC: An Implementation of Four Position Synthesis for Planar and Spherical 4R Linkages,” CD-ROM Proc. of the ASME DETC’97, paper no. DETC97/DAC-3860, Sept. 14–17, Sacramento, CA.
10.
Larochelle, P. M., 1998, “Spades: Software for Synthesizing Spatial 4C Linkages,” CD-ROM Proc. of the ASME DETC’98, paper no. DETC98/Mech-5889, Sept. 13–16, Atlanta, GA.
11.
Joshi
, S. A.
, and Tsai
, L. W.
, 2002
, “Jacobian Analysis of Limited-DOF Parallel Manipulators
,” ASME J. Mech. Des.
, 124
(2
), pp. 254
–258
.12.
Huang
, Z.
, Wang
, J.
, and Fang
, Y. F.
, 2002
, “Analysis of Instantaneous Motions of Deficient-Rank 3-RPS Parallel Manipulators
,” Mech. Mach. Theory
, 37
(2
), pp. 229
–240
.13.
Gregorio
, R. D.
, and Parenti-Castelli
, V.
, 2001
, “Position Analysis in Analytical Form of the 3-PSP Mechanism
,” ASME J. Mech. Des.
, 123
(1
), pp. 51
–57
.14.
Hertz
, R. B.
, and Hughes
, P. C.
, 1998
, “Kinematic Analysis of a General Double-Tripod Parallel Manipulator
,” Mech. Mach. Theory
, 33
(6
), pp. 683
–696
.15.
Merlet
, J. P.
, 2001
, “A Generic Trajectory Verifier for the Motion Planning of Parallel Robots
,” ASME J. Mech. Des.
, 123
(4
), pp. 510
–515
.16.
Fluckiger, L., Baur, C., and Clavel, Reymond, 1998, “CINEGEN: A Rapid Prototyping Tool for Robot Manipulators,” Proc. of the 4th International Conference on Motion and Vibration Control(MOVIC’98), Vol. 1, pp. 129–134, Zurich(CH), August.
17.
Ahlers, S. G., and McCarthy, J. M., 2000, “The Clifford Algebra of Double Quaternions and the Optimization of TS Robot Design,” Applications of Clifford Algebras in Computer Science and Engineering, E. Bayro and G. Sobczyk, eds., Birkhauser.
18.
Etzel, K., and McCarthy, J. M., 1996, “Spatial Motion Interpolation in an Image Space of SO(4),” CD-ROM Proc. 1996 ASME Design Engineering Technical Conference, paper no. 96-DETC/MECH-1164, August 18–22, Irvine, CA.
19.
Ge, Q. J., Varshney, A., Menon, J. P., and Chang, C.-F., 1998, “Double Quaternions for Motion Interpolation,” CD-ROM Proc. of the ASME DETC’98, paper no. DETC98/DFM-5755, Sept. 13–16, Atlanta, GA.
20.
Srinivasan
, L.
, and Ge
, Q. J.
, 1998
, “Fine Tuning of Rational B-Spline Motions
,” ASME J. Mech. Des.
, 120
(1
), pp. 46
–51
.21.
Craig, J. J., 1989, Introduction to Robotics: Mechanics and Control. Second Edition, Addison-Wesley.
22.
Tsai, L. W., 2001, Mechanism Design, Enumeration of Kinematic Structures According to Function, CRC Press, Boca Raton.
23.
Tuttle
, E. R.
, Peterson
, S. W.
, and Titus
, J. E.
, 1989
, “Enumeration of Basic Kinematic Chains Using the Theory of Finite Groups
,” ASME J. Mech., Transm., Autom. Des.
, 111
, pp. 498
–503
.24.
Lee
, J. J.
, and Tsai
, L. W.
, 2002
, “Structural Synthesis of Multi-Fingered Hands
,” ASME J. Mech. Des.
, 124
(2
), pp. 272
–276
.25.
Zou
, H. L.
, Abdel-Malek
, K. A.
, and Wang
, J. Y.
, 1997
, “Design Propagation in Mechanical Systems: Kinematic Analysis
,” ASME J. Mech. Des.
, 119
(3
), pp. 338
–345
.26.
Bottema, O., and Roth, B., 1979, Theoretical Kinematics, North Holland. (reprinted Dover Publications 1990).
27.
McCarthy, J. M., 1990, An Introduction to Theoretical Kinematics, MIT Press, Boston, MA.
28.
Dietmaier, P., and Pavlin, G., 1995: Automatic Computation of Direct and Inverse Kinematics of General Spatial Mechanisms and Structures, Proc. of 9th World Congress IFToMM, Vol. 1, 80–84, Milano.
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