Geometric Design of Cylindric PRS Serial Chains

[+] Author and Article Information
Hai-Jun Su

Robotics and Automation Laboratory, Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697e-mail: suh@eng.uci.edu

Charles W. Wampler

General Motors R&D Center, Warren, Michigan 48090-9055e-mail: charles.w.wampler@gm.com

J. Michael McCarthy

Robotics and Automation Laboratory, Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697e-mail: jmmccart@uci.edu

J. Mech. Des 126(2), 269-277 (May 05, 2004) (9 pages) doi:10.1115/1.1667965 History: Received March 01, 2003; Online May 05, 2004
Copyright © 2004 by ASME
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McCarthy, J. M., 2000, Geometric Design of Linkages, Springer-Verlag, New York, NY.
Tsai, L.-W., 1972, “Design of Open Loop Chains for Rigid Body Guidance,” Ph.D. Thesis, Department of Mechanical Engineering, Stanford University.
Tsai,  L.-W., and Roth,  B., 1972, “Design of Dyads with Helical, Cylindrical, Spherical, Revolute and Prismatic Joints,” Mech. Mach. Theory, 7, pp. 591–598.
Krovi,  V., Ananthasuresh,  G. K., and Kumar,  V., 2001, “Kinematic Synthesis of Spatial RR Dyads for Path Following with Applications to Coupled Chain Mechanisms,” ASME J. Mech. Des., 123(3), pp. 359–366.
Liao,  Q., and McCarthy,  J. M., 2001, “On the Seven Position Synthesis of a 5-SS Platform Linkage,” ASME J. Mech. Des., 123(1), pp. 74–79.
Mavroidis,  C., Lee,  E., and Alam,  M., 2001, “A New Polynomial Solution to the Geometric Design Problem of Spatial RR Robot Manipulators Using the Denavit-Hartenberg Parameters,” ASME J. Mech. Des., 123(1), pp. 58–67.
Kihonge,  J. N., Vance,  J. M., and Larochelle,  P. M., 2002, “Spatial Mechanism Design in Virtual Reality with Networking,” ASME J. Mech. Des., 124(3), pp. 435–440.
Chen,  P., and Roth,  B., 1967, “Design Equations for Finitely and Infinitesimally Separated Position Synthesis of Binary Link and Combined Link Chains,” ASME J. Eng. Ind., 91, pp. 209–219.
Nielsen, J., and Roth, B., 1995, “Elimination Methods For Spatial Synthesis,” Computational Kinematics J.-P. Merlet and B. Ravani eds., Kluwer Academic Press, Netherlands.
Verschelde,  J., and Haegemans,  A., 1993, “The GBQ-Algorithm for Constructing Start Systems of Homotopies for Polynomial Systems,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal., 30(2), pp. 583–594.
Morgan,  A. P., Sommese,  A. J., and Wampler,  C. W., 1995, “A Product-Decomposition Bound for Bezout Numbers,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal., 32(4), pp. 1308–1325.
Morgan, A. P., 1987, Solving Polynomial Systems Using Continuation for Scientific and Engineering Problems, Printice-Hall, Englewood Cliffs, NJ.
Wampler,  C., Morgan,  A., and Sommese,  A., 1990, “Numerical Continuation Methods for Solving Polynomial Systems Arising in Kinematics,” ASME J. Mech. Des., 112(1), pp. 59–68.
Li,  T. Y., 1997, “Numerical Solution of Multivariate Polynomial Systems by Homotopy Continuation Methods,” Acta Numerica, 6, pp. 399–436.
Sommese,  A. J., Verschelde,  J., and Wampler,  C. W., 2003, “Advances in Polynomial Continuation for Solving Problems in Kinematics,” ASME J. Mech. Des., in press.
Lee,  E., and Mavroidis,  D., 2002, “Solving the Geometric Design Problem of Spatial 3R Robot Manipulators Using Polynomial Homotopy Continuation,” ASME J. Mech. Des., 124(4), pp. 652–661.
Verschelde,  J., 1999, “Algorithm 795:PHCpack: A General-Purpose Solver for Polynomial Systems by Homotopy Continuation,” ACM Trans. Math. Softw., 25(2), pp. 251–276.
Ryu, S. J., Kim, J. W., Hwang, J. C., Park, C., Cho, H. S., Lee, K., Lee, Y., Cornel, U., Park, F. C., and Kim, J., 1998, “ECLIPSE: An Overactuated Parallel Mechanism for Rapid Machining,” 1998 ASME International Mechanical Engineering Congress and Exposition, Vol. 8, pp. 681–689.
Kim,  J., Park,  F. C., and Lee,  J. M., 1999, “A New Parallel Mechanism Machine Tool Capable of Five-Face Machining,” CIRP Ann., 48(1), pp. 337–340.
Bernshtein,  D. N., 1975, “The Number of Roots of a System of Equations,” Funct. Anal. Appl., 9(3), pp. 183–185.
Wampler,  C., 2003, “Displacement Analysis of Spherical Mechanisms Having Three or Fewer Loops,” ASME J. Mech. Des., in press.
Möller,  H. M., and Stetter,  H. J., 1995, “Multivariate Polynomial Equations with Multiple Zeros Solved by Matrix Computations,” Numer. Math., 70, pp. 311–329.
Mourrain,  B., 1998, “Computing Isolated Polynomial Roots by Matrix Methods,” J. Symb. Comput., 26(6), pp. 715–738.
Morgan,  A. P., and Sommese,  A. J., 1989, “Coefficient Parameter Polynomial Continuation,” Appl. Math. Comput., 29, pp. 123–160.
Su, H.-J., Collins, C., and McCarthy, J. M., 2002, “An Extensible Java Applet for Spatial Linkage Synthesis,” DETC2002/MECH-34371, ASME Design Engineering Technical Conference, Montreal, Canada, Sept. 29–Oct.02.


Grahic Jump Location
The cylindric PRS serial chain
Grahic Jump Location
The set of six task positions in Table 6
Grahic Jump Location
The 4th solution in Table 7 is shown reaching the six design positions



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