Application of Workspace Generation Techniques to Determine the Unconstrained Motion of Parallel Manipulators

[+] Author and Article Information
Philip Voglewede, Imme Ebert-Uphoff

Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0405

J. Mech. Des 126(2), 283-290 (May 05, 2004) (8 pages) doi:10.1115/1.1649967 History: Received January 01, 2002; Revised July 01, 2003; Online May 05, 2004
Copyright © 2004 by ASME
Your Session has timed out. Please sign back in to continue.


Han,  C., Kim,  J., Kim,  J., and Park,  F. C., 2002, “Kinematic Sensitivity Analysis of the 3-UPU Parallel Mechanism,” Mech. Mach. Theory, 37(8), pp. 787–798, August.
Chen,  J., and Chao,  L.-M., 1997, “Positioning Error Analysis for Robot Manipulators With All Rotary Joints,” IEEE J. Rob. Autom., RA-3(6), pp. 539–545, December.
Wu,  C.-H., 1984, “A Kinematic CAD Tool for the Design and Control of a Robot Manipulator,” Int. J. Robot. Res., 3(1), pp. 58–67, Spring.
Horie,  M., Funabashi,  H., Ogawa,  K., and Kobayashi,  H., 1980, “A Displacement Analysis of Plane Multilink Mechanisms With Clearances and Tolerances,” Bull. JSME, 23(183), pp. 1522–1529, September.
Horie,  M., Funabashi,  H., Ogawa,  K., and Kobayashi,  H., 1985, “A Displacement Analysis of Spatial Four-Bar Mechanisms With Clearances and Tolerances,” Bull. JSME, 28(241), pp. 1535–1542, July.
Choi,  J.-H., Lee,  S. J., and Choi,  D.-H., 1998, “Stochastic Linkage Modeling for Mechanical Error Analysis of Planar Mechanisms,” Mech. Struct. Mach., 26(3), pp. 257–276, August.
Rhyu,  J. H., and Kwak,  B. M., 1988, “Optimal Stochastic Design of Four-Bar Mechanisms for Tolerance and Clearance,” ASME J. Mech. Transm., Autom. Des., 110(3), pp. 255–262, September.
Shi,  Z., 1997, “Synthesis of Mechanical Error in Spatial Linkages Based on Reliability Concept,” Mech. Mach. Theory, 32(2), pp. 255–259.
Wang, J., and Masory, O., 1993, “On the Accuracy of a Stewart Platform—Part I: The Effect of Manufacturing Tolerances,” Proceedings of the 1993 IEEE International Conference on Robotics and Automation, Vol. 1, pp. 114–120, May.
Hartenberg, R. S., and Denavit, J., 1964, Kinematic Synthesis of Linkages, McGraw-Hill Book Company, New York.
Fogarasy,  A. A., and Smith,  M. R., 1998, “The Influence of Manufacturing Tolerances on the Kinematic Performance of Mechanisms,” Proc. Inst. Mech. Eng., Part C: Mech. Eng. Sci., 212(1), pp. 35–47.
Vocaturo,  J., 1983, “Evaluating the Repeatability of Linkages,” Mach. Des., pp. 67–71, June 23.
Hoeltzel, D. A., and Chieng, W.-H., 1989, “A Unified Approach to the Kinematic Analysis of Joint Clearances and Link Length Tolerances for Determination of the Rotational and Positional Accuracy of Planar Mechanisms,” Advances in Design Automation (ASME Design Engineering Division), Vol. 19–3, pp. 345–356, Montreal, Canada, September.
Innocenti,  C., 2002, “Kinematic Clearance Sensitivity Analysis of Spatial Structures With Revolute Joints,” ASME J. Mech. Des., 124, pp. 52–57, March.
Parenti-Castelli, V., and Venanzi, S., 2002, “On the Joint Clearance Effects in Serial and Parallel Manipulators,” Proceedings of the Workshop on Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators, pp. 215–223, Quebec City, Quebec, Canada, October.
Parenti-Castelli, V., and Venanzi, S., 2002, “A New Technique for Clearance Influence Analysis in Planar Mechanisms,” Proceedings of DETC’02: ASME 2002 Design Engineering Technical Conferences and Computer Information in Engineering Conference, pp. 1003–1009, Montreal, Canada, September.
Wohlhart,  K., 1999, “Degrees of Shakiness,” Mech. Mach. Theory, 34(7), pp. 1103–1126, October.
Husty, M. L., and Zsombor-Murray, P., 1994, “A Special Type of Singular Stewart-Gough Platform,” Advances in Robot Kinematics and Computational Geometry, A. J. Lenarcic and B. B. Ravani, eds., pp. 449–458. Kluwer Academic Publishers, Dordrecht, The Netherlands.
Husty, M. L., and Karger, A., 2000, “Self-Motions of Griffis-Duffy Type Parallel Manipulators,” Proceedings of the 2000 IEEE International Conference on Robotics and Automation, Vol. 1, pp. 7–12, San Francisco, CA, April.
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., pp. 339–348. Kluwer Academic Publishers.
Karger,  A., and Husty,  M., 1998, “Classification of All Self-Motions of the Original Stewart-Gough Platform,” Comput.-Aided Des., 30(3), pp. 205–215.
Gosselin,  C., and Angeles,  J., 1990, “Singularity Analysis of Closed Loop Kinematic Chains,” IEEE Trans. Rob. Autom., 6(3), pp. 281–290, June.
Merlet, J.-P., 2000, Parallel Robots., Kluwer Academic Publishers, Dordrecht.
Gosselin,  C., 1990, “Determination of the Workspace of 6-DOF Parallel Manipulators,” ASME J. Mech. Des., 112, pp. 331–336, September.
Merlet,  J.-P., Gosselin,  C. M., and Mouly,  N., 1998, “Workspaces of Planar Parallel Manipulators,” Mech. Mach. Theory, 33(1/2), pp. 7–20, January–February.
Husty, M. L., 1996, “On the Workspace of Planar Three-Legged Platforms,” Proceedings ISRAM—World Congress of Automation, pp. 1790–1796, Montpellier.
Chirikjian,  G. S., and Zhou,  S., 1998, “Metrics on Motion and Deformation of Solid Models,” ASME J. Mech. Des., 120, pp. 252–261, June.


Grahic Jump Location
Example five bar mechanism (2 DOF)
Grahic Jump Location
Schematic of 3R_RR manipulator
Grahic Jump Location
Close up view of a passive revolute joint
Grahic Jump Location
Possible motion of mounting point C1
Grahic Jump Location
Unconstrained EE motion of the five-bar mechanism shown in the shaded region at C
Grahic Jump Location
Unconstrained EE motion of 3R_RR manipulator for one particular EE orientation φ the intersection of three translated annuli
Grahic Jump Location
Equivalent clearance mechanism for the 5 bar example
Grahic Jump Location
Equivalent model for the three DOF manipulator (3R_RR)
Grahic Jump Location
Unconstrained EE motion while approaching two different singular configurations
Grahic Jump Location
Unconstrained EE motion of 3R_RR manipulator for a non-singular configuration
Grahic Jump Location
Unconstrained EE motion of 3R_RR manipulator for a singular configuration
Grahic Jump Location
Unconstrained EE motion of 3R_RR manipulator for a singular configuration




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In