Investigation of Parallel Manipulators Using Linear Complex Approximation

[+] Author and Article Information
A. Wolf, M. Shoham

Robotics Laboratory, Department of Mechanical Engineering, Technion—Israel Institute of Technology, Haifa 32000, Israel

J. Mech. Des 125(3), 564-572 (Sep 04, 2003) (9 pages) doi:10.1115/1.1582876 History: Received November 01, 2001; Revised November 01, 2002; Online September 04, 2003
Copyright © 2003 by ASME
Your Session has timed out. Please sign back in to continue.


Merlet,  J. P., 1992, “Singular Configurations of Parallel Manipulators and Grassmann Geometry,” Int. J. Robot. Res., 8(5), pp. 45–56.
Hunt,  K. H., 1983, “Structural Kinematics of In-Parallel-Actuated Robot Arms,” ASME J. Mech. Des., 105(4), pp. 705–712.
St-Onge,  B. M., and Gosselin,  C. M., 2000, “Singularity Analysis and Representation of the General Gaugh-Stewart Platform,” Int. J. Robot. Res., 19(3), pp. 271–288.
Dasgupta,  B., and Mruthyunjaya,  T. S., 1998, “Singularity-Free Path Planning for the Stewart Platform Manipulator,” Mech. Mach. Theory, 33(6), pp. 711–725.
Gosselin,  C., and Angeles,  J., 1990, “Singularity Analysis of Closed-Loop Kinematic Chains,” IEEE Trans. Rob. Autom., 6(3), pp. 281–290.
Zlatanov, D., Fenton, R. G., and Benhabib, B., 1994, “Singularity Analysis of Mechanisms and Robots via a Motion-Space Model of the Instantaneous Kinematics,” Proceedings of the IEEE International Conference on Robotics and Automation, Vol. 2, pp. 980–991.
Ma,  O., and Angeles,  J., 1992, “Architecture Singularities of Parallel Manipulators,” Int. J. Robot. Res., 7(1), pp. 23–29.
Mohammadi Daniali,  H. R., Zsombor-Murray,  P. J., and Angeles,  J., 1955, “The Isotropic Design of Two General Classes of Planar Parallel Manipulators,” J. Rob. Syst., 12(2), pp. 795–805.
Zlatanov,  D., Fenton,  R. G., and Benhabib,  B., 1995, “A Unifying Framework for Classification and Interpretation of Mechanism Singularities,” ASME J. Mech. Des., 117, pp. 566–572.
Mayer St-Onge, B., and Gosselin, C. M., 1996, “Singularity Analysis and Representation of Spatial Six-Degree of Freedom Parallel Manipulator,” Advances in Robot Kinematics (ARK), J. Lenarcic and V. Parenti-Castelli, eds., Kluwer Academic Publisher, pp. 389–398.
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.
Collins,  C. L., and McCarthy,  J. M., 1998, “The Quartic Singularity Surface of Planar Platforms in the Clifford Algebra of the Projective Plane,” Mech. Mach. Theory, 33(7), pp. 931–944.
Feng-Cheng,  Y., and Haug,  E. J., 1994, “Numerical Analysis of the Kinematic Working Capability of Mechanisms,” ASME J. Mech. Des., 116, pp. 111–117.
Funabashi, H., and Takeda, Y., 1995, “Determination of Singular Points and Their Vicinity in Parallel Manipulators Based on the Transmission Index,” Ninth World Congress on the Theory of Machines and Mechanisms, pp. 1977–1981.
Karger, A., and Husty, M., 1996, “On Self-Motion of a Class of Parallel Manipulators,” Advances in Robot Kinematics, J. Lenarcic and V. Parenti-Castelli, eds., Kluwer Academic Publisher, pp. 339–348.
Karger, A., 1998, “Architecture Singular Parallel Manipulators,” Advanced in Robot Kinematics: Analysis and Control, J. Lenarcic and M. L. Husty, eds., Kluwer Academic Publisher, pp. 445–454.
Merlet, J. P., 1989, “Parallel Manipulators Part 2: Theory, Singular Configurations and Grassmann Geometry,” Rapport de Recherche INRIA No 791, F’evrier.
Merlet, J. P., 1992, “On the Infinitesimal Motion of a Parallel Manipulator in Singular Configurations,” IEEE Int. Conf. on Robotics and Automation, pp. 320–325, Nice, France.
Fichter,  E. F., 1986, “A Stewart Platform-Based Manipulator: General Theory and Practical Construction,” Int. J. Robot. Res., 5(2), pp. 155–182.
Collins,  C. L., and Long,  G. L., 1995, “The Singularity Analysis of an In-Parallel Hand Controller for Force-Reflected Teleoperation,” IEEE Trans. Rob. Autom., 11(5), pp. 661–669.
Dandurand,  A., 1984, “The Rigidity of Compound Spatial Grid,” Structural Topology,10, pp. 41–55.
Ben Horin, R., 1997, “Criteria for Analysis of Parallel Robots,” Doctoral Dissertation, Technion-Israeli Institute of Technology.
Simaan,  N., and Shoham,  M., 2001, “Singularity Analysis of a Class of Composite Serial In-Parallel Robots,” IEEE Trans. Rob. Autom., 17(3), pp. 301–311.
Hao,  F., and McCarthy,  J. M., 1998, “Conditions for Line-Based Singularities in Spatial Platform Manipulators,” J. Rob. Syst., 15(1), pp. 43–55.
Hunt, K. H., 1978, “Kinematic Geometry of Mechanisms,” Department of Mechanical Engineering, Monash University, Clayton, Victoria, Australia.
Pottmann,  H., Peternell,  M., and Ravani,  B., 1999, “An Introduction to Line Geometry With Applications,” Comput.-Aided Des., 31, pp. 3–16.
Klein,  F., 1871, “Uber Liniengeometrie und Metrische Geometrie,” Mathematische Annalen, pp. 257–303.
Ball, R. S., 1900, A Treatise on the Theory of Screws, Cambridge University Press, Cambridge.
Ciblak, N., and Lipkin, H., 1999, “Synthesis of Cartesian Stiffness for Robotic Applications,” Proceedings of the 1999 IEEE International Conference on Robotics and Automation, Detroit, Michigan., pp. 2147–2152.
Tsai,  L.-W., and Joshi,  S., 2000, “Kinematics and Optimization of a Spatial 3-UPU Parallel Manipulator,” ASME J. Mech. Des., 122(4), pp. 439–446.
Tsai, L.-W., 1996, “Kinematics of a Three-DOF Platform With Three Extensible Limbs,” Advances in Robot Kinematics (ARK), J. Lenarcic and V. Parenti-Castelli, eds., Kluwer Academic Publisher, pp. 401–410.
Di Gregorio,  R., and Parenti-Castelli,  V., 2002, “Mobility Analysis of the 3-UPU Parallel Mechanism Assembled in a Pure Translational Motion,” ASME J. Mech. Des., 124, pp. 259–264.
Tsai, L.-W., 1998, “The Jacobian Analysis of a Parallel Manipulator Using Reciprocal Screws,” Advances in Robot Kinematics (ARK): Analysis and Control, Lenarcic, J., and Husty, M. L., eds., Kluwer Academic Publishers, pp. 327–336.
Parenti-Castelli,  V., Di Gregorio,  R., and Bubani,  F., 2000, “Workspace and Optimal Design of a Pure Translation Parallel Manipulator,” Meccanica 35, pp. 203–214; (anche presentato al 14th Italian Congress on Theoretical and Applied Mechanics AIMETA, Como, Italy, October 6–9, 1999).
Sommerville, D. M. Y., 1934, Analytical Geometry of Three Dimensions, Cambridge University press.
Bonev, I., and Zlatanov, D., 2001, “The Mystery of the Singular SNU Translational Parallel Robot,” http://www.parallemic.org/Reviews/Review004.html.
Zlatanov, D., Bonev, I., and Gosselin, C., 2001, “Constraint Singularities as Configuration Space Singularities,” http://www.parallemic.org/Reviews/Review008.html.


Grahic Jump Location
Gough-Stewart platform, the lines Li and the resulting twists
Grahic Jump Location
(a) Hunt’s singularity—two limbs and the moving platform are coplanar; (b) λ as function of the moving, platform rotation angle, α, about the LCA axis of Fig. 2(a)
Grahic Jump Location
(a) Fichter’s singularity—90 deg rotation of the moving platform about the Z axis, top views; (b) Fichter’s singularity—90 deg rotation of the moving platform, from home position, about the Z axis: isometric views; (c) λ as a function of the moving platform rotation angle about the Z axis. (d) Values of the closest linear complex’s pitch as a function of the moving platform rotation angle about the Z axis.
Grahic Jump Location
The TSSM Manipulator, Merlet 17
Grahic Jump Location
Type 3c singularity with four line-1,2,3,5-intersect at vertex B1
Grahic Jump Location
(a) Type 4d singularity where lines LCA1 and LCA2 cross the plane spanned by L1 and L2, vertex B3 joining L5 and L6 and intersect a line along limb 4: top view; (b) Type 4d singularity (LCA2 not shown for clarity): side view.
Grahic Jump Location
(a) A 3-DOF 3-UPU parallel manipulator 31; (b) A 3-DOF 3-UPU parallel manipulator (SNU)
Grahic Jump Location
Equivalent kinematic structure of the UPU robot’s limb
Grahic Jump Location
Force and moment transmitted to the moving platform
Grahic Jump Location
3-UPU with two zero-pitch linear complexes
Grahic Jump Location
Pitch of linear complex with max λ at each point of Fig. 12
Grahic Jump Location
Two pitches corresponding to the two linear complexes with minimum λ at each point of Fig. 12
Grahic Jump Location
The path of the moving platform on a sphere centered at IPL
Grahic Jump Location
Maximum λ at each point of Fig. 12
Grahic Jump Location
Minimum λ corresponding to two LCA in points of Fig. 12
Grahic Jump Location
Points in the vicinity of the base configuration, on a sphere centered at IPL



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