Research Papers

Classification of Screw Systems Composed of Three Planar Pencils of Lines for Singularity Analysis of Parallel Mechanisms1

[+] Author and Article Information
Xianwen Kong

School of Engineering and Physical Sciences,
Heriot-Watt University,
Edinburgh EH14 4AS, UK
e-mail: x.kong@hw.ac.uk

Andrew Johnson

School of Engineering and Physical Sciences,
Heriot-Watt University,
Edinburgh EH14 4AS, UK

The original version of this paper was presented at the ASME 2012 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Aug. 12–15, 2012, Chicago, IL, Paper No. DETC2012-70636.

For alternative classification of singularities, see Refs. [1,3,4].

2Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received June 8, 2013; final manuscript received November 16, 2013; published online March 6, 2014. Assoc. Editor: Jian S. Dai.

J. Mechanisms Robotics 6(2), 021008 (Mar 06, 2014) (10 pages) Paper No: JMR-13-1107; doi: 10.1115/1.4026340 History: Received June 08, 2013; Revised November 16, 2013

Screw systems composed of (the sum of) three planar pencils of lines are closely related to the singularity analysis of a number of three-legged parallel manipulators (PMs) in which the passive joints in each leg are a spherical joint and a single-DOF (degree of freedom) kinematic joint or generalized kinematic joint. This paper systematically classifies the screw systems composed of three planar pencils of lines based on the intersection of two planar pencils of lines, the classification of screw systems of order 2, and the reciprocal screw system of the three planar pencils of lines. The classification in this paper is more comprehensive than those in the literature. The above results are illustrated using CAD figures. This work may help readers better understand the geometric characteristics of singular configurations of a number of three-legged parallel manipulators.

Copyright © 2014 by ASME
Topics: Screws
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Gosselin, C., and Angeles, J., 1990, “Singularity Analysis of Closed-Loop Kinematic Chains,” IEEE Trans. Rob. Autom., 6(3), pp. 281–290. [CrossRef]
Agrawal, S., and Roth, B., 1992, “Statics of In-Parallel Manipulator Systems,” ASME J. Mech. Des., 114(4), pp. 564–568. [CrossRef]
Zlatanov, D., Bonev, I., and Gosselin, C., 2002, “Constraint Singularities as Configuration Space Singularities,” Advances in Robot Kinematics: Theory and Applications, F.Thomas and J.Lenarcic, eds., Kluwer, Dordrecht, The Netherlands, pp. 183–192.
Conconi, M., and Carricato, M., 2009, “A New Assessment of Singularities of Parallel Kinematic Chains,” IEEE Trans. Robot., 25(4), pp. 757–769. [CrossRef]
Merlet, J.-P., 1989, “Singular Configurations of Parallel Manipulators and Grassmann Geometry,” Int. J. Robot. Res., 8(5), pp. 45–56. [CrossRef]
McCarthy, J. M., 2011, Geometric Design of Linkages, 2nd ed., Springer, New York.
Amine, S., Tale-Masouleh, M., Caro, S., Wenger, P., and Gosselin, C., 2012, “Singularity Conditions of 3T1R Parallel Manipulators With Identical Limb Structures,” ASME J. Mech. Rob., 4(1), p. 011011. [CrossRef]
Huang, Z., Zhao, Y. S., Wang, J., and Yu, J. J., 1999, “Kinematic Principle and Geometrical Condition of General-Linear-Complex Special Configuration of Parallel Manipulators,” Mech. Mach. Theory, 34, pp. 1171–1186. [CrossRef]
Ebert-Uphoff, I., Lee, J.-K., and Lipkin, H., 2002, “Characteristic Tetrahedron of Wrench Singularities for Parallel Manipulators With Three Legs,” IMechE J. Mech. Eng. Sci., 216(C1), pp. 81–93. [CrossRef]
Kong, X., and Gosselin, C. M., 2001, “Uncertainty Singularity Analysis of Parallel Manipulators Based on the Instability Analysis of Structures,” Int. J. Robot. Res., 20(11), pp. 847–856. [CrossRef]
Yang, G., Chen, I.-M., Lin, W., and Angeles, J., 2001, “Singularity Analysis of Three-Legged Parallel Robots Based on Passive Joint Velocities,” Trans. Rob. Autom., 17(4), pp. 413–422. [CrossRef]
Downing, D. M., Samuel, A. E., and Hunt, K. H., 2002, “Identification of Special Configurations of the Octahedral Manipulator Using the Pure Condition,” Int. J. Robot. Res., 21(2), pp. 147–159. [CrossRef]
Huang, Z., Chen, L. H., and Li, Y. W., 2003, “The Singularity Principle and Property of Stewart Parallel Manipulator,” J. Rob. Syst., 20(4), pp. 163–176. [CrossRef]
Di Gregorio, R., 2005, “Forward Problem Singularities in Parallel Manipulators Which Generate SX-YS-ZS Structures,” Mech. Mach. Theory, 40(5), pp. 600–612. [CrossRef]
Ben-Horin, P., and Shoham, M., 2006, “Singularity Condition of Six Degree-of-Freedom Three-Legged Parallel Robots Based on Grassmann-Cayley Algebra,” IEEE Trans. Rob., 22(4), pp. 577–590. [CrossRef]
Pendar, H., Mahnama, M., and Zohoor, H., 2011, “Singularity Analysis of Parallel Manipulators Using Constraint Plane Method,” Mech. Mach. Theory, 48(1), pp. 33–43. [CrossRef]
Kong, X., Yu, J., and Gosselin, C. M., 2011, “Geometric Interpretation of Singular Configurations of a Class of Parallel Manipulators,” Proceedings of the 2011 ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Aug. 28–31, ASME, Washington, DC, Paper No. DETC2005/MECH-48165 [CrossRef].
Hunt, K. H., 1990, Kinematic Geometry of Mechanisms, Cambridge University Press, Cambridge, UK.
Davidson, J. K., and Hunt, K. H., 2004, Robots and Screw Theory: Applications of Kinematics and Statics to Robotics, Oxford University Press, New York.
Kong, X., and Gosselin, C., 2007, Type Synthesis of Parallel Mechanisms, Springer, New York.
Dai, J. S., and Rees Jones, J., 2001, “Interrelationship Between Screw Systems and Corresponding Reciprocal Systems and Applications,” Mech. Mach. Theory, 36(5), pp. 633–651. [CrossRef]
Dai, J. S., Huang, Z., and Lipkin, H., 2006, “Mobility of Overconstrained Parallel Mechanisms,” ASME J. Mech. Des., 128(1), pp. 220–229. [CrossRef]
Rico, J. M., Gallardo, J., and Duffy, J., 1999, “Screw Theory and Higher Order Kinematic Analysis of Open Serial and Closed Chains,” Mech. Mach. Theory, 34(4), pp. 559–586. [CrossRef]
Dai, J. S., 2012, “Finite Displacement Screw Operators With Embedded Chasles' Motion,” ASME J. Mech. Rob., 4(4), p. 041002. [CrossRef]


Grahic Jump Location
Fig. 1

A 2-RPS-1-SPR parallel mechanism

Grahic Jump Location
Fig. 4

Reciprocal screw systems of three 4-$0-systems: (a) S⊥ is a 1-$-1-$0-system, (b) S⊥ is a special 2-$0-system, and (c) S⊥ is a general 2-$0-system

Grahic Jump Location
Fig. 5

Intersection of two PPLs: (a) Case I of a 1-$0-system, (b) Case II of a 1-$0-system, (c) Case III of 1-$0-system, and (d) Empty case

Grahic Jump Location
Fig. 6

Characteristics of case 4c 2-PPL-system of order 4

Grahic Jump Location
Fig. 7

Construction of a 3-PPL-system of order 5 using Eq. (4): (a) Case 5b, (b) Case 5c, (c) Case 5d, and (d) Case 5e

Grahic Jump Location
Fig. 8

Construction of a 3-PPL-system of order 5 using Eq. (3)

Grahic Jump Location
Fig. 9

Singularity analysis of a 2-RPS-1-SPR parallel manipulator: (a) Wrench system and plane of constraint force pencil of an RPS leg, and (b) Manipulator in a singular configuration




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