Huang, Tian, Liu, H. T. and Chetwynd, D. G. (Derek G.), 1948-. (2011) Generalized Jacobian analysis of lower mobility manipulators. Mechanism and Machine Theory, Vol.46 (No.6). pp. 831-844. ISSN 0094-114X

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Abstract

Mainly drawing on screw theory and linear algebra, this paper presents a general approach for Jacobian analysis of lower mobility manipulators. Given the definitions of twist/wrench spaces and their subspaces of the end-effector, the underlying relationships amongst these subspaces are identified using the virtual work principle. Using the orthogonal and dual properties of these subspaces and variational representation to account for the permitted and restricted instantaneous motions of the end-effector, a general and systematic procedure for the formulation of a generalized Jacobian is proposed. The merit of the generalized Jacobian allows the first order kinematic and static modeling (velocity, accuracy, force and stiffness) to be integrated into a unified mathematical framework. The generalized Jacobians for three well-known parallel manipulators are derived as examples to illustrate generality and effectiveness of this approach.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics T Technology > TJ Mechanical engineering and machinery
Divisions:	Faculty of Science > Engineering
Library of Congress Subject Headings (LCSH):	Manipulators (Mechanism) -- Mathematical models, Jacobians
Journal or Publication Title:	Mechanism and Machine Theory
Publisher:	Elsevier BV
ISSN:	0094-114X
Date:	June 2011
Volume:	Vol.46
Number:	No.6
Number of Pages:	14
Page Range:	pp. 831-844
Identification Number:	10.1016/j.mechmachtheory.2011.01.009
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Guo jia zi ran ke xue ji jin wei yuan hui (China) [National Natural Science Foundation of China] (NSFC), National NC Key Program
Grant number:	50535010 (NSFC), 50775158 (NSFC), 2009ZXO4014-021 (NNCKP)
References:	[1] L.-W. Tsai, Robot analysis: the Mechanics of Serial and Parallel Manipulators, New York, John Wiley & Sons, 1999. [2] J. Angeles, Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms, 3rd ed., New York, Springer-Verlag, 2003. [3] J.-P. Merlet, Parallel Robots, 2nd ed., New York, Springer-Verlag, 2006. [4] J.-P. Merlet, Jacobian, manipulability, condition number, and accuracy of parallel robots, ASME J. Mech. Des., 128(1) (2006) 199–206. [5] F. Tahmasebi, L. W. Tsai, Jacobian and stiffness analysis of a novel class of six-DOF parallel minimanipulators, ASME Des. Eng. Division, 47 (1992) 95–102. [6] R. S. Stoughton and T. Arai, Modified Stewart platform manipulator with improved dexterity, IEEE Trans. Robot. Autom., 9(2) 1993 166–172. [7] J. Wang, C. M. Gosselin, Kinematic analysis and singularity representation of spatial five-degree-of-freedom parallel mechanisms, J. Robot. Syst., 14(12) (1997) 851–869. [8] B. Siciliano, Tricept robot: inverse kinematics, manipulability analysis and closed-loop direct kinematics algorithm, Robotica, 17(4) (1999) 437–445. [9] K.-S. Hong and J.-G. Kim, Manipulability analysis of a parallel machine tool: Application to optimal link length design,” J. Robot. Syst., 17(8) (2000) 403–415. [10] S. Joshi, L.-W. Tsai, A comparison study of two 3-DOF parallel manipulators: One with three and the other with four supporting legs, IEEE Trans. Robot. Autom., 19(2) (2003), 200–209. [11] Y. Fang, L. W. Tsai, Inverse velocity and singularity analysis of low-DOF serial manipulators, J. Robot. Syst., 20(4) (2003) 177–188. [12] M. Callegari, M. Tarantini, Kinematic analysis of a novel translational platform, ASME J. Mech. Des., 125(2) (2003) 308–315. [13] T. Huang, M. Li, Z. Li, D. G. Chetwynd, D. J. Whitehouse, Optimal kinematic design of 2-DOF parallel manipulators with well-shaped workspace bounded by a specified conditioning index, IEEE Trans. Robot. Autom., 20(3) (2004) 538–543. [14] G. Alici, B. Shirinzadeh, Optimum synthesis of planar parallel manipulators based on kinematic isotropy and force balancing, Robotica, 22(1) (2004) 97–108. [15] C. H. Liu and S. Cheng, Direct singular positions of 3RPS parallel manipulators, ASME J. Mech. Des., 126(6) (2004) 1006–1016. [16] K. K. Oh, X.-J. Liu, D. S. Kang, J. Kim, Optimal design of a micro parallel positioning platform. Part I: Kinematic analysis, Robotica, 22(6) (2004) 599–609. [17] T. Huang, M. Li, X. M. Zhao, J. P. Mei, D. G. Chetwynd, S. J. Hu, Conceptual design and dimensional synthesis for a 3-DOF module of the TriVariant - A novel 5-DOF reconfigurable hybrid robot, IEEE Trans. Robot., 21(3) (2005) 449–456. [18] D.S. Milutinovic, M. Glavonjic, V. Kvrgic, S. Zivanovic, A new 3-DOF spatial parallel mechanism for milling machines with long X travel, Annals of the CIRP, 54(1) (2005) 345–348. [19] M. Li, T. Huang, D. Zhang, X. Zhao, S. J. Hu, D. G. Chetwynd, Conceptual design and dimensional synthesis of a reconfigurable hybrid robot, ASME J. Manuf. Sci. Eng., 127(3), (2005) 647–653. [20] H. Liu, T. Huang, J. Mei, X. Zhao, D. G. Chetwynd, M. Li, S. J. Hu, Kinematic design of a 5-DOF hybrid robot with large workspace/ limb-stroke ratio, ASME J. Mech. Des., 129(5) (2007) 530–537. [21] P. L. Richard, C. M. Gosselin, X. Kong, Kinematic analysis and prototyping of a partially decoupled 4-DOF 3T1R parallel manipulator, ASME J. Mech. Des., 129(6) (2007) 611–616. [22] K. H. Hunt, Kinematic Geometry of Mechanisms, Oxford University Press, 1978. [23] K. Sugimoto, J. Duffy, Application of linear algebra to screw systems, Mechanism and Machine Theory, 17(1) (1982) 73–83. [24] D. R. Kerr, D.J. Sanger, The inner product in the evaluation of reciprocal screws, Mech. Mach. Theory, 24(2) (1989) 87–92. [25] A.E. Samuel, P.R. McAree, P. R., K. H. Hunt, Unifying screw geometry and matrix transformations. Int. J. Robot. Res., 10(5) (1991) 454–472. [26] J. M. Martinez, J. Duffy, Orthogonal spaces and screw systems, Mech. Mach. Theory, 27(4) (1992) 451–458. [27] S. Joshi and L. W. Tsai, Jacobian analysis of limited-DOF parallel manipulators, ASME J. Mech. Des., 124(2)(2002) 254–258. [28] J.K. Davison, K.H. Hunt, Robotics and Screw Theory, Application of Kinematics and Statics to Robots, Oxford Univ. Press, 2004. [29] D. Kim, W. K. Chung, Analytic formulation of reciprocal screws and its application to non-redundant robot manipulators. ASME J. Mech. Des., 125(1) (2003) 158–164. [30] M. Zoppi, D. Zlatanov, and R. Molfino, On the velocity analysis of interconnected chains mechanisms, Mech. Mach. Theory, 41(11) (2006) 1346–1358. [31] M. B. Hong and Y. J. Choi, Kinestatic analysis of nonsingular lower mobility manipulators, IEEE Trans. Robot., 25(4) (2009) 938-942.
URI:	http://wrap.warwick.ac.uk/id/eprint/41475

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