The Library
Generalized Jacobian analysis of lower mobility manipulators
Tools
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. 831844. ISSN 0094114X

PDF
WRAP_Huang_030212generalized_jacobian_analysis_of_lower_mobility_manipulators_mmt_2011.pdf  Accepted Version  Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader Download (1142Kb) 
Official URL: http://dx.doi.org/10.1016/j.mechmachtheory.2011.01...
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 endeffector, 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 endeffector, 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 wellknown parallel manipulators are derived as examples to illustrate generality and effectiveness of this approach.
[error in script] [error in script]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:  0094114X 
Date:  June 2011 
Volume:  Vol.46 
Number:  No.6 
Number of Pages:  14 
Page Range:  pp. 831844 
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), 2009ZXO4014021 (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, SpringerVerlag, 2003. [3] J.P. Merlet, Parallel Robots, 2nd ed., New York, SpringerVerlag, 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 sixDOF 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 fivedegreeoffreedom parallel mechanisms, J. Robot. Syst., 14(12) (1997) 851–869. [8] B. Siciliano, Tricept robot: inverse kinematics, manipulability analysis and closedloop 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 3DOF 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 lowDOF 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 2DOF parallel manipulators with wellshaped 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 3DOF module of the TriVariant  A novel 5DOF reconfigurable hybrid robot, IEEE Trans. Robot., 21(3) (2005) 449–456. [18] D.S. Milutinovic, M. Glavonjic, V. Kvrgic, S. Zivanovic, A new 3DOF 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 5DOF hybrid robot with large workspace/ limbstroke 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 4DOF 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 limitedDOF 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 nonredundant 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) 938942. 
URI:  http://wrap.warwick.ac.uk/id/eprint/41475 
Data sourced from Thomson Reuters' Web of Knowledge
Actions (login required)
View Item 