W.Z. Guo, F. Gao, and S. Mekid


Planar manipulator, workspace atlas, orientation capability, charac-teristics chart, physical model, joint space map


A systematic study is performed for the workspace characteristics and orientation capability analysis of 3R planar manipulators. This study will aid the design and control of this kind of manipulators. This particular manipulator is well suited for industrial applications in aided automation manufacturing as well as medical applications for orthopaedic surgery robotics and micro holder for tactile sensing fingers. Based on the characteristics chart method proposed for closed-loop chains in former work (W.Z. Guo, H.J. Zou, B. Han, & Q. Zhang, Mobility of 4R1P-type five-bars using characteristics chart, Proc. ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Con- ference, Salt Lake City, Utah, 2004, 627–634; W.Z. Guo, Q.G. Huang, H.J. Zou et al., Grashof criteria for 4R1P-type five-bar planar parallel mechanisms with active/passive prismatic joint, Chi- nese Journal of Mechanical Engineering, 41 (8), 2005, 66–73. [in Chinese]), a complete classification and workspace composition are obtained for all the possible 3R planar manipulators. Class I manip- ulators have one inner circular dexterous regions, while Class II and III manipulators have no inner dexterous regions. If the three-link lengths are not equal to each other at all, the three classes of manip- ulators have an annular dexterous workspace when the shortest link is serving as the end-effector link. Furthermore, if any two links are the same in length, Class II and III manipulators have no dexterous workspace. By introducing the physical model of the solution space, workspace atlases are produced to show the global performance distributions over the link dimension range in terms of workspace classification, workspace shape, and workspace size. To investigate the joint rotation ranges of the manipulators including orientation capability of the end-effectors, joint space maps are displayed over the characteristics chart by using angled arc at end-effector position which denotes the joint rotation angle range. The study presents a ∗ State Key Laboratory of Mechanical System and Vibration, Institute of Design and Control Engineering for Heavy Equip- ments, Shanghai Jiao Tong University, Shanghai, 200240, China; e-mail: {wzguo, fengg}@sjtu.edu.cn ∗∗ School of Mechanical, Aerospace, and Civil Engineering, The University of Manchester, P.O. Box 88, Sackville Street, Manchester M60 1QD, UK; e-mail: S.Mekid@manchester.ac.uk Recommended by Prof. A. Alimi useful tool to assist synthesis, analysis and motion planning of pla- nar manipulators by describing global performances over the whole design space and the whole reachable workspace.

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