Abstract
This paper presents a classification on the workspaces of planar serial three-link manipulators, that is, position workspace and orientation angle workspace. Position workspace indicates the region reached by the reference point on the end-effector. Orientation angle workspace indicates a set of angle ranges by which the end-effector can reach with certain orientation for every point in the reachable position workspace. By introducing a virtual equivalent mechanism, reachable position workspace can be divided into several Grashof intervals and non-Grashof intervals. The calculation equations of orientation angle workspace are deduced in three situations according to the relationships among four link lengths in the virtual four-bar chain. Three examples are given for three kinds of relationship of link lengths. The orientation angle workspace of extended groups, that is, two of the three link lengths equal, and the orientation angle workspace when the reference point on the end-effector moves along a non-radial direction are also discussed. A program is developed to calculate orientation angle workspaces and output variation curves of orientation angle workspace and key data within the position workspace. The approach and program in this paper can be used for fast calculation and identification of the variation rule of the orientation angle workspace of any given planar serial three-link manipulator on the basis of its link parameters, and for the design of a highly dexterous serial manipulator with proposed link relations.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Kumar A, Waldron K J. The dexterous workspace. ASME Paper No. 80-DET-108, 1980
Yang F C, Haug E J. Numerical analysis of the kinematic working capability of mechanisms. ASME J Mech Des, 1994, 116(1): 111–118
Yang F C, Haug E J. Numerical analysis of the kinematic dexterity of mechanisms. ASME J Mech Des, 1994, 116(1): 119–126
Dai J S, Shah P. Orientation capability of planar serial manipulators using rotatability analysis based on workspace decomposition. Proc Instn Mech Engrs, Part C, J Mech Eng Sci, 2002, 216(C4): 275–288
Dai J S, Shah P. Orientation capability of planar manipulators using virtual joint angle analysis. Mech Mach Theory, 2003, 38(3): 241–252
Dai J S, Holland N, Kerr D R. Finite twist mapping and its application to planar serial manipulators with revolute joints. Proc Instn Mech Engrs, Part C, J Mech Eng Sci, 1995, 209(C3): 263–271
Dai J S, Kerr D R. Analysis and synthesis of planar grasping in an image space. In: Proceedings of 22nd ASME Biennial Mechanisms Conference, Scottsdale, Arizona, September 1992, DE-45: 283–292
Williams R L, Reinholtz C F. Proof of Grashof’s law using polynomial discriminants. ASME J Mech, Transm, Autom Des, 1986, 108(4): 562–564
Williams R L, Reinholtz C F. Mechanism link rotatability and limit position analysis using polynomial discriminants. ASME J Mech, Transm, Autom Des, 1987, 109(2): 178–182
Ting K L, Liu Y W. Rotatability laws for N-bar kinematic chains and their proofs. ASME J Mech Des, 1991, 113(3): 32–39
Wampler C W. Solving the kinematics of planar mechanisms. ASME J Mech Des, 1999, 121(3): 387–391
Guo W Z, DU R, Wang J X. On the mobility of single loop N-bar linkage with one prismatic joint. In: ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Long Beach, California, USA, 2005
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the Natural Science Foundation of Shanxi Province (Grant No. 20041070)
Rights and permissions
About this article
Cite this article
Li, R., Dai, J.S. Orientation angle workspaces of planar serial three-link manipulators. Sci. China Ser. E-Technol. Sci. 52, 975–985 (2009). https://doi.org/10.1007/s11431-009-0083-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11431-009-0083-7