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Dynamic dexterity of a planar 2-DOF parallel manipulator in a hybrid machine tool

Published online by Cambridge University Press:  01 January 2008

Jun Wu ,
Jinsong Wang ,
Tiemin Li ,
Liping Wang  and
Liwen Guan
Jun Wu*
Affiliation:
Institute of Manufacturing Engineering, Department of Precision Instruments and Mechanology, Tsinghua University, Beijing 100084, P. R. China.
Jinsong Wang
Affiliation:
Institute of Manufacturing Engineering, Department of Precision Instruments and Mechanology, Tsinghua University, Beijing 100084, P. R. China.
Tiemin Li
Affiliation:
Institute of Manufacturing Engineering, Department of Precision Instruments and Mechanology, Tsinghua University, Beijing 100084, P. R. China.
Liping Wang
Affiliation:
Institute of Manufacturing Engineering, Department of Precision Instruments and Mechanology, Tsinghua University, Beijing 100084, P. R. China.
Liwen Guan
Affiliation:
Institute of Manufacturing Engineering, Department of Precision Instruments and Mechanology, Tsinghua University, Beijing 100084, P. R. China.
*
*Corresponding author. E-mail: wu-j03@mails.tsinghua.edu.cn.
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Summary

This paper addresses the dynamic dexterity of a planar 2-degree of freedom (DOF) parallel manipulator with virtual constraint. Without simplification, the dynamic formulation is derived by using the virtual work principle. The condition number of the inertia matrix of the dynamic equation is presented as a criterion to evaluate the dynamic dexterity of a manipulator. In order to obtain the best isotropic configuration of the dynamic dexterity in the whole workspace, two global performance indices, which consider the mean value and standard deviation of the condition number of the inertia matrix, respectively, are proposed as the objective function. For a given set of geometrical and inertial parameters, the dynamic dexterity of the parallel manipulator is more isotropic in the center than at the boundaries of the workspace.

Keywords

Dynamic dexterityParallel manipulatorDynamic formulationCondition number
Type
Article
Information
Robotica , Volume 26 , Issue 1 , January 2008 , pp. 93 - 98
Copyright
Copyright © Cambridge University Press 2007

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References

1.Dasgupta, B., Mruthyunjaya, T. S., “A Newton–Euler formulation for the inverse dynamics of the stewart platform manipulator,” Mech. Mach. Theory 33 (8), 1135–1152 (1998).CrossRefGoogle Scholar
2.Zhang, C. D., Song, S. M., “An efficient method for inverse dynamics of manipulators based on the virtual work principle,” J. Robot. Syst. 10 (5), 605–627 (1993).CrossRefGoogle Scholar
3.Li, Y., Xu, Q., “Kinematics and inverse dynamics analysis for a general 3-PRS spatial parallel mechanism,” Robotica 23 (2), 219–229 (2005).CrossRefGoogle Scholar
4.Wang, L.-P., Wang, J.-S. and Chen, J., “The dynamic analysis of a 2-PRR planar parallel mechanism,” Proc. Inst. Mech. Engrs. C: J. Mech. Eng. Sci. 219 (9), 901–909 (2005).Google Scholar
5.Wang, L. P., Wang, J. S., Li, Y. W. and Lu, Y., “Kinematic and dynamic equations of a planar parallel manipulator,” Proc. Inst. Mech. Engrs. C: J. Mech. Eng. Sci. 217 (5), 525–531 (2003).Google Scholar
6.Wu, J., Wang, J., Li, T. and Wang, L., “Analysis and application of a 2-DOF planar parallel mechanism,” ASME J. Mech. Design 129 (4), 434–437 (2007).CrossRefGoogle Scholar
7.Tadokoro, S., Kimura, I. and Takamori, T., “A measure for evaluation of dynamic dexterity based on a stochastic interpretation of manipulator motion,” Proceedings of the Fifth International Conference on Advanced Robotics (1991) pp. 509–514.Google Scholar
8.Yoshikawa, T., “Dynamic manipulability of robot manipulators,” J. Robot. Syst. 2 (1), 113–124 (1985).Google Scholar
9.Yoshikawa, T., “Manipulability of robotic mechanisms,” Int. J. Robot. Res. 4 (2), 3–9 (1985).CrossRefGoogle Scholar
10.Park, F. C. and Kim, J. W., “Manipulability of closed kinematic chains,” ASME J. Mech. Design 120 (4), 542–548 (1998).CrossRefGoogle Scholar
11.Liu, X.-J., Wang, Q.-M. and J. Wang “Kinematics, dynamics and dimensional synthesis of a novel 2-DoF translational manipulator,” J. Intell. Robot. Syst. 41 (4), 205–224 (2005).CrossRefGoogle Scholar
12.Chiacchio, P., Bouffard-Vercelli, Y. and Pierrot, F., “Force polytope and force ellipsoid for redundant manipulators,” J. Robot. Syst. 14 (8), 613–620 (1997).3.0.CO;2-P>CrossRefGoogle Scholar
13.Chiacchio, P., “New dynamic manipulability ellipsoid for redundant manipulators,” Robotica 18 (4), 381–387 (2000).CrossRefGoogle Scholar
14.Asada, H., “A geometrical representation of manipulator dynamics and its application to arm design,” J. Dynam. Syst. Meas. Control 105 (3), 131–135 (1983).CrossRefGoogle Scholar
15.Asada, H. and Youcef-Toumi, K., “Analysis and design of a direct-drive arm with a five-bar-link parallel drive mechanism,” ASME J. Dynam. Syst. Meas. Control 106 (3), 225–230 (1984).CrossRefGoogle Scholar
16.Li, M., Huang, T., Mei, J. et al. , “Dynamic formulation and performance comparison of the 3-DOF modules of two reconfigurable PKM-the Tricept and the TriVariant,” ASME J. Mech. Design 127 (6), 1129–1136 (2005).CrossRefGoogle Scholar
17.Gosselin, C. M. and Angeles, J., “A global performance index for the kinematic optimization of robotic manipulators,” ASME J. Mech. Design 113 (3), 220–226 (1991).CrossRefGoogle Scholar
18.Liu, X.-J., Jin, Z.-L. and Gao, F., “Optimum design of 3-DOF spherical parallel manipulators with respect to the conditioning and stiffness indices,” Mech. Mach. Theory 35 (9), 1257–1267 (2000).CrossRefGoogle Scholar