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Research Papers

Evaluation of Force/Torque Transmission Quality for Parallel Manipulators

[+] Author and Article Information
Xiang Chen

The State Key Laboratory of Tribology and
Institute of Manufacturing Engineering,
Department of Mechanical Engineering,
Tsinghua University,
Beijing 100084, China

Chao Chen

Mem. ASME
Department of Mechanical
and Aerospace Engineering,
Monash University,
Clayton, Victoria 3802, Australia
e-mail: chao.chen@monash.edu

Xin-Jun Liu

The State Key Laboratory of Tribology and
Institute of Manufacturing Engineering,
Department of Mechanical Engineering,
Tsinghua University,
Beijing 100084, China
e-mail: xinjunliu@mail.tsinghua.edu.cn

1Corresponding author.

Manuscript received April 26, 2014; final manuscript received November 13, 2014; published online April 6, 2015. Assoc. Editor: Yuefa Fang.

J. Mechanisms Robotics 7(4), 041013 (Nov 01, 2015) (9 pages) Paper No: JMR-14-1094; doi: 10.1115/1.4029188 History: Received April 26, 2014; Revised November 13, 2014; Online April 06, 2015

Performance evaluation is one of the most important issues in the analysis and design of parallel manipulators. The internal forces and torques in parallel manipulators contribute to manipulating the end-effectors and resisting the external loads. In this work, we propose a transmission index to evaluate the force and torque transmission quality of parallel manipulators. The index is normalized and used to analyze the exactly constrained parallel manipulators, based on the transmission matrix spanned by transmission wrench screws (TWSs). Furthermore, the index is applied to parallel manipulators with different degrees of freedom (DOF) in order to illustrate and validate the proposed approach and index. Finally, a typical parallel manipulator is selected to address the comparison analysis between different indices, which demonstrates that the proposed index, possessing respective merits, could be complementary to other existing indices.

Copyright © 2015 by ASME
Topics: Manipulators , Torque
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References

Patel, Y. D., and George, P. M., 2012, “Parallel Manipulators Applications—A Survey,” Mod. Mech. Eng., 2(3), pp. 57–64. [CrossRef]
Togai, M., 1986, “An Application of the Singular Value Decomposition to Manipulability and Sensitivity of Industrial Robots,” SIAM J. Algebraic Discrete Meth., 7(2), pp. 315–320. [CrossRef]
Dubey, R., and Luh, J. Y. S., 1988, “Redundant Robot Control Using Task Based Performance Measures,” J. Rob. Syst., 5(5), pp. 409–432. [CrossRef]
Firmani, F., Zibil, A., Nokleby, S. B., and Podhorodeski, R. P., 2008, “Wrench Capabilities of Planar Parallel Manipulators. Part I: Wrench Polytopes and Performance Indices,” Robotica, 26(6), pp. 791–802. [CrossRef]
Kim, S. G., and Ryu, J., 2003, “New Dimensionally Homogeneous Jacobian Matrix Formulation by Three End-Effector Points for Optimal Design of Parallel Manipulators,” IEEE Trans. Rob. Autom., 19(4), pp. 731–737. [CrossRef]
Salisbury, J. K., and Craig, J. J., 1982, “Articulated Hands: Force Control and Kinematic Issues,” Int. J. Rob. Res., 1(1), pp. 4–17. [CrossRef]
Yoshikawa, T., 1985, “Manipulability of Robotic Mechanisms,” Int. J. Rob. Res., 4(2), pp. 3–9. [CrossRef]
Duffy, J., 1996, Statics and Kinematics With Applications to Robotics, Cambridge University Press, New York.
Prajapati, J. M., and Patel, L. N., 2007, “Dynamic (Forward and Inverse Force Transmission Capability) Analysis of the Stewart Platform as Robot Manipulator,” IEEE International Conference on Mechatronics and Automation (ICMA 2007), Harbin, China, Aug. 5–8, pp. 2848–2853. [CrossRef]
Merlet, J. P., 1998, “Efficient Estimation of the Extremal Articular Forces of a Parallel Manipulator in a Translation Workspace,” IEEE International Conference on Robotics and Automation, Leuven, Belgium, May 16–20, pp. 1982–1987. [CrossRef]
Kim, H. S., and Choi, Y. J., 2001, “Forward/inverse Force Transmission Capability Analyses of Fully Parallel Manipulators,” IEEE Trans. Rob. Autom., 17(4), pp. 526–531. [CrossRef]
Merlet, J. P., 2006, “Jacobian, Manipulability, Condition Number, and Accuracy of Parallel Robots,” ASME J. Mech. Des., 128(1), pp. 199–206. [CrossRef]
Kosuge, K., Okuda, M., Kawamata, H., and Fukuda, T., 1993, “Input/Output Force Analysis of Parallel Link Manipulators,” IEEE International Conference on Robotics and Automation, Atlanta, GA, May 2–6, pp. 714–719. [CrossRef]
Chen, C., and Angeles, J., 2007, “Generalized Transmission Index and Transmission Quality for Spatial Linkages,” Mech. Mach. Theory, 42(9), pp. 1225–1237. [CrossRef]
Tsai, M. J., and Lee, H. W., 1994, “The Transmissivity and Manipulability of Spatial Mechanisms,” ASME J. Mech. Des., 116(1), pp. 137–143. [CrossRef]
Hunt, K. H., 1990, “Kinematic Geometry of Mechanisms,” Oxford University Press, New York.
Angeles, J., 2006, Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms, 3rd ed., Springer-Verlag, New York.
Bonev, I. A., Zlatanov, D., and Gosselin, C. M., 2003, “Singularity Analysis of 3-DOF Planar Parallel Mechanisms Via Screw Theory,” ASME J. Mech. Des., 125(3), pp. 573–581. [CrossRef]
Chen, X., Xie, F. G., Liu, X-J, Xie, F., and Sun, T., 2014, “A Comparison Study on Motion/Force Transmissibility of Two Typical 3-DOF Parallel Manipulators: The Sprint Z3 and A3 Tool Heads,” Int. J. Adv. Rob. Syst., 11(5), pp. 1–10. [CrossRef]
Liu, X.-J., and Bonev, I. A., 2008, “Orientation Capability, Error Analysis, and Dimensional Optimization of Two Articulated Tool Heads With Parallel Kinematics,” ASME J. Manuf. Sci. Eng., 130(1), p. 011015 [CrossRef]
Dasgupta, B., and Mruthyunjaya, T. S., 2000, “The Stewart Platform Manipulator: A Review,” Mech. Mach. Theory, 35(1), pp. 15–40. [CrossRef]
Gosselin, C., and Angeles, J., 1989, “The Optimum Kinematic Design of a Spherical Three-Degree-of-Freedom Parallel Manipulator,” ASME J. Mech. Des., 111(2), pp. 202–207. [CrossRef]
Liu, X-J., Wang, J. S., and Kim, J. W., 2006, “Determination of the Link Lengths for a Spatial 3-DOF Parallel Manipulator,” ASME J. Mech. Des., 128(2), pp. 365–373. [CrossRef]
Wang, J. S., Wu, C., and Liu, X-J., 2010, “Performance Evaluation of Parallel Manipulators: Motion/Force Transmissibility and Its Index,” Mech. Mach. Theory, 45(10), pp. 1462–1476. [CrossRef]
Angeles, J., 2006, “Is There a Characteristic Length of a Rigid-Body Displacement?,” Mech. Mach. Theory, 41(8), pp. 884–896. [CrossRef]
Pierrot, F., Reynaud, C., and Fournier, A., 1990, “Delta: A Simple and Efficient Parallel Robot,” Robotica, 8(2), pp. 105–109. [CrossRef]

Figures

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Fig. 1

A platform constrained by a set of TWSs

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Fig. 2

Unit wrench on the platform

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Fig. 3

A RPRPR parallel manipulator

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Fig. 4

Distribution of the NPI in the workspace of RPRPR parallel manipulator

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Fig. 5

A parallel singular configuration of RPRPR parallel manipulator

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Fig. 6

A 3-RRR manipulator

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Fig. 7

Distribution of the index in the translational workspace with rotational angle ϕ = 0

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Fig. 8

Distribution of the index in the translational workspace with rotational angle ϕ = -30 deg

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Fig. 9

Relationship between index and rotational angles with constant position: x = 0,y = 0

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Fig. 10

A parallel singular configuration when the moving platform locates at x = 1,y = 5.2 and ϕ = -30 deg

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Fig. 11

A parallel singular configuration when the moving platform locates at x = 0,y = 0 and ϕ = 136 deg

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Fig. 12

A spatial 3-RPS parallel manipulator

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Fig. 13

Distribution atlas of the index in the chosen spatial workspace

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Fig. 14

Distribution atlas of the index in the selected slice with change of x- and y-coordinates when fixing z-axis, z = 6

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Fig. 15

A spatial Stewart manipulator

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Fig. 16

Distribution of the index in the translational spatial workspace while fixing the three rotational angles as zero

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Fig. 17

Distribution of the index in the selected middle slice by fixing the z-axis and three rotational angles, z = 1.5, φ = 0 ,θ = 0 ,ϕ = 0 

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Fig. 18

Distributions of the index in a rotational workspace while fixing translational coordinates as x,y = 0, and z = 1.5

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Fig. 19

A spatial Delta robot

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Fig. 20

Distribution of LCI index in the chosen workspace of Delta robot with respect to (a) o-xyz and (b) o-x′y′z′ coordinates

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Fig. 21

Distribution of NPI index in the chosen workspace of Delta robot with respect to (a) o-xyz, and (b) o-x′y′z′ coordinates

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