0
Journal of Mechanisms and Robotics | Volume 6 | Issue 3 | research-article
Research Papers

Force/Motion Transmissibility Analysis of Six Degree of Freedom Parallel Mechanisms

[+] Author and Article Information
Tian Huang

Key Laboratory of Mechanism Theory and
Equipment Design of Ministry of Education,
Tianjin University,
Tianjin 300072, China
e-mail: tianhuang@tju.edu.cn, tian.huang@warwick.ac.uk

Manxin Wang

Key Laboratory of Mechanism Theory and
Equipment Design of Ministry of Education,
Tianjin University,
Tianjin 300072, China
e-mail: wangmxtju@aliyun.com

Shuofei Yang

Key Laboratory of Mechanism Theory and
Equipment Design of Ministry of Education,
Tianjin University,
Tianjin 300072, China
e-mail: yangsf@tju.edu.cn

Tao Sun

Key Laboratory of Mechanism Theory and
Equipment Design of Ministry of Education,
Tianjin University,
Tianjin 300072, China
e-mail: stao@tju.edu.cn

Derek G. Chetwynd

School of Engineering,
University of Warwick,
Coventry CV4 7AL, UK
e-mail: D.G.Chetwynd@warwick.ac.uk

Fugui Xie

Department of Mechanical Engineering,
Tsinghua University,
Beijing 100084, China
e-mail: xiefg@mail.tsinghua.edu.cn

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received August 15, 2013; final manuscript received December 24, 2013; published online April 21, 2014. Assoc. Editor: Yuefa Fang.

J. Mechanisms Robotics 6(3), 031010 (Apr 21, 2014) (5 pages) Paper No: JMR-13-1161; doi: 10.1115/1.4026631 History: Received August 15, 2013; Revised December 24, 2013
Article
References
Figures
Citing Articles

Drawing mainly on the concepts of dual space and dual basis in linear algebra and on existing screw theory, this paper presents a novel and systematic approach for the force/motion transmissibility analysis of 6DOF parallel mechanisms. By taking the reciprocal product of a wrench on a twist as a linear functional, the property exhibited by the dual basis allows the formulation of the force/motion transmissibility between the joint space and operation space in an accurate and concise manner. The consistency between the force/motion transmissibility and the minimum singular value of the Jacobian for singularity identification is rigorously proved. This leads to the development of a set of homogeneously dimensionless local and global transmission indices for measuring the closeness to singular configurations as well as for kinematic performance evaluation over a given workspace. A Stewart platform is employed an exemplar to illustrate the effectiveness of the approach.
FIGURES IN THIS ARTICLE
<>
Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

1
Merlet, J. P., 2006, “Jacobian, Manipulability, Condition Number, and Accuracy of Parallel Robots,” ASME J. Mech. Des., 128(1), pp. 199–206. [CrossRef]
2
Ma, O., and Angeles, J., 1991, “Optimum Architecture Design of Platform Manipulators,” Proceedings of the Fifth International Conference on Advanced Robotics, pp. 1130–1135.
3
Tandirci, M., Angeles, J., and Ranjbaran, F., 1992, “The Characteristic Point and the Characteristic Length of Robotic Manipulators,” Proceedings of ASME 22nd Biennial Conference Robotics, Spatial Mechanisms and Mechanical System, Scotsdale, AZ, Vol. 45, pp. 203–208.
4
Angeles, J., 2006, “Is There a Characteristic Length of a Rigid-Body Displacement,” Mech. Mach. Theory, 41(8), pp. 884–896. [CrossRef]
5
Khan, W. A., and Angeles, J., 2006, “The Kinetostatic Optimization of Robotic Manipulators: The Inverse and the Direct Problems,” ASME J. Mech. Des., 128(1), pp. 168–178. [CrossRef]
6
Pond, G., and Carretero, J. A., 2006 “Formulating Jacobian Matrices for the Dexterity Analysis of Parallel Manipulators,” Mech. Mach. Theory, 41(12), pp. 1505–1519. [CrossRef]
7
Pond, G., and Carretero, J. A., 2007, “Quantitative Dexterous Workspace Comparison of Parallel Manipulators,” Mech. Mach. Theory, 42(10), pp. 1388–1400. [CrossRef]
8
Liu, H. T., Huang, T., and Chetwynd, D. G., 2011, “A Method to Formulate a Dimensionally Homogeneous Jacobian of Parallel Manipulators,” IEEE Trans. Rob., 27(1), pp. 150–156. [CrossRef]
9
Ball, R. S., 1990, A Treatise on the Theory of Screws, Cambridge University, Oxford, UK.
10
Yuan, M. S. C., Freudenstwin, F., and Woo, L. S., 1971, “Kinematic Analysis of Spatial Mechanism by Means of Screw Coordinates. Part 2-Analysis of Spatial Mechanisms,” ASME J. Eng. Ind., 91(1), pp. 67–73. [CrossRef]
11
Sutherland, G., and Roth, B., 1973, “A Transmission Index for Spatial Mechanisms,” ASME J. Eng. Ind., 95(2), pp. 589–597. [CrossRef]
12
Tsai, M. J., and Lee, H. W., 1994, “Generalized Evaluation for the Transmission Performance of Mechanisms,” Mech. Mach. Theory, 29(4), pp. 607–618. [CrossRef]
13
Chen, C., and Angeles, J., 2007, “Generalized Transmission Index and Transmission Quality for Spatial Linkages,” Mech. Mach. Theory, 42(9), pp. 1225–1237. [CrossRef]
14
Takeda, Y., and Funabashi, H., 2001, “A Transmission Index for in–Parallel Wire–Driven Mechanisms,” JSME Int. J. Ser. C, 44(1), pp. 180–187. [CrossRef]
15
Chang, W. T., Lin, C. C., and Lee, J. J., 2003, “Force Transmissibility Performance of Parallel Manipulators,” J. Rob. Syst., 20(11), pp. 659–670. [CrossRef]
16
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]
17
Liu, X. J., Wu, C., and Wang, J. S., 2012, “A New Approach for Singularity Analysis and Closeness Measurement to Singularities of Parallel Manipulators,” ASME J. Mech. Rob., 4(4), p. 041001. [CrossRef]
18
Huang, T., Liu, H. T., and Chetwynd, D. G., 2011, “Generalized Jacobian Analysis of Lower Mobility Manipulators,” Mech. Mach. Theory, 46(6), pp. 831–844. [CrossRef]
19
Hogben, L., 2007, Handbook of Linear Algebra, Chapman & Hall/CRC, Boca Raton, FL.
20
Kong, X. W., and Gosselin, C. M., 2007, Type Synthesis of Parallel Mechanisms, Springer Tracts in Advanced Robotics. Springer-Verlag, Berlin.
21
Hunt, K. H., 1978, Kinematic Geometry of Mechanisms, Oxford University, Oxford.
22
Joshi, S., and Tsai, L. W., 2002, “Jacobian Analysis of Limited-DOF Parallel Manipulators,” ASME J. Mech. Des., 124(2), pp. 254–258. [CrossRef]
23
Huang, T., Wang, J. S., Gosselin, M. C., and Whitehouse, D. J., 1999, “Determination of Closed Form Solution to the 2D-Orientation Workspace of Gough–Stewart Parallel Manipulators,” IEEE Trans. Rob. Autom., 15(6), pp.1121–1125. [CrossRef]
24
Tsai, L. W., 1999, Robot Analysis: The Mechanics of Serial and Parallel Manipulators, Wiley-Interscience Publication, New York.
25
Huang, Z., Chen, L. H., and Li, Y. W., 2003, “The Singularity Principle and Property of Stewart Parallel Manipulator,” J. Rob. Syst., 20(4), pp. 163–176. [CrossRef]
26
Hunt, K. H., 1983, “Structural Kinematics of In-Parallel-Actuated Robot-Arms,” ASME J. Mech. Des., 105(4), pp. 705–712.
27
Fichter, E. F., 1986, “A Stewart Platform–Based Manipulator: General Theory and Practical Construction,” Int. J. Rob. Res., 5(2), pp. 157–181. [CrossRef]

Figures

Grahic Jump Location
Fig. 2

Distribution of ηP versus ψ = 0-360 deg and θ = 0-120 deg of a 3/6 Stewart platform

+Distribution of ηP versus ψ = 0-360 deg and θ = 0-120 deg of a 3/6 Stewart platform
View Large  |  Save Figure  |  Download Slide (.ppt)
Distribution of ηP versus ψ = 0-360 deg and θ = 0-120 deg of a 3/6 Stewart platform
Grahic Jump Location
Fig. 1

The schematic diagram of a 3/6 Stewart platform

+The schematic diagram of a 3/6 Stewart platform
View Large  |  Save Figure  |  Download Slide (.ppt)
The schematic diagram of a 3/6 Stewart platform

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Infinitesimal Mechanics of the PKMs
Mechanics of Accuracy in Engineering Design of Machines and Robots Volume I: Nominal Functioning and Geometric Accuracy
Accuracy of an Axis
Mechanics of Accuracy in Engineering Design of Machines and Robots Volume I: Nominal Functioning and Geometric Accuracy
Feedback-Aided Minimum Joint Motion
Robot Manipulator Redundancy Resolution
Pseudoinverse Method and Singularities Discussed
Robot Manipulator Redundancy Resolution
Manipulability-Maximizing SMP Scheme
Robot Manipulator Redundancy Resolution
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
This site uses cookies. By continuing to use our website, you are agreeing to our privacy policy. | Accept
Sign In