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.
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August 2014
Research-Article
Force/Motion Transmissibility Analysis of Six Degree of Freedom Parallel Mechanisms
Tian Huang,
Tian Huang
1
Key Laboratory of Mechanism Theory and
Equipment Design of Ministry of Education,
e-mail: tianhuang@tju.edu.cn, tian.huang@warwick.ac.uk
Equipment Design of Ministry of Education,
Tianjin University
,Tianjin 300072
, China
e-mail: tianhuang@tju.edu.cn, tian.huang@warwick.ac.uk
1Corresponding author.
Search for other works by this author on:
Manxin Wang,
Manxin Wang
Key Laboratory of Mechanism Theory and
Equipment Design of Ministry of Education,
e-mail: wangmxtju@aliyun.com
Equipment Design of Ministry of Education,
Tianjin University
,Tianjin 300072
, China
e-mail: wangmxtju@aliyun.com
Search for other works by this author on:
Shuofei Yang,
Shuofei Yang
Key Laboratory of Mechanism Theory and
Equipment Design of Ministry of Education,
e-mail: yangsf@tju.edu.cn
Equipment Design of Ministry of Education,
Tianjin University
,Tianjin 300072
, China
e-mail: yangsf@tju.edu.cn
Search for other works by this author on:
Tao Sun,
Tao Sun
Key Laboratory of Mechanism Theory and
Equipment Design of Ministry of Education,
e-mail: stao@tju.edu.cn
Equipment Design of Ministry of Education,
Tianjin University
,Tianjin 300072
, China
e-mail: stao@tju.edu.cn
Search for other works by this author on:
Fugui Xie
Fugui Xie
Department of Mechanical Engineering,
e-mail: xiefg@mail.tsinghua.edu.cn
Tsinghua University
,Beijing 100084
, China
e-mail: xiefg@mail.tsinghua.edu.cn
Search for other works by this author on:
Tian Huang
Key Laboratory of Mechanism Theory and
Equipment Design of Ministry of Education,
e-mail: tianhuang@tju.edu.cn, tian.huang@warwick.ac.uk
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,
e-mail: wangmxtju@aliyun.com
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,
e-mail: yangsf@tju.edu.cn
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,
e-mail: stao@tju.edu.cn
Equipment Design of Ministry of Education,
Tianjin University
,Tianjin 300072
, China
e-mail: stao@tju.edu.cn
Derek G. Chetwynd
Fugui Xie
Department of Mechanical Engineering,
e-mail: xiefg@mail.tsinghua.edu.cn
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. Aug 2014, 6(3): 031010 (5 pages)
Published Online: April 21, 2014
Article history
Received:
August 15, 2013
Revision Received:
December 24, 2013
Citation
Huang, T., Wang, M., Yang, S., Sun, T., Chetwynd, D. G., and Xie, F. (April 21, 2014). "Force/Motion Transmissibility Analysis of Six Degree of Freedom Parallel Mechanisms." ASME. J. Mechanisms Robotics. August 2014; 6(3): 031010. https://doi.org/10.1115/1.4026631
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