0
Journal of Mechanisms and Robotics | Volume 10 | Issue 3 | Technical Brief
Technical Brief

Identification of Canonical Basis of Screw Systems Using General-Special Decomposition

[+] Author and Article Information
Genliang Chen

State Key Laboratory of Mechanical System and Vibration,
Shanghai Key Laboratory of Digital Manufacture for
Thin-walled Structures,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: leungchan@sjtu.edu.cn

Hao Wang

State Key Laboratory of Mechanical System and Vibration,
Shanghai Key Laboratory of Digital Manufacture for
Thin-walled Structures,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: wanghao@sjtu.edu.cn

Zhongqin Lin

State Key Laboratory of Mechanical System and Vibration,
Shanghai Key Laboratory of Digital Manufacture for
Thin-walled Structures,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: zqlin@sjtu.edu.cn

Xinmin Lai

State Key Laboratory of Mechanical System and Vibration,
Shanghai Key Laboratory of Digital Manufacture for
Thin-walled Structures,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: xmlai@sjtu.edu.cn

Manuscript received July 9, 2015; final manuscript received June 27, 2017; published online April 5, 2018. Assoc. Editor: Jian S. Dai.

J. Mechanisms Robotics 10(3), 034501 (Apr 05, 2018) (8 pages) Paper No: JMR-15-1194; doi: 10.1115/1.4039218 History: Received July 09, 2015; Revised June 27, 2017
Article
References
Figures

The theory of screws plays a fundamental role in the field of mechanisms and robotics. Based on the rank-one decomposition of positive semidefinite (PSD) matrices, this paper presents a new algorithm to identify the canonical basis of high-order screw systems. Using the proposed approach, a screw system can be decomposed into the direct sum of two subsystems, which are referred to as the general and special subsystems, respectively. By a particular choice of the general subsystem, the canonical basis of the original system can be obtained by the direct combination of the subsystems' principal elements. In the proposed decomposition, not only the canonical form of the screw system but also the corresponding distribution of all those possible base elements can be determined in a straightforward manner.
FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Topics: Screws
Your Session has timed out. Please sign back in to continue.

References

1
Joshi, S. A. , and Tsai, L. W. , 2002, “ Jacobian Analysis of Limited-DOF Parallel Manipulators,” ASME J. Mech. Des., 124(2), pp. 254–258. [CrossRef]
2
Li, Q. C. , and Huang, Z. , 2003, “ Mobility Analysis of Lower-Mobility Parallel Manipulators Based on Screw Theory,” IEEE International Conference on Robotics and Automation (ICRA), Taipei, Taiwan, Sept. 14–19, pp. 1179–1184.
3
Dai, J. S. , Huang, Z. , and Lipkin, H. , 2006, “ Mobility of Overconstrained Parallel Mechanisms,” ASME J. Mech. Des., 128(1), pp. 220–229. [CrossRef]
4
Kong, X. W. , and Gosselin, C. M. , 2002, “ Kinematics and Singularity Analysis of a Novel Type of 3-CRR 3-DOF Translational Parallel Manipulator,” Int. J. Rob. Res., 21(9), pp. 791–798. [CrossRef]
5
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]
6
Kong, X. W. , and Gosselin, C. M. , 2004, “ Type Synthesis of 3T1R 4-DOF Parallel Manipulators Based on Screw Theory,” IEEE Trans. Rob. Autom., 20(2), pp. 181–190. [CrossRef]
7
Carricato, M. , and Parenti-Castelli, V. , 2002, “ Singularity-Free Fully-Isotropic Translational Parallel Mechanisms,” Int. J. Rob. Res., 21(2), pp. 161–174. [CrossRef]
8
Huang, Z. , and Li, Q. C. , 2003, “ Type Synthesis of Symmetrical Lower-Mobility Parallel Mechanisms Using the Constraint-Synthesis Method,” Int. J. Rob. Res., 22(1), pp. 59–79.
9
Su, H. J. , Dorozhkin, D. V. , and Vance, J. M. , 2009, “ A Screw Theory Approach for the Conceptual Design of Flexible Joints for Compliant Mechanisms,” ASME J. Mech. Rob., 1(4), p. 041009. [CrossRef]
10
Yu, J. J. , Li, S. Z. , Su, H. J. , and Culpepper, M. L. , 2011, “ Screw Theory Based Methodology for the Deterministic Type Synthesis of Flexure Mechanisms,” ASME J. Mech. Rob., 3(3), p. 031008. [CrossRef]
11
Ball, R. S. , 1900, A Treatise on the Theory of Screws, Cambridge University Press, Cambridge, UK.
12
Hunt, K. H. , 1978, Kinematic Geometry of Mechanisms, Oxford University Press, London.
13
Gibson, C. G. , and Hunt, K. H. , 1990, “ Geometry of Screw Systems—1: Screws: Genesis and Geometry,” Mech. Mach. Theory, 25(1), pp. 1–10. [CrossRef]
14
Gibson, C. G. , and Hunt, K. H. , 1990, “ Geometry of Screw Systems—2: Classification of Screw Systems,” Mech. Mach. Theory, 25(1), pp. 11–27. [CrossRef]
15
Donelan, P. S. , and Gibson, C. G. , 1993, “ On the Hierarchy of Screw Systems,” Acta Appl. Math., 32(3), pp. 267–296. [CrossRef]
16
Rico, J. M. , and Duffy, J. , 1992, “ Classification of Screw Systems—I: One- and Two-Systems,” Mech. Mach. Theory, 27(4), pp. 459–470. [CrossRef]
17
Rico, J. M. , and Duffy, J. , 1992, “ Classification of Screw Systems—II: Three-Systems,” Mech. Mach. Theory, 27(4), pp. 471–490. [CrossRef]
18
Tsai, M. J. , and Lee, H. W. , 1993, “ On the Special Bases of Two- and Three-Screw Systems,” ASME J. Mech. Des., 115(3), pp. 540–546. [CrossRef]
19
Dai, J. S. , 1993, “ Screw Image Space and Its Application to Robotic Grasping,” Ph.D. thesis, University of Salford, Manchester, UK.
20
Bandyopadhyay, S. , and Ghosal, A. , 2009, “ An Eigenproblem Approach to Classical Screw Theory,” Mech. Mach. Theory, 44(6), pp. 1256–1269. [CrossRef]
21
Fang, Y. F. , and Huang, Z. , 1998, “ Analytical Identification of the Principal Screws of the Third Order Screw System,” Mech. Mach. Theory, 33(7), pp. 987–992. [CrossRef]
22
Zhao, J. S. , Zhou, H. X. , Feng, Z. J. , and Dai, J. S. , 2009, “ An Algebraic Methodology to Identify the Principal Screws and Pitches of Screw Systems,” J. Mech. Eng. Sci., 223(8), pp. 1931–1941. [CrossRef]
23
Altuzarra, O. , Salgado, O. , Pinto, C. , and Hernández, A. , 2013, “ Analytical Determination of the Principal Screws for General Screw Systems,” Mech. Mach. Theory, 60, pp. 28–46. [CrossRef]
24
Dai, J. S. , and Jones, J. R. , 2003, “ A Linear Algebraic Procedure in Obtaining Reciprocal Screw Systems,” J. Rob. Syst., 20(7), pp. 401–412. [CrossRef]
25
Kim, D. , and Chung, W. K. , 2003, “ Analytic Formulation of Reciprocal Screws and Its Application to Nonredundant Robot Manipulators,” ASME J. Mech. Des., 125(1), pp. 158–164. [CrossRef]
26
Dai, J. , 2014, Screw Algebra and Lie Groups and Lie Algebra, Higher Education Press, Beijing, China.
27
Murray, R. M. , Sastry, S. S. , and Li, Z. X. , 1994, A Mathematical Introduction to Robotic Manipulation, CRC Press, Boca Raton, FL.
28
Selig, J. M. , 2005, Geometric Fundamentals of Robotics, Springer, New York.
29
Chen, G. L. , Wang, H. , Lin, Z. Q. , and Lai, X. M. , 2015, “ The Principal Axes Decomposition of Spatial Stiffness Matrices,” IEEE Trans. Rob., 31(1), pp. 191–207. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Construction of the principal frames for the subsystems

+Construction of the principal frames for the subsystems
View Large  |  Save Figure  |  Download Slide (.ppt)
Construction of the principal frames for the subsystems
Grahic Jump Location
Fig. 2

Influences of L1 on the structure of the associated G1

+Influences of L1 on the structure of the associated G1
View Large  |  Save Figure  |  Download Slide (.ppt)
Influences of L1 on the structure of the associated G1
Grahic Jump Location
Fig. 3

Flowchart of the general-special decomposition

+Flowchart of the general-special decomposition
View Large  |  Save Figure  |  Download Slide (.ppt)
Flowchart of the general-special decomposition
Grahic Jump Location
Fig. 4

Canonical basis of the systems belonging to G2⊕L2

+Canonical basis of the systems belonging to G2⊕L2
View Large  |  Save Figure  |  Download Slide (.ppt)
Canonical basis of the systems belonging to G2⊕L2

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
Simulation and Agitation Characteristic Model of Screw Shaft in Bituminous Mixture Transfer Vehicle Based on PSO and L-M Algorithm
International Conference on Advanced Computer Theory and Engineering (ICACTE 2009)
Singularity Analysis for 5-5R Parallel Manipulator Based on Screw Theory
Proceedings of the 2010 International Conference on Mechanical, Industrial, and Manufacturing Technologies (MIMT 2010)
Study on Screw Drill Wear When Drilling Low Carbon Stainless Steel and Accompanying Phenomena in the Cutting Zone
International Conference on Instrumentation, Measurement, Circuits and Systems (ICIMCS 2011)
Accuracy of an Axis
Mechanics of Accuracy in Engineering Design of Machines and Robots Volume I: Nominal Functioning and Geometric Accuracy
Fatigue Analysis in the Connecting Rod of MF285 Tractor by Finite Element Method
International Conference on Advanced Computer Theory and Engineering, 4th (ICACTE 2011)
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
Sign In