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Enumeration of parallel manipulators

Published online by Cambridge University Press:  01 July 2009

Roberto Simoni ,
Andrea Piga Carboni  and
Daniel Martins
Roberto Simoni*
Affiliation:
Mechanical Engineering Department, Universidade Federal de Santa Catarina 88040-900, Florianópolis, SC, Brazil.
Andrea Piga Carboni
Affiliation:
Mechanical Engineering Department, Universidade Federal de Santa Catarina 88040-900, Florianópolis, SC, Brazil.
Daniel Martins
Affiliation:
Mechanical Engineering Department, Universidade Federal de Santa Catarina 88040-900, Florianópolis, SC, Brazil.
*
*Corresponding author. E-mail: roberto.emc@gmail.com
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Summary

In this paper, we present a new method of enumeration of parallel manipulators with one end-effector. The method consists of enumerating all the manipulators possible with one end-effector that a single kinematic chain can originate. A very useful simplification for kinematic chain, mechanism and manipulator enumeration is their representation through graphs. The method is based on group theory where abstract structures are used to capture the internal symmetry of a structure in the form of automorphisms of a group. The concept used is orbits of the group of automorphisms of a colored vertex graph. The theory and some examples are presented to illustrate the method.

Keywords

Kinematic chainMechanismManipulatorGroup theoryGraph theoryAutomorphismActionOrbit

Information

Type
Article
Information
Robotica , Volume 27 , Issue 4 , July 2009 , pp. 589 - 597
Copyright
Copyright © Cambridge University Press 2008

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References

1.Sunkari, R. P. and Schmidt, L. C., “Structural synthesis of planar kinematic chains by adapting a mckay-type algorithm,” Mech. Mach. Theory 41, 1021–1030 (2006).CrossRefGoogle Scholar
2.McKay, B. D., Nauty User's Guide (version 1.5). Technical Report, TR-CS-90-02. Department Computer Science, Australian National University (1990).Google Scholar
3.McKay, B. D., “Isomorph-free exhaustive generation,” J. Algorithms 26, 306–324 (1998).CrossRefGoogle Scholar
4.Simoni, R., Martins, D. and Carboni, A. P., “Enumeration of kinematic chains and mechanisms,” Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science, submitted.Google Scholar
5.Simoni, R. and Martins, D., “Criteria for Structural Synthesis and Classification of Mechanism,” Proceedings of the 19th International Congress of Mechanical Engineering – COBEM, Brasília - DF (2007).Google Scholar
6.Martins, D. and Carboni, A. P., “Variety and connectivity in kinematic chains,” Mech. Mach. Theory. doi:10.1016/j.mechmachtheory.2007.10.011.Google Scholar
7.Tuttle, E. R., “Generation of planar kinematic chains,” Mech. Mach. Theory 31, 729–748 (1996).CrossRefGoogle Scholar
8.Tuttle, E. R., Peterson, S. W. and Titus, J. E., “Enumeration of basic kinematic chains using the theory of finite groups,” ASME J. Mech. Transm. Autom. Design 111, 498–503 (1999).CrossRefGoogle Scholar
9.Tuttle, E. R., Peterson, S. W. and Titus, J. E., “Further applications of group theory to the enumeration and structural analysis of basic kinematic chains,” ASME J. Mech. Transm. Autom. Design 111, 494–497 (1989).CrossRefGoogle Scholar
10.Alizade, R. and Bayram, C., “Structural synthesis of parallel manipulators,” Mech. Mach. Theory 39, 857–870 (2004).CrossRefGoogle Scholar
11.Tsai, L. W., Mechanism Design: Enumeration of Kinematic Structures According to Function (Mechanical Engineering series, CRC Press, Boca Raton, Florida, 2001).Google Scholar
12.Belfiore, N. P. and Benedetto, A. D., “Connectivity and redundancy in spatial robots,” Int. J. Robot. Res. 19, 1245–1261 (2000).CrossRefGoogle Scholar
13.Tischler, C., Samuel, A. and Hunt, K., “Selecting multi-freedom multi-loop kinematic chains to suit a given task,” Mech. Mach. Theory 36, 925–938 (2001).CrossRefGoogle Scholar
14.Ionescu, T. G., “Terminology for mechanisms and machine science,” Mech. Mach. Theory. 38, 597–1111 (2003).Google Scholar
15.Merlet, J. P., Parallel Robots (Kluwer, Academic Publishers, Boston, 2002).Google Scholar
16.Alperin, J. L. and Bell, R. B., Groups and Representations (Springer, New York, 1995).CrossRefGoogle Scholar
17.Burrow, M., Representation Theory of Finite Groups (Dover: New York, 1993).Google Scholar
18.Rotman, J. J., An Introduction to the Theory of Groups (Springer, New York, 1995).CrossRefGoogle Scholar
19.Scott, W. R., Group Theory (Prentice-Hall Englewood Cliffs, 1964).Google Scholar
20.McKay, B. D., The nauty page. URL: http://cs.anu.edu.au/~bdm/nauty, Australian National University, 1992.Google Scholar
21.Tischler, C. R., Alternative Structures for Robot Hands. Ph.D. dissertation (University of Melbourne, 1995).Google Scholar
22.Simoni, R., Martins, D. and Carboni, A. P., “Mãos Robóticas: Critérios para síntese Estrutural e Classificação,” Proceedings of the 15th Jornadas de Jóvenes Investigadores da Asociación de Universidades Grupo Montevideo, Campus de la UNA, Paraguy (2007).Google Scholar