Structural synthesis of planar kinematic chains by adapting a Mckay-type algorithm

Mechanism and Machine Theory

Volumn 41, Issue 9, 2006, Pages 1021-1030

  Sunkari, Rajesh P ^a   Schmidt, Linda C ^a  

^a UNIVERSITY OF MARYLAND   (United States)

Author keywords

Graph generation; Isomorph free generation; Kinematic synthesis; McKay type algorithms

Indexed keywords

ALGORITHMS; EFFICIENCY; GRAPH THEORY; INVERSE KINEMATICS; STRUCTURAL ANALYSIS;

GRAPH GENERATION; ISOMORPH-FREE GENERATION; KINEMATIC SYNTHESIS; MCKAY-TYPE ALGORITHM;

CHAINS;

EID: 33745506086     PISSN: 0094114X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mechmachtheory.2005.11.007     Document Type: Article

References (36)

1. Crossley F. Developments in Theoretical and Applied Mechanics. Permutations of kinematic chains with eight members or less from graph-theoretic view point Vol. 2 (1965), Pergamon Press, Oxford pp. 467-486
2. Woo L. Type synthesis of plane linkages. J. Eng. Industry Trans. ASME Ser. B 89 (1967) 158-172
3. Manolescu N., and Tempea I. Structural synthesis of plane kinematic chains with multiple joints and five degree of freedom. Rev. Roumaine des Sci. Tech. Serie de Mecanique Appl. 12 (1967) 1117-1140
4. Manolescu N., and Tempea I. Structural and kinematic synthesis of plane driving mechanisms with multiple joints and two degrees of mobility. Rev. Roumaine des Sci. Tech. Serie de Mecanique Appl. 12 (1967) 1251-1275
5. Huang M., and Soni A. Application of linear and nonlinear graphs in structural synthesis of kinematic chains. J. Eng. Industry Trans. ASME Ser. B 95 (1973) 525-532
6. Tuttle E., Peterson S., and Titus J. Enumeration of basic kinematic chains using the theory of finite groups. J. Mech. Transm. Autom. Des. Trans. ASME 111 (1989) 498-503
7. Hwang W., and Hwang Y. Computer aided structural synthesis of planar kinematic chains with simple joints. Mech. Machine Theory 27 (1992) 189-199
8. Tsai L. Mechanism Design: Enumeration of kinematic structures according to function (2000), CRC Press LLC, Boca Raton
9. Gruebler M. Allgemeine eigenschaften der zwanglaufigen ebenen inematischen ketten: Part I. Civilingenieur 29 (1885) 167-200
10. Gruebler M. Allgemeine eigenschaften der zwanglaufigen ebenen inematischen ketten: Part II. Verh. Ver. Bef. Gew. 64 (1885) 179-223
11. Olson D., Erdman A., and Riley D. A systematic procedure for type synthesis of mechanisms with literature review. Mech. Machine Theory 20 4 (1985) 285-295
12. Mruthyunjaya T. Kinematic structure of mechanisms revisited. Mech. Machine Theory 38 (2003) 279-320
13. Davies T., and Crossley F. Structural analysis of plane linkages by Franke's condensed notation. J. Mech. 1 (1966) 171-184
14. Freudenstein F., and Dobrjanskyj L. On a theory of type synthesis of mechanisms. Proc. of 11th Int. Congress of Applied Mechanics (1964), Springer, Berlin 420-428
15. Tuttle E., Peterson S., and Titus J. Further applications of group theory to the enumeration and structural analysis of basic kinematic chains. J. Mech. Transm. Autom. Des. Trans. ASME 111 (1989) 494-497
16. Tuttle E. Generation of planar kinematic chains. Mech. Machine Theory 31 (1996) 729-748
17. Manolescu N. A unitary method for construction of the kinematic plane chains and plane mechanisms with different degrees of mobility. Rev. Roumaine des Sci. Tech. Serie de Mecanique Appl. 9 (1964) 1263-1313
18. 3p = 2. Rev. Roumaine des Sci. Tech. Serie de Mecanique Appl. 10 (1965) 999-1042
19. Manolescu N. For a united point of view in the study of the structural analysis of kinematic chains and mechanisms. J. Mech. 3 (1968) 149-169
20. Tischler C., Samuel A., and Hunt K. Kinematic chains for robot hands-I: Orderly number synthesis. Mech. Machine Theory 30 (1995) 1193-1215
21. Tischler C., Samuel A., and Hunt K. Kinematic chains for robot hands-II: Kinematic constraints, classification, connectivity and actuation. Mech. Machine Theory 30 (1995) 1217-1239
22. Colburn C., and Read R. Orderly algorithms for graph generation. Int. J. Comput. Math. (1979) 167-172
23. Mruthyunjaya T. Structural synthesis by transformation of binary chains. Mech. Machine Theory 14 (1979) 221-231
24. Hwang W., and Hwang Y. An algorithm for the detection of degenerate kinematic chains. Math. Comput. Model. 15 11 (1991) 9-15
25. Schmidt L., Shetty H., and Chase S. A graph grammar approach for structure synthesis of mechanisms. J. Mech. Des. Trans. ASME 122 (2000) 371-376
26. Hopcroft J., and Wong J. A linear time algorithm for the isomorphism of planar graphs. Proc. of the 6th Annual ACM Symp. On Theory of Computing (1974), ACM Press, New York 172-184
27. Rao A., and Deshmukh P. Computer aided structural synthesis of planar kinematic chains obviating the test for isomorphism. Mech. Machine Theory 36 (2001) 489-506
28. McKay B. Isomorph-free exhaustive generation. J. Algorithm. 26 (1998) 306-324
29. Brinkmann G. Discrete Mathematical Chemistry. Isomorphism rejection in structure generation programs. DIMACS Series on Discrete Mathematics and Theoretical Computer Science Vol. 51 (2000), AMS, Providence, RI pp. 25-38
30. Lovasz L. Combinatorial Problems and Exercises. second ed. (1993), North-Holland Publishing Co., Amsterdam
31. Lee H., and Yoon Y. Detection of rigid structure in enumerating basic kinematic chain by sequential removal of binary link string. JSME Int. J. 35 4 (1992) 647-651
32. B. McKay, Nauty user's guide (version 1.5), Tech. Rep. TR-CS-90-02, Australian National University, 1990.
33. R. Sunkari, L. Schmidt, Critical review of existing degeneracy testing and mobility type identification algorithms for kinematic chains, in: Proc. of CD-ROM of the ASME 2005, 29th Mechanisms and Robotics Conference, Long Beach, CA, 2005.
34. Lee H., and Yoon Y. Automatic method for enumeration of complete set of kinematic chains. JSME Int. J. 37 4 (1994) 812-818
35. Lang S. Algebra. Graduate Texts in Mathematics. third ed. Vol. 211 (2002), Springer-Verlag, New York
36. Artin M. Algebra (1991), Prentice Hall