Kinematic study of the original and revised general line-symmetric Bricard 6R linkages

Journal of Mechanisms and Robotics

Volumn 6, Issue 3, 2014, Pages

  Song, Chao Yang ^a   Chen, Yan ^b   Chen, I Ming ^c  

^a SINGAPORE UNIVERSITY OF TECHNOLOGY AND DESIGN   (Singapore)

^b TIANJIN UNIVERSITY   (China)

^c NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

Closure equations; Kinematics; Multiple closures; The Bricard linkage

Indexed keywords

BRICARD LINKAGES; CLOSURE EQUATIONS;

KINEMATICS;

EID: 84906959489     PISSN: 19424302     EISSN: 19424310     Source Type: Journal    
DOI: 10.1115/1.4026339     Document Type: Article

References (32)

1. Bricard, R., 1897, "Me´moire sur la the´orie de l'octae`dre articule´," J. Pure Appl. Math., 3, pp. 113-150.
2. Bricard, R., 1927, Lec¸ons de cine´matique, Gauthier-Villars, Paris.
3. Baker, J. E., 1980, "An Analysis of the Bricard Linkages," Mech. Mach. Theory, 15(4), pp. 267-286.
4. Phillips, J., 1984, Freedom in Machinery I: Introducing Screw Theory, Cambridge University Press, Cambridge, UK.
5. Phillips, J., 1990, Freedom in Machinery II: Screw Theory Exemplified, Cambridge University Press, Cambridge, UK.
6. Bennett, G. T., 1911, "Deformable Octahedra," Proc. London Math. Soc., 2(10), pp. 309-343.
7. Baker, J. E., 1986, "Limiting Positions of a Bricard Linkage and Their Possible Relevance to the Cyclohexane Molecule," Mech. Mach. Theory, 21(3), pp. 253-260.
8. Lee, C. C., 1996, "On the Generation Synthesis of Movable Octahedral 6R Mechanisms," ASME Design Engineering Technical Conferences and Computers in Engineering Conference, Irvine, CA, August 18-22, ASME Paper No. 96-DETC/MECH-1576.
9. Chai, W. H., and Chen, Y., 2010, "The Line-Symmetric Octahedral Bricard Linkage and Its Structural Closure," Mech. Mach. Theory, 45(5), pp. 772-779.
10. Husty, M. L., and Karger, A., 1996, "On Self-Motions of a Class of Parallel Manipulators," Advances in Robot Kinematics, J. Lenarcic and V. Parenti-Castelli, eds., Kluwer Academic Publishers, Dordrecht, Netherlands, pp. 339-348.
11. Husty, M. L., 2000, "E. Borel's and R. Bricard's Papers on Displacements With Spherical Paths and Their Relevance to Self-Motions of Parallel Manipulators," International Symposium on History of Machines and Mechanisms (HMM 2000), M. Ceccarelli, ed., Kluwer Academic Publisher, Dordrecht, Netherlands, pp. 163-172.
12. Husty, M. L., and Zsombor-Murray, J., 1994, "A Special Type of Singular Stewart-Gough Platform," Advances in Robot Kinematics, J. Lenarcic and B. Ravani, eds., Springer, Dordrecht, Netherlands, pp. 449-458.
13. Nawratil, G., 2011, "Self-Motions of TSSM Manipulators With Two Parallel Rotary Axes," ASME J. Mech. Robot., 3(3), p. 031007.
14. Nawratil, G., 2010, "Flexible Octahedra in the Projective Extension of the Euclidean 3-Space," J. Geometry Graphics, 14(2), pp. 147-169.
15. Nelson, G. D., 2010, "Extending Bricard Octahedra," arXiv:1011.5193v1. Available at: http://arxiv.org/ftp/arxiv/papers/1011/1011.5193.pdf
16. Goldberg, M., 1974, "A 6-Plate Linkage in Three Dimensions," Math. Gazette, 58, pp. 287-289.
17. Yu, H. C., 1981, "The Deformable Hexahedron of Bricard," Mech. Mach. Theory, 16(6), pp. 621-629.
18. Wohlhart, K., 1993, "The Two Types of the Orthogonal Bricard Linkage," Mech. Mach. Theory, 28(6), pp. 809-817.
19. Baker, J. E., and Wohlhart, K., 1994, "On the Single Screw Reciprocal to the General Line-Symmetric Six-Screw Linkage," Mech. Mach. Theory, 29(1), pp. 169-175.
20. Baker, J. E., 1997, "The Single Screw Reciprocal to the General Plane-Symmetric Six-Screw Linkage," J. Geometry Graphics, 1(1), pp. 5-12.
21. Lee, C. C., 2000, "Computational and Geometric Investigation on the Reciprocal Screw Axis of Bricard Six-Revolute Mechanisms," ASME Design Engineering Technical Conference and Computers and Information in Engineering Conference (DETC'00), Baltimore, MD, September 10-13, ASME Paper No. DET00/MECH-6104, pp. 93-101.
22. Chen, Y., You, Z., and Tarnai, T., 2005, "Threefold-Symmetric Bricard Linkages for Deployable Structures," Int. J. Solids Struct., 42(8), pp. 2287-2301.
23. Chen, Y., and Chai, W. H., 2011, "Bifurcation of a Special Line and Plane Symmetric Bricard Linkage," Mech. Mach. Theory, 46(4), pp. 515-533.
24. Lee, C. C., and Yan, H. S., 1993, "Movable Spatial 6R Mechanisms With Three Adjacent Parallel Axes," ASME J. Mech. Des., 115(3), pp. 522-529.
25. Racila, L., and Dahan, M., 2010, "Spatial Properties of Wohlhart Symmetric Mechanism," Meccanica, 45(2), pp. 153-165.
26. Chen, Y., 2003, "Design of Structural Mechanisms," Ph.D. dissertation, University of Oxford, Oxford, UK.
27. Wohlhart, K., 1987, "A New 6R Space Mechanism," 7th World Congress on the Theory of Machines and Mechanisms, Sevilla, Spain, September 17-22, pp. 193-198.
28. Denavit, J., and Hartenberg, R. S., 1955, "A Kinematic Notation for Lower-Pair Mechanisms Based on Matrices," ASME J. Appl. Mech., 22(2), pp. 215-221.
29. Mavroidis, C., and Roth, B., 1994, "Analysis and Synthesis of Overconstrained Mechanisms," ASME Design Technical Conferences, Minneapolis, MN, September 11-14, pp. 115-133.
30. Pellegrino, S., 1993, "Structural Computations With the Singular Value Decomposition of the Equilibrium Matrix," Int. J. Solids Struct., 30(21), pp. 3025-3035.
31. Gan,W. W., and Pellegrino, S., 2006, "A Numerical Approach to the Kinematic Analysis of Deployable Structures Forming a Closed Loop," Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci., 220(7), pp. 1045-1056.
32. Bricard, R., 1897, "Me´moire sur la the´orie de l'octae`dre articule´," J. Pure Appl. Math., 3, pp. 113-150 (English translation by E. A. Coutsias, 2010, e-print, http://arxiv.org/abs/1203.1286).