Extension of graph theory to the duality between static systems and mechanisms

Journal of Mechanical Design

Volumn 128, Issue 1, 2006, Pages 179-191

  Shai, Offer ^a   Pennock, Gordon R ^b  

^a TEL AVIV UNIVERSITY   (Israel)

^b PURDUE UNIVERSITY   (United States)

Author keywords

Beams; Dead center positions; Duality; Graph representations; Kinematics; Planetary gear trains; Platform type robots; Serial robots; Static pillar systems; Statics; Synthesis; Unstable truss

Indexed keywords

BEAMS AND GIRDERS; KINEMATICS; MECHANISMS; ROBOTICS; TRUSSES;

DEAD-CENTER POSITIONS; GRAPH REPRESENTATIONS; PLANETARY GEAR TRAINS; PLATFORM-TYPE ROBOTS; SERIAL ROBOTS; STATIC PILLAR SYSTEMS; UNSTABLE TRUSS;

GRAPH THEORY;

EID: 33645758488     PISSN: 10500472     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2120827     Document Type: Article

References (26)

1. Girvin, S. M., 1996, "Duality in Perspective," Science, New Series, Genome Issue, October, 274(5287), pp. 524-525.
2. Maxwell, J. C., 1864, "On Reciprocal Figures and Diagrams of Forces," Philos. Mag., Series 4, 27, pp. 250-261.
3. Davies, T., 1983, "Mechanical Networks - III, Wrenches on Circuit Screws," Mechanism and Machine Theory, Pergamon, New York, Vol. 18(2), pp. 107-112.
4. McGuire, W., Gallagher, R. H., and Ziemian, R. D., 2000, Matrix Structural Analysis, 2nd ed., Wiley, New York.
5. Phillips, J., 1984, Freedom in Machinery, Vol. 1, Cambridge University Press, Cambridge, England.
6. Gosselin, F., and Lallemand, J.-P., 2001, "A New Insight into the Duality Between Serial and Parallel Non-Redundant and Redundant Manipulators," Robotica, Cambridge University Press, Cambridge, Vol. 19(4), pp. 365-370.
7. Ball, R. S., 1998, The Theory of Screws, Cambridge University Press, Cambridge, England. (Originally published in 1876 and revised by the author in 1900, now reprinted with an introduction by H. Lipkin and J. Duffy).
8. Collins, C. L., and Long, G. L., 1995, "On the Duality of Twist/ Wrench Distributions in Serial and Parallel Chain Robot Manipulators," IEEE International Conference on Robotics and Automation, May, Vol. 1, pp. 526-531.
9. Mohamed, M. G., and Duffy, J., 1985, "A Direct Determination of the Instantaneous Kinematics of Fully Parallel Robot Manipulators," ASME J. Mech., Transm., Autom. Des., Vol. 107(2), pp. 226-229.
10. Duffy, J., 1996, Statics and Kinematics with Applications to Robotics, Cambridge University Press, Cambridge, England.
11. Waldron, K. J., and Hunt, K. H., 1991, "Series-Parallel Dualities in Actively Coordinated Mechanisms," The International Journal of Robotics Research, The MIT Press, October, Vol. 10(5), pp. 473-480.
12. Davidson, J. K., and Hunt, K. H., 2004, Robots and Screw Theory: Applications of Kinematics and Statics to Robotics. Oxford University Press, New York.
13. Swamy, M. N. S., and Thulasiraman, K., 1981, Graphs, Networks, and Algorithms, Wiley, New York.
14. Shai, O., 2001, "The Duality Relation Between Mechanisms and Trusses," Mechanism and Machine Theory, Pergamon, New York, 36(3), pp. 343-369.
15. Shai, O., and Mohr, Y., 2004, "Towards Transferring Engineering Knowledge Through Graph Representations: Transferring Willis Method to Mechanisms and Trusses," Eng. Comput., 20(1), pp. 2-10.
16. Shai, O., 2001, "The Multidisciplinary Combinatorial Approach and its Applications in Engineering," AIEDAM-AI for Engineering Design, Analysis and Manufacturing, Vol. 15(2), pp. 109-144.
17. Shai, O., 2002, "Utilization of the Dualism Between Determinate Trusses and Mechanisms," Mechanism and Machine Theory, Pergamon, New York, Vol. 37(11), pp. 1307-1323.
18. Shai, O., and Rubin, D., 2003, "Representing and Analyzing Integrated Engineering Systems Through Combinatorial Representations," Eng. Comput., 19(4), pp. 221-232.
19. Shai, O., and Pennock, G. R., 2005, "A Study of the Duality Between Planar Kinematics and Statics," ASME J. Mech. Des. (in press).
20. Shai, O., and Polansky, I., 2004, "Finding Dead Point Positions of Linkages Through Graph Theoretical Duality Principle," ASME J. Mech. Des. (in press).
21. Uicker, J. J., Jr., Pennock, G. R., and Shigley, J. E., 2003, Theory of Machines and Mechanisms, 3rd ed., Oxford University Press, Inc., New York.
22. Dobrjanskyj, L., and Freudenstein, F., 1967, "Some Applications of Graph Theory to the Structural Analysis of Mechanisms," ASME J. Eng. Ind., 89, pp. 153-158.
23. Stewart, D., 1965, "A Platform with Six Degrees of Freedom," The Institution of Mechanical Engineers, Great Britain, Vol. 180(15), pp. 371-384.
24. Yan, H.-S., and Wu, L.-L., 1989, "On The Dead-Center Positions of Planar Linkage Mechanisms," ASME J. Mech., Transm., Autom. Des., 111(1), pp. 40-46.
25. Merlet, J. P., 1989, "Singular Configurations of Parallel Manipulators and Grassmann Geometry," The International Journal of Robotics Research, The MIT Press, Vol. 8(5), pp. 45-56.
26. Waldron, K. J., and Kinzel, G. L., 2004, Kinematics, Dynamics, and Design of Machinery, 2nd ed., Wiley, New York.