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TECHNICAL PAPERS

Kinematic Synthesis of Spatial R-R Dyads for Path Following With Applications to Coupled Serial Chain Mechanisms

[+] Author and Article Information
Venkat Krovi, G. K. Ananthasuresh, Vijay Kumar

Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104-6315

J. Mech. Des 123(3), 359-366 (Oct 01, 1999) (8 pages) doi:10.1115/1.1370977 History: Accepted October 01, 1999
Copyright © 2001 by ASME
Topics: Chain , Design , Equations , Rotation
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References

Krovi, V., Ananthasuresh, G. K., and Kumar, V., 1997, “Synthesis of Coupled Multi-Link Serial Chain Mechanisms,” Proceedings of the 5th National Applied Mechanisms & Robotics Conference, Cincinnati, Ohio, October 12–15, 1997.
Krovi, V., 1998, “Design and Virtual Prototyping of User-Customized Assistive Devices,” Ph.D. Dissertation, Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, USA. (URL:http://www.cim.mcgill.ca/∼Venkat/publications.htm).
Bodduluri, R. M. C., Ge, Q. J., McCarthy, J. M., and Roth, B., 1994, “The Synthesis of Spatial Linkages,” Section 5.4 in Modern Kinematics: Developments in the Last Forty Years, Ed. A. G. Erdman, John Wiley & Sons, Inc., New York, pp. 159–164.
Roth,  B., 1967, “The Kinematics of Motion Through Finitely Separated Positions,” ASME J. Appl. Mech., 34 (E), pp. 591–598.
Roth,  B., 1967, “On the Screw Axes and Other Special Lines Associated with Spatial Displacements of a Rigid Body,” ASME J. Appl. Mech., 89 (B), pp. 102–110.
Tsai,  L.-W., and Roth,  B., 1972, “Design of Dyads With Helical, Cylindrical, Spherical, Revolute, and Prismatic Joints,” Mech. Mach. Theory, 7, pp. 591–598.
Suh, C. H., and Radcliffe, C. W., 1978, Kinematics and Mechanism Design, John Wiley and Sons, New York.
Sandor,  G. N., 1968, “Principles of a General Quaternion Operator Method of Spatial Kinematic Synthesis,” ASME J. Appl. Mech., 90 (E), pp 40–46.
Sandor,  G. N., and Bisshopp,  K. E., 1969, “On a General Method of Spatial Kinematic Synthesis by Means of a Stretch Rotation Tensor,” ASME J. Eng. Ind., 91, Feb., pp. 115–122.
Sandor,  G. N., Xu,  Y., and Weng,  T.-C., 1986, “Synthesis of 7R Spatial Motion Generators With Prescribed Crank Rotations and Elimination of Branching,” Int. J. Robot Res., 5, No. 2, pp. 143–156.
Sandor,  G. N., Weng,  T.-C., and Xu,  Y., 1988, “The Synthesis of Spatial Motion Generators With Prismatic Revolute and Cylindric Pairs Without Branching Defects,” Mech. Mach. Theory, 23, No. 4, pp. 269-274.
Lee,  K.-W., and Yoon,  Y.-S., 1993, “Kinematic Synthesis of RRSS Spatial Motion Generators Using Euler Parameters and Quaternion Algebra,” J. Mech. Eng. Sci., 207, pp. 355–359.
Suh,  C. H., 1969, “On the Duality in the Existence of R-R Links for Three Positions,” ASME J. Eng. Ind., 9, (1) pp. 129–134.
Tsai,  L.-W., and Roth,  B., 1973, “A Note on the Design of Revolute-Revolute Cranks,” Mech. Mach. Theory, 8, pp. 23–31.
Strang, G., 1984, Linear Algebra and its Applications, Harcourt Brace Jovanovich Publishers, San Diego.
Gere, J., and Weaver, W., Jr., 1984, Matrix Algebra for Engineers, Brooks/Cole Publishing Company, Monterrey, CA.

Figures

Grahic Jump Location
(a) Spatial R-R dyad with two degrees of freedom; (b) the coupled R-R dyad with only one degree of freedom
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Single crank passing through two points in space
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Spatial R-R dyad passing through three design positions
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The nullspace dyad, a geometric interpretation of M
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Nullspace triad, a geometric interpretation of the nullspace of M
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(a) Optimized coupled R-R dyad OLMN of example 1 shown in its first position; (b) snapshots of the optimized dyad of example 1 during its entire motion
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(a) Optimized coupled R-R dyad OLMN of example 2 shown in its first position; (b) snapshots of the optimized dyad of example 2 during its entire motion

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