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TECHNICAL PAPERS

Designing Two-Revolute Manipulators for Prescribed Feasible Workspace Regions

[+] Author and Article Information
Marco Ceccarelli

Dipartimento di Meccanica, Strutture, Ambiente e Territorio, Università di Cassino, Via Di Biasio 43, 03043 Cassino (Fr), Italye-mail: ceccarelli@ing.unicas.it

J. Mech. Des 124(3), 427-434 (Aug 06, 2002) (8 pages) doi:10.1115/1.1485743 History: Received April 01, 1998; Online August 06, 2002
Copyright © 2002 by ASME
Topics: Design , Manipulators
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References

Gupta,  K. C., and Roth,  B., 1982, “Design Considerations for Manipulator Workspace,” ASME J. Mech. Des., 104, pp. 704–711.
Freudenstein,  F., and Primrose,  E. J. F., 1984, “On the Analysis and Synthesis of the Workspace of a Three-Link Turning-Pair Connected Robot Arm,” ASME Journal of Mechanisms, Transmissions and Automation in Design, 106, pp. 365–370.
Tsai,  Y. C., and Soni,  A. H., 1985, “Workspace Synthesis of 3R, 4R, 5R and 6R Robots,” Mech. Mach. Theory, 20(4), pp. 555–563.
Roth, B., 1987, “Analytical Design of Two-Revolute Open Chains,” Sixth CISM-IFToMM Symposium on Theory and Practice of Robots and Manipulators, The MIT Press, Cambridge, pp. 207–214.
Ceccarelli, M., and Vinciguerra, A., 1990, “A Design Method of Three-Revolute Open Chain Manipulators,” Proceedings of VIIth CISM-IFToMM Symposium on Theory and Practice of Robots and Manipulators, Hermes, Paris, pp. 318–325.
Ceccarelli,  M., 1995, “A Synthesis Algorithm for Three-Revolute Manipulators by Using an Algebraic Formulation of Workspace Boundary,” ASME J. Mech. Des., 117, pp. 298–302.
Roth, B., 1986, “Analytical Design of Open Chains,” Third International Symposium on Robotic Research, MIT Press, Cambridge, pp. 281–288.
Yang,  D. C. H., and Lee,  T. W., 1984, “Heuristic Combinatorial Optimization in the Design of Manipulator Workspace,” IEEE Trans. Syst. Man Cybern., SMC-14(4), pp. 571–580.
Lin,  C. D., and Freudenstein,  F., 1986, “Optimization of the Workspace of a Three-Revolute Open Chain Manipulators,” Int. J. Robot. Res., 5(1), pp. 104–111.
Ceccarelli,  M., Mata,  V., and Valero,  F., 1994, “Optimal Synthesis of Three-Revolute Manipulators,” AIMETA International Journal Meccanica, Kluwer, Dordrecht, 29(1), pp. 95–103.
Fichter,  E. F., and Hunt,  K. H., 1975, “The Fecund Torus, its Bitangent-Circles and Derived Linkages,” Mech. Mach. Theory, 10, pp. 167–176.
Ceccarelli, M., and Scaramuzza, G., 1995, “Analytical Constraints for a Workspace Design of 2R Manipulators,” Computational Kinematics ’95, Kluwer, Dordrecht, pp. 173–182.
Ceccarelli, M., 1996, “Feasible Workspace Regions for a Two-Revolute Manipulator Design,” Recent Advances in Robot Kinematics, Kluwer, Dordrecht, pp. 189–198.
Ceccarelli,  M., 1996, “A Formulation for the Workspace Boundary of General N-Revolute Manipulators,” Mech. Mach. Theory, 31(5), pp. 637–646.
Ghizzetti, A., and Rosati F., 1972, Lezioni di Analisi Matematica—Vol. II, Veschi, Roma, pp. 58–62. (in Italian).
Belding, W. G., ed., 1983, ASM Handbook of Engineering Mathematics, American Society for Metals, Metals Park, pp. 19–21.
Desa, S., and Roth, B., 1985, “Mechanics: Kinematics and Dynamics,” Recent Advances in Robotics, Beni G. and Hackwood S., eds., J. Wiley & Sons, New York, Ch. 3, pp. 71–130.

Figures

Grahic Jump Location
A two-revolute manipulator and its design parameters
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General geometry of feasible workspace regions FW for two-revolute manipulators depicted as grew area
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A degenerated case for feasible workspace regions when RA=RU (Coordinates are expressed in u unit length)
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A degenerate case for feasible workspace regions when the prominent area of RC collapses into the boundary of RARU (Coordinates are expressed in u unit length)
Grahic Jump Location
A degenerated case for feasible workspace regions when P2,P3 and P4 are collinear (Coordinates are expressed in u unit length)
Grahic Jump Location
Characteristic geometry of the toroids within feasible workspace regions FW as a function of P1 location for the case with P2=(4,2),P3=(3,4),P4=(6,5) (Coordinates are expressed in u unit length)
Grahic Jump Location
A numerical example of the proposed design procedure: given workspace points P1=(8,3),P2=(4,2),P3=(3,3),P4=(5,5), in the computed feasible workspace regions and the toroid workspace (dotted line) for the synthesized manipulators (Coordinates are expressed in u unit length)

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