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TECHNICAL PAPERS

Dual Quaternion Synthesis of Constrained Robotic Systems

[+] Author and Article Information
Alba Perez, J. M. McCarthy

Robotics and Automation Laboratory, Dept. of Mechanical and Aerospace Engineering, University of California, Irvine, California 92697e-mail: jmmccart@uci.edu

J. Mech. Des 126(3), 425-435 (Oct 01, 2003) (11 pages) doi:10.1115/1.1737378 History: Received February 01, 2003; Revised October 01, 2003
Copyright © 2004 by ASME
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References

Schoenflies, A., 1886, Geometrie der Bewegung in Synthetischer Darstellung, Leipzig, Germany. (See also the French translation: La Géométrie du Movement, Paris, 1983.)
Burmester, L., 1886, Lehrbuch der Kinematik, Verlag Von Arthur Felix, Leipzig, Germany.
Roth,  B., 1967, “Finite Position Theory Applied to Mechanism Synthesis,” ASME J. Appl. Mech., 34E, pp. 599–605.
Hartenberg, R., and Denavit, J., 1964, Kinematic Synthesis of Linkages, McGraw-Hill, New York, NY.
Sandor, G. N., and Erdman, A. G., 1984, Advanced Mechanism Design: Analysis and Synthesis, Vol. 2. Prentice-Hall, Englewood Cliffs, NJ.
Suh, C. H., and Radcliffe, C. W., 1978, Kinematics and Mechanisms Design, John Wiley & Sons, New York.
McCarthy, J. M., 2000, Geometric Design of Linkages, Springer-Verlag, New York.
Hunt, K. H., 1978, Kinematic Geometry of Mechanisms, Clarendon Press.
Suh,  C. H., 1968, “Design of Space Mechanisms for Rigid-Body Guidance,” ASME J. Ind., 90B, pp. 499–506.
McCarthy,  J. M., 1995, “The Synthesis of Planar RR and Spatial CC Chains and the Equation of a Triangle,” ASME J. Mech. Des., 117(B), pp. 101–106.
Huang, C., and Chang, Y-J., 2000, “Polynomial Solution to the Five-Position Synthesis of Spatial C-C Dyads via Dialytic Elimination,” Proc. ASME Design Engineering Technical Conference, Paper No. DETC2000/MECH-14102, Baltimore, Maryland, Sept. 10–13.
Kihonge,  J. N., Vance,  J. M., and Larochelle,  P. M., 2002, “Spatial Mechanism Design in Virtual Reality with Networking,” ASME J. Mech. Des., 124(3), pp. 435–440.
Innocenti,  C., 1995, “Polynomial Solution of the Spatial Burmester Problem,” ASME J. Mech. Des., 117(1).
Liao,  Q., and McCarthy,  J. M., 2001, “On the Seven Position Synthesis of a 5-SS Platform Linkage,” ASME J. Mech. Des., 123(1), pp. 74–79.
Chen,  P., and Roth,  B., 1967, “Design Equations for Finitely and Infinitesimally Separated Position Synthesis of Binary Link and Combined Link Chains,” ASME J. Ind., 91, pp. 209–219.
Nielsen, J., and Roth, B., 1995, “Elimination Methods for Spatial Synthesis,” Computational Kinematics, J. P. Merlet and B. Ravani eds., Vol. 40 of Solid Mechanics and Its Applications, pp. 51–62, Kluwer Academic Publishers.
Kim,  H. S., and Tsai,  L. W., 2003, “Kinematic Synthesis of Spatial 3-RPS Parallel Manipulators,” ASME J. Mech. Des., 125(1), pp. 92–97.
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.
Tsai, L. W., 1972, “Design of Open Loop Chains for Rigid Body Guidance,” Ph.D. Thesis, Department of Mechanical Engineering, Stanford University.
Tsai,  L. W., and Roth,  B., 1973, “A Note on the Design of Revolute-Revolute Cranks,” Mech. Mach. Theory, 8, pp. 23–31.
Perez, A., and McCarthy, J. M., 2000, “Dimensional Synthesis of Bennett Linkages,” Proc. 2000 ASME Design Engineering Technical Conferences, Baltimore, MD, Sept. 10–13.
Sandor,  G. N., 1968, “Principles of a General Quaternion-Operator Method of Spatial Kinematic Synthesis,” ASME J. Appl. Mech., 35(1), 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. Ind., 91, pp. 115–122.
Sandor,  G. N., Weng,  T. C., and Xu,  Y., 1988, “The Synthesis of Spatial Motion Generators With Prismatic, Revolute and Cylindric Pairs Without Branching Defect,” Mech. Mach. Theory, 23(4), pp. 69–274.
Sandor,  G. N., Xu,  Y., and Weng,  T. C., 1986, “Synthesis of 7-R Spatial Motion Generators with Prescribed Crank Rotations and Elimination of Branching,” Int. J. Robot. Res., 5(2), pp. 143–156.
Mavroidis,  C., Lee,  E., and Alam,  M., 2001, “A New Polynomial Solution to the Geometric Design Problem of Spatial RR Robot Manipulators Using the Denavit-Hartenberg Parameters,” ASME J. Mech. Des., 123(1), pp. 58–67.
Lee, E., Mavroidis, C., and Merlet, J. P., 2002, “Five Precision Points Synthesis of Spatial RRR Manipulators Using Interval Analysis,” Proc. ASME 2002 Design Eng. Tech. Conf., paper no. DETC2002/MECH-34272, Sept. 29-Oct. 2, Montreal, Canada.
Lee,  E., and Mavroidis,  D., 2002, “Solving the Geometric Design Problem of Spatial 3R Robot Manipulators Using Polynomial Homotopy Continuation,” ASME J. Mech. Des., 124(4), pp. 652–661.
Lee, E., and Mavroidis, D., 2002, “Geometric Design of Spatial PRR Manipulators Using Polynomial Elimination Techniques,” Proc. ASME 2002 Design Eng. Tech. Conf., paper no. DETC2002/MECH-34314, Sept. 29-Oct. 2, Montreal, Canada.
Gupta,  K. C., 1986, “Kinematic Analysis of Manipulators Using Zero Reference Position Description,” Int. J. Robot. Res., 5(2), pp. 5–13.
Tsai, L. W., 1999, Robot Analysis: The Mechanics of Serial and Parallel Manipulators, John Wiley and Sons, New York, NY.
Yang,  A. T., and Freudenstein,  F., 1964, “Application of Dual-Number Quaternion Algebra to the Analysis of Spatial Mechanisms,” ASME J. Appl. Mech., June , pp. 300–308.
McCarthy, J. M., 1990, Introduction to Theoretical Kinematics, The MIT Press, Cambridge, MA.
Shoham,  M., and Jen,  F. H., 1994, “On Rotations and Translations with Application to Robot Manipulators,” Advanced Robotics, 8(2), pp. 203–229.
Angeles, J., 1998, “The Application on Dual Algebra to Kinematic Analysis,” Computational Methods in Mechanical Systems, NATO ASI Series, J. Angeles and E. Zakhariev, eds., Springer, Berlin.
Ravani, B., and Ge Q. J., 1991, “Kinematic Localization for World Model Calibration in Off-Line Robot Programming Using Clifford Algebra,” Proc. of IEEE International Conf. on Robotics and Automation, Sacramento, CA, April, pp. 584–589.
Larochelle, P., 2000, “Approximate Motion Synthesis via Parametric Constraint Manifold Fitting,” Advances in Robot Kinematics, J. Lenarcic and M. M. Stanisic, eds., Kluwer Acad. Publ., Dordrecht.
Perez, A., and McCarthy, J. M., 2002, “Dual Quaternion Synthesis of Constrained Robots,” Advances in Robot Kinematics, J. Lenarcic and F. Thomas, eds., Kluwer Academic Publ. 443–454. Caldes de Malavella, Spain, June 24–29.
Craig, J. J., 1989, Introduction to Robotics, Mechanics and Control, Addison Wesley Publ. Co, Reading, MA.
Bottema, O., and Roth, B., 1979, Theoretical Kinematics, North Holland Press, NY.
Perez, A., 2003, “Dual Quaternion Synthesis of Constrained Robotic Systems,” Ph.D. Thesis, Department of Mechanical Engineering, University of California, Irvine.
Verschelde,  J., 1999, “Algorithm 795: PHCpack: A Generalpurpose Solver for Polynomial Systems by Homotopy Continuation,” ACM Trans. Math. Softw., 25(2), 251276, 1999. Software available at http://www.math.uic.edu/jan.
Su, H., Collins, C., and McCarthy, J. M., “An Extensible Java Applet for Spatial Linkage Synthesis,” Proc. ASME Des, Eng. Technical Conferences, paper no. DETC2002/MECH-24271, Montreal, Canada, 2002.
Collins,  C., McCarthy,  J. M., Perez,  A., and Su,  H., 2002, “The Structure of an Extensible Java Applet for Spatial Linkage Synthesis,” ASME J. Computing and Information Science in Engineering, 2(1), pp. 45–49.

Figures

Grahic Jump Location
A constrained serial robot and three specified task positions
Grahic Jump Location
The five complete plus four translational task positions
Grahic Jump Location
The RPRP robot reaching the task positions 1, 2, 3 and 4
Grahic Jump Location
The RPRP robot reaching the task positions 5, 6, 7, 8, and 9
Grahic Jump Location
Four RPC solutions for a 5-position synthesis problem

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