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TECHNICAL PAPERS

Optimal Kinematic Design of Spatial Parallel Manipulators: Application to Linear Delta Robot

[+] Author and Article Information
Michael Stock, Karol Miller

School of Mechanical Engineering, The University of Western Australia, Crawley/Perth WA 6009, Australia

J. Mech. Des 125(2), 292-301 (Jun 11, 2003) (10 pages) doi:10.1115/1.1563632 History: Received August 01, 2001; Revised August 01, 2002; Online June 11, 2003
Copyright © 2003 by ASME
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References

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Clavel, R., 1991, “Conception d’un robot parallele rapide a 4 degres de liberte,” PhD Thesis No. 925. Swiss Federal Institute of Technology (EPFL), Lausanne.
Herve, J. M., 1994, “Methodological Design of New Parallel Robots via the Lie Group of Displacements,” Proc. of CISM/IFToMM Conference Ro.Man.Sy. ’94, Gdansk, pp. 301–306.
Merlet, J. P., 1990, Les Robots Paralleles, Hermes, Paris.
Miller,  K., 2001, “Maximization of Workspace Volume of 3-dof Spatial Parallel Manipulators,” ASME J. Mech. Des., 124(2), pp. 347–350.
Pierrot, F., Dauchez, P., and Fournier, A., 1991, “Hexa, a Fast 6-Degree of Freedom Fully Parallel Robot,” Proc. of International Conference on Advanced Robotics, Pisa, Vol. 2/2, pp. 1158–1163.
Stewart,  D., 1966, “A Platform With Six Degrees of Freedom,” Proc. Inst. Mech. Eng., 180(I), No. 15, pp. 371–386.
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Miller, K., and Clavel, R., 1992, “The Lagrange-based Model of Delta-4 Robot Dynamics,” Robotersysteme 8, Springer-Verlag, pp. 49–54.
Merlet,  J.-P., 1993, “Direct Kinematics of parallel manipulators,” IEEE Trans. Rob. Autom., 9(6), pp. 842–846.
Carretero, J. A., Nahon, M., and Podhorodeski, R. P., 1998, “Workspace Analysis of a 3-dof Parallel Mechanism,” Proceedings of the 1998 IEEE/RSJ International Conference on Intelligent Robots and Systems, IEEE Piscataway, NJ, Vol. 2, pp. 1021–1026.
Stamper, R. E., Tsai, L.-W., and Walsh, G. C., 1997, “Optimization of a Three DOF Translational Platform for Well-Conditioned Workspace,” Proceedings of the 1997 IEEE International Conference on Robotics and Automation, IEEE Piscataway, NJ, Vol. 4 pp. 3250–3255.
Wang,  L.-C. T., and Hsieh,  J.-H., 1998, “Extreme Reaches and Reachable Workspace Analysis of General Parallel Robotic Manipulators,” J. Rob. Syst., 15(3), pp. 145–159.
Gosselin,  C., and Angeles,  J., 1989, “The Optimum Kinematic Design of a Spherical Three-Degree-of-Freedom Parallel Manipulator,” ASME J. Mech. Trans., Autom. Des. 111(2), pp. 202–207.
Tsai, L.-W., Walsh, G. C., and Stamper, R. E., 1996, “Kinematics of a Novel Three DOF Translation Platform,” Proceedings of the 1996 IEEE 13th International Conference on Robotics and Automation, IEEE Piscataway, NJ, Vol. 4, pp. 3446–3451.
Merlet, J.-P., 1992, “On the Infinitesimal Motion of Parallel Manipulators in Singular Configurations,” Proceedings of the 1992 IEEE International Conference on Robotics and Automation, IEEE Piscataway, NJ, Vol. 1, pp. 320–325.
Gosselin,  C., and Angeles,  J., 1988, “The Optimum Kinematic Design of a Planar Three-Degree-of-Freedom Parallel Manipulator,” ASME J. Mech., Trans., Autom. Des., 110(1), pp. 35–41.
Kurtz,  R., and Hayward,  V., 1992, “Multiple-goal Kinematic Optimization of a Parallel Spherical Mechanism with Actuator Redundancy,” IEEE Trans. Rob. Autom., 8(5), pp. 644–651.

Figures

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Rendered MATLAB representation of the Linear Delta
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Wireframe representation of Linear Delta showing nomenclature
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End view (y-z plane) of wireframe representation showing nomenclature
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Stick representation of the eight solutions for the inverse kinematics of the Linear Delta
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Forward kinematics of the Linear Delta visualized as the intersection of three spheres
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Workspace cross section for case 1
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Workspace cross section for case 2
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Workspace cross section of optimal design, with colors showing value of 1/κJ

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