Forward Kinematics Analysis of a 3-PRS Parallel Manipulator
In this article the homotopy continuation method (HCM) to solve the forward kinematic problem of the 3-PRS parallel manipulator is used. Since there are many difficulties in solving the system of nonlinear equations in kinematics of manipulators, the numerical solutions like Newton-Raphson are inevitably used. When dealing with any numerical solution, there are two troublesome problems. One is that good initial guesses are not easy to detect and another is related to whether the used method will converge to useful solutions. Results of this paper reveal that the homotopy continuation method can alleviate the drawbacks of traditional numerical techniques.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1080782Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2195
 B. Dasgupta and T. S. Mruthyunjaya, 2000, "The stewart platform manipulator: a review, "Mech. Mach Theory, Vol. 35, pp. 15-40.
 M. Griffis and J. Duffy, 1989, "A forward displacement analysis of a class of Stewart Platforms, "Journal of Robotic Systems, Vol. 6, No. 6, pp. 703-720.
 L. W. Tsai, G. C. Walsh, and R. E. Stamper, 1996, "Kinematics of a novel three DOF translational platform, "Proceedings of IEEE international conference on robotics and automation, Minneapolis, Minnesota, pp. 3446-51.
 R. Di. Gregorio and V. Parenti-Castelli, 1998, "A translational 3-DOF parallel manipulator, "In: J. Lenarcic, M. L. Husty, (Eds), Advances in robot kinematics: analysis and control. Dordrecht: Kluwer Academic Publishers, pp. 49-58.
 Y. Li and Q. Xu, 2006, "Kinematic analysis and design of a new 3-DOF translational parallel manipulator, "ASME J. Mech. Des., Vol. 128, pp. 729-737.
 X. J. Liu, X. Tang, and j. Wang, 2005, "HANA: a novel spatial parallel manipulator with one rotational and two translational degrees of freedom, "Robotica, Vol. 23, No. 2, pp. 257-70.
 K. M. Lee and S. Arjunan, 1991, "A three-degrees-of-freedom micromotion in parallel actuated manipulator, "IEEE Trans Robot Automat, Vol. 7, No. 5, pp. 634-41.
 D. Liu, R. Che, Z. Li, and Luo, X., 2003, "Research on the theory and the virtual prototype of 3-DOF parallel-link coordinating-measuring machine, "IEEE Trans Instrum Meas, Vol. 52, No. 1, pp. 119-25.
 J. A. Carretero, R. P. Podhorodeski, M. A. Nahon, and C. M. Gosselin, , 2000, "Kinematic analysis and optimization of a new three degree-of freedom spatial parallel manipulator, "ASME J Mech Des., Vol. 122, No. 1, pp. 17-24.
 M. S. Tsai, T. N. Shiau, Y. J. Tsai, and T. H. Chang, 2003, "Direct kinematic analysis of a 3-PRS parallel mechanism, "Mech. Mach Theory, Vol. 38, No. 1, pp. 71-83.
 I. A. Bonev and J. Ryu, 2000, "A new method for solving the direct kinematics of general 6-6 Stewart Platforms, "Mech. Mach Theory, Vol. 35, pp. 423-436.
 J. H. He, 2000, "A coupling method of a homotopy technique and a perturbation technique for nonlinear problems, "International journal of non-linear mechanics 35, 37-43.
 J. H. He, 1999, "Variational iteration method-a kind of non-linear analytical technique: some examples, "International journal of non-linear mechanics, Vol. 34, pp. 699-708.
 T. M. Wu, 2006, "The inverse kinematics problem of spatial 4P3R robot manipulator by the homotopy continuation method with an adjustable auxiliary homotopy function, "Nonlinear Analysis, Vol. 64, pp. 2373-2380.
 T. M. Wu, 2005, "A study of convergence on the Newton- homotopy continuation method, "Applied Mathematics and Computation, Vol. 168, pp. 1169-1174.
 T. M. Wu, 2006, "Solving the nonlinear equations by the Newtonhomotopy continuation method with adjustable auxiliary homotopy function, "Applied Mathematics and Computation, Vol. 173, pp. 383- 388.
 D. D. Ganji, G. A. Afrouzi, and R. A. Talarposhti, 2007, "Application of variational iteration method and homotopy-perturbation, "Physics Letters A, Vol. 368, pp. 450-457.
 A. P. Morgan, 1981, "A method for computing all Solutions to Systems of Polynomial Equations, "GM Research Publication, GMR 3651.
 A. P. Morgan and C. W. Wampler, 1990, "Solving a planar four-bar design problem using continuation, "ASME J. Mech. Des., Vol. 112, pp. 544 -550.
 C. B. Garcia and W. I. Zangwill, 1981, "Pathways to solutions, fixed points, and equilibria, "Prentice-Hall Book Company, Inc., Englewood Cliffs, New Jersey.
 E. L. Allgower and K. Georg, 1990, "Numerical Continuation Methods, An Introduction, "Springer, NewYork.
 S. M. Varedi, H. M. Daniali, and D. D. Ganji, 2008, "Kinematics of an offset 3-UPU translational parallel manipulator by the homotopy continuation method, "Nonlinear Analysis: Real World Applications, doi:10.1016/j.nonrwa.2008.02.014.
 Y. Li. and Q. Xu, 2007, "Kinematic analysis of a 3-PRS parallel manipulator, "Robotics and Computer-Integrated Manufacturing, Vol. 23, pp. 395-408.