Kinematics Optimization of a 3-SPS Parallel Redundant Motion Mechanism Using Conformal Geometric Algebra

Abstract:

In this paper, an actuation mechanism for high-speed aiming of a target is proposed. The mechanism is a 3DOF-SPS (spherical-prismatic-spherical) parallel manipulator and can be used for a missile defense system with a fast reaction time. This type of parallel mechanism has high rigidity against external disturbances and accordingly high stiffness and precision. The target aiming requires 2 degrees of freedom and this 3 DOF mechanism has one redundancy. For fast manipulation of the proposed mechanism, the redundancy can be exploited and an optimal solution can be found out of the infinite number of inverse kinematic solutions. For finding a near time-optimal solution, a cost function is formulated considering displacement of each parallel link and an optimization technique is used for solution of the inverse kinematic problem.

• Periodical: Applied Mechanics and Materials (Volumes 789-790)
• Pages: 889-895
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.789-790.889
• Online since: September 2015
• Authors: Jahng Hyon Park, Jeseok Kim, Jin Han Jeong
• Keywords: 3-SPS Parallel Redundant Motion Mechanism, Conformal Geometric Algebra, Inverse Kinematics

References

[1] Kim, S.H., et al. Design of a 6 dof flight simulator based on a full spinning parallel mechanism platform. AIAA Modeling and Simulation Technologies Conf., 2005, 15-18.

DOI: 10.2514/6.2005-6105

[2] Tsai, T. -C. and Y. -L. Hsu. Development of a parallel surgical robot with automatic bone drilling carriage for stereotactic neurosurgery. Systems, Man and Cybernetics, 2004 IEEE International Conf., 2004, 2156-2161.

DOI: 10.1109/icsmc.2004.1400646

[3] Alici, G. and B. Shirinzadeh, Topology optimisation and singularity analysis of a 3-SPS parallel manipulator with a passive constraining spherical joint. Mechanism and Machine Theory, 39(2), 2004, 215-235.

DOI: 10.1016/s0094-114x(03)00116-2

[4] Hildenbrand, D., Foundations of Geometric Algebra Computing, 1-12, 27-44 (Springer, 2012).

[5] Dorst, L., Honing geometric algebra for its use in the computer sciences, in Geometric computing with Clifford algebras, 127-152 (Berlin Heidelberg, Springer, 2001).

DOI: 10.1007/978-3-662-04621-0_6

[6] Lasenby, J., et al., New geometric methods for computer vision: An application to structure and motion estimation, International Journal of Computer Vision, 26(3), 1998, 191-213.

[7] Li, H., D. Hestenes, and A. Rockwood, Generalized homogeneous coordinates for computational geometry, in Geometric Computing with Clifford Algebras, 27-59 (Berlin Heidelberg, Springer, 2001).

DOI: 10.1007/978-3-662-04621-0_2

[8] D'Orangeville, C. and A.N. Lasenby, Geometric algebra for physicists (Cambridge University Press, 2003).

[9] Press, W.H., Numerical recipes 3rd edition: The art of scientific computing, 366-372 (Cambridge University Press, 2007).