This paper studies the problem of spatial linkage synthesis for motion generation from the perspective of extracting geometric constraints from a set of specified spatial displacements. In previous work, we have developed a computational geometric framework for integrated type and dimensional synthesis of planar and spherical linkages, the main feature of which is to extract the mechanically realizable geometric constraints from task positions, and thus reduce the motion synthesis problem to that of identifying kinematic dyads and triads associated with the resulting geometric constraints. The proposed approach herein extends this data-driven paradigm to spatial cases, with the focus on acquiring the point-on-a-sphere and point-on-a-plane geometric constraints which are associated with those spatial kinematic chains commonly encountered in spatial mechanism design. Using the theory of kinematic mapping and dual quaternions, we develop a unified version of design equations that represents both types of geometric constraints, and present a simple and efficient algorithm for uncovering them from the given motion.
A Computational Geometric Approach for Motion Generation of Spatial Linkages With Sphere and Plane Constraints
Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received June 6, 2018; final manuscript received October 11, 2018; published online December 10, 2018. Assoc. Editor: Andrew P. Murray.
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Li, X., Ge, Q. J., and Gao, F. (December 10, 2018). "A Computational Geometric Approach for Motion Generation of Spatial Linkages With Sphere and Plane Constraints." ASME. J. Mechanisms Robotics. February 2019; 11(1): 014504. https://doi.org/10.1115/1.4041788
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