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Technical Brief

A Computational Geometric Approach for Motion Generation of Spatial Linkages with Sphere and Plane Constraints

[+] Author and Article Information
Xiangyun Li

School of Mechanical Engineering, Southwest Jiaotong University, Chengdu, P.R.China, 610031
xiangyun.app@gmail.com

Qiaode Jeffrey Ge

Department of Mechanical Engineering, Stony Brook University, Stony Brook, USA, 11794
qiaode.ge@stonybrook.edu

Feng Gao

School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, P.R.China, 200240
fengg@sjtu.edu.cn

1Corresponding author.

ASME doi:10.1115/1.4041788 History: Received June 06, 2018; Revised October 11, 2018

Abstract

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.

Copyright (c) 2018 by ASME
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