On the Configurations of Closed Kinematic Chains in threedimensional Space
Abstract
A kinematic chain in threedimensional Euclidean space consists of $n$ links that are connected by spherical joints. Such a chain is said to be within a closed configuration when its link lengths form a closed polygonal chain in three dimensions. We investigate the space of configurations, described in terms of joint angles of its spherical joints, that satisfy the the loop closure constraint, meaning that the kinematic chain is closed. In special cases, we can find a new set of parameters that describe the diagonal lengths (the distance of the joints from the origin) of the configuration space by a simple domain, namely a cube of dimension $n3$. We expect that the new findings can be applied to various problems such as motion planning for closed kinematic chains or singularity analysis of their configuration spaces. To demonstrate the practical feasibility of the new method, we present numerical examples.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.14588
 Bibcode:
 2021arXiv210714588Z
 Keywords:

 Computer Science  Robotics;
 Computer Science  Computational Geometry;
 51k05;
 51N20;
 F.0;
 G.0;
 I.0
 EPrint:
 20 pages, 9 figures