TY - JOUR

T1 - On the Configurations of Closed Kinematic Chains in Three-dimensional Space

AU - Zangerl, Gerhard

AU - Steinicke, Alexander

PY - 2022/4/30

Y1 - 2022/4/30

N2 - A kinematic chain in three-dimensional 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 n−3. 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.

AB - A kinematic chain in three-dimensional 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 n−3. 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.

KW - Configuration space

KW - Closed kinematic chain

KW - closed continuous random walk

KW - path planning

U2 - 10.36890/iejg.972576

DO - 10.36890/iejg.972576

M3 - Article

VL - 15.2022

SP - 96

EP - 115

JO - International Electronic Journal of Geometry

JF - International Electronic Journal of Geometry

SN - 1307-5624

IS - 1

ER -