On the Use of Ternary Products to Characterize the Dexterity of Spatial Kinematic Chains

TitleOn the Use of Ternary Products to Characterize the Dexterity of Spatial Kinematic Chains
Publication TypeConference Paper
Year of PublicationIn Press
AuthorsBongardt B, Müller A
Conference NameAdvances in Robot Kinematics
Date Published06/2022
Conference LocationBilbao, Spain
Keywordsdual number algebra, Kinematics in space, line geometry, manipulability analysis, screw theory, singularity analysis
Abstract

Two performance indices are introduced that characterize the singularities and the manipulability of a general spatial kinematic chain in a threefold, physically significant manner. The ternary volume and shape indices are obtained as characteristic scalars of two ternary product matrices that capture the geometry of the joint axes in a certain configuration coherently. It is suggested to interpret the product matrices as set generalizations of ternary versions of the scalar product and the dyadic product for dual vector pairs by relaxing the condition "epsilon^2 = 0".