Invariant measures of the closeness to linear dependence of six lines or screws

Abstract

Line and screw systems, used in robotics and machinery analysis, become singular at particular geometric configurations. When not singular, measures are required that describe how far they are from being so. A new system of measures is proposed whose outcome is strictly invariant with respect to coordinate frame, origin and unit of length. Examples of the application of the new measures to sixfold systems of lines and screws in the context of work-holding systems and robotic manipulators are given.