Invariant Measures of Closeness to Linear Dependency of Screw Systems

Abstract

This paper describes a new, general analytical method of determining the closeness to linear dependence of any system of lines and screws, giving n invariant scalars for an n-system of screws. The method proposed evaluates the maximum available scalar or Klein product between the unit screw under test and any unit combination of screws reciprocal to all of the set except the test screw. Examples are given of the application of this theory to the behaviour of a partially complete system of kinematic restraint such as those used in manufacturing fixtures of a simple structure and of a serial robotic manipulator.