Transversality and its applications to kinematics

Abstract

Transversality is a mathematical concept, widely used in singularity theory, which generalises the idea of regularity of a function. One of its uses is in providing a method for certifying that a property of a given set of functions or mappings is generic, which is to say that it holds for almost all members of that set. Its application in kinematics is illustrated via a prototype for showing that in a given class of parallel mechanisms, for almost all choices of design parameter the configuration space is non-singular and hence a manifold.