Analytical determination of the principal screws for general screw systems

The instantaneous motion capability of a link of a mechanism, specifically the end-effector of a manipulator, is readily described by the type of screw system spanned. Such systems are classified by finding their principal screws, i.e. a basis of the motion space. The analytical determination of such a base has been researched in the past using different techniques. The contribution of this paper is that the procedure presented is a comprehensive method with a simple and intuitive reasoning, allows the systematic finding of the principal screws in closed form for screw systems of any order, introduces the concept of partitioning of the input space, solves for every special system, and is applicable to Inverse Kinematic singular postures where some dimension of the screw system is lost. The method is adequate for computation, by means of a simple generalized eigen problem. The method is applied to every special system and to some complex mechanical systems.