On the Design of Spatial 4C Mechanisms for Rigid-Body Guidance Through 4 Positions

Abstract

Abstract This paper presents a procedure for determining the fixed and moving congruences associated with four finitely separated spatial positions. Furthermore, a methodology is derived for selecting the lines from the congruences which define the joint axes of a 4C mechanism. The result is a design procedure for performing the kinematic dimensional synthesis of spatial 4C mechanisms for four position rigid body guidance. Associated with four finitely separated positions in space are a fixed and a moving congruence. These congruences are a two dimensional set of lines, where each line defines the axis of a cylindrical joint that guides a body through the four prescribed positions. In order to uniquely determine a 4C mechanism from the congruences four free parameters must be specified. We present procedures for determining these free design parameters which result in mechanisms with joint axes that are nearest to some desired location. Moreover, included is a detailed numerical example illustrating the design process.