Relative motion of manipulator's rigid segments with respect to one another – kinematics

Abstract

Immobile base manipulators each in the form of an open unbranched kinematical chain with kinematical pairs of the fifth class are considered. The manipulator’s segments are assumed to be ideally rigid bodies and each joint can be either revolute or prismatic. This paper deals with the kinematics of the segments in relative motion with respect to one another and gives formulae in vector form for kinematical quantities that describe the relative motion of the segments. The mathematical formalism for obtaining the equation of motion of a class of robotic systems developed in [3] is used to present obtained results. The paper ought to broaden and generalize some existing results in the kinematics of rigid bodies and contribute to a deeper understanding of motion of multibody systems.