Structural Analysis of Kinematic Chains and Mechanisms Based on Matrix Representation

Abstract

A method based on Bocher’s formulae has been presented for determining the characteristic coefficients (which have recently been suggested [19] as an index of isomorphism) of the matrix associated with the kinematic chain. The method provides an insight into the physical meaning of these coefficients and leads to a possible way of arriving at the coefficients by an inspection of the chain. A modification to the matrix notation is proposed with a view to permit derivation of all possible mechanisms from a kinematic chain and distinguishing the structurally distinct ones. Algebraic tests are presented for determining whether a chain possesses total, partial or fractionated freedom. Finally a generalized matrix notation is proposed to facilitate representation and analysis of multiple-jointed chains.