Analysis of kinematic systems : a generalized approach

The goal of the designer of kinematic systems is a deterministic and stable design. An analysis method must, therefore, be able to quantify both aspects. The generalized approach to the analysis of kinematic systems presented herein reduces the analysis of kinematic systems to simple matrix analysis. The system matrix containing the geometry of the system is introduced as the key to the analysis of kinematic systems. The procedure calculates the magnitudes of the contact forces from the external forces. Then Hertz's theory is used to estimate the deflections at the contact points, from which global error motions are computed. The method has been developed for two-body systems with an arbitrary number of unconstrained degrees of freedom. From these elementary building blocks, more complex systems can be assembled. We show how friction can be included in the model, based on simplifying assumptions. The quality/performance of the design can be checked at various points throughout the analysis. We show that the stability of kinematic systems is closely linked to the eigen values of the system matrix. The general formulation naturally includes previous work on such special cases as couplings and linear motion systems.