ANALYSIS OF KINEMATIC SYSTEMS - A GENERALIZED-APPROACH

The goal of the designer of kinematic systems is a deterministic and s table design. An analysis method must, therefore, be able to quantify both aspects. The generalized approach to the analysis of kinematic sy stems presented herein reduces the analysis of kinematic systems to si mple 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 th e external forces. Then Hertz's theory is used to estimate the deflect ions at the contact points, from which global error motions are comput ed. The method has been developed for two-body systems with an arbitra ry number of unconstrained degrees of freedom. From these elementary b uilding blocks, more complex systems can be assembled. We show how fri ction 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 syst ems is closely linked to the eigen values of the system matrix. The ge neral formulation naturally includes previous work on such special cas es as couplings and linear motion systems.