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.