Unification of mathematical descriptions of compliant behavior centers with physical realizations of those behaviors

Abstract A more intuitive appreciation of spatial compliant behavior can be obtained through analysis and description of the behavior in terms of its centers , specifically the center of stiffness, the center of compliance, and the center of elasticity. This paper investigates the properties of each of these centers. Necessary and sufficient conditions for the coincidence of these centers are identified. A physical appreciation of those compliant behaviors that have coincident centers is obtained in terms of restrictions on the geometry of topologically simple mechanisms that realize those behaviors. The results can be used in the design of compliant mechanisms for robotic manipulation, especially when the compliance is characterized by the location of its center.