Requirements on the Spatial Distribution of Elastic Components Used in Compliance Realization

In this paper, necessary conditions on the loca- tions and orientations of elastic components in a compliant mechanism used to realize any given spatial compliance are identified. The topologies considered are either fully parallel or fully serial mechanisms having an arbitrary number of lumped elastic components. It is shown that the requirements on elastic components are characterized by a sphere for the location distribution and by three cones for the orientation distribution. The easy to assess conditions on the set of components can be used to achieve a more desirable mechanism geometry when used in conjunction with existing spatial compliance synthesis procedures.