Realization of point planar elastic behaviors using revolute joint serial mechanisms having specified link lengths

• Means to achieve any compliance in E(2) with a given serial mechanism are provided.
• Necessary and sufficient conditions to realize a given compliance are identified.
• The realization conditions are interpreted in terms of mechanism configuration.
• Conditions on relative link lengths to realize all compliances in E(2) identified
• Synthesis procedures to achieve a realizable compliance are developed.

This paper presents methods for the realization of 2 × 2 translational compliance matrices using serial mechanisms having only revolute joints, each with selectable compliance. The link lengths of the mechanism and the location of the compliant frame relative to the mechanism base are arbitrary but specified. The realizability of a given compliant behavior is investigated, and necessary and sufficient conditions for the realization of a given compliance with a given mechanism are obtained. These realization conditions are interpreted in terms of geometric relationships among the joints. We show that, for an appropriately sized 3R serial mechanism, any single 2 × 2 compliance matrix can be realized by properly choosing the joint compliances and the mechanism configuration. Requirements on mechanism geometry to realize every particle planar elastic behavior at a given location just by changing the mechanism configuration are also identified.