Synthesis of kinematic chains with two inversions

A kinematic chain with two inversions is a chain which can result in two nonisomorphic mechanisms by grounding every link of the chain. This paper presents a methodology for the synthesis of kinematic chains with two inversions. The characteristics of kinematic chains with two inversions are studied and applied to develop some basic theorems. Based on these theorems, an algorithm is proposed for the synthesis of all kinematic chains with two inversions. An atlas of kinematic chains with two inversions up to fifteen links is also obtained. Results obtained in this work are helpful to synthesizing the number of kinematic chains.