A Numerical Approach to Find Distinct Mechanisms of a Planar Kinematic Chain Using Linkage Coordinates

In a planar kinematic chain, different mechanisms are possible when on link’s mobility is restricted by fixing it. These mechanisms obtained are called as inversions. In the present paper, a numerical approach is proposed which is based on new concept defined as ‘linkage coordinates’ related to connectivity of a link in a closed planar kinematic chain. The proposed method is tested on various linkages (8, 9, 10) with varying degree of freedom (DoF) for which identified inversions are in correlation with earlier results in the literature. The proposed method can be applied to analyze other characteristics of kinematic chains with higher linkages and higher DoF. 8-link 1-DoF completed results are presented in the results section of the paper.