This paper use the topological characteristic constants for isomorphism identification, such as the power value sequence (PVS), least distance matrix sequence (LDMS), and loop number (LN). The fourth PVS, the LDMS, and the LN are compared and arranged in descending order, forming a strong complementary chain. Our results show that solving the problem of the isomorphism identification of the kinematic chain (KC) based on graph theory definition has no advantage in efficiency.

The creation method of a 1 degree of freedom double plant carrier gear train (DPGT) transplanting mechanism was proposed based on the functional constraints. Within the eight components of the DPGT, the automatic creation of a transplanting mechanism was realized. A total of 528 DPGTs, which are suitable for transplanting, including 3 five-bar, 13 six-bar, 92 seven-bar, and 420 eight-bar configurations, were obtained for the first time.

To obtain all mechanical schemes, scholars in this field have proposed an innovative design method using kinematic chain configuration synthesis. However, the existing innovative design method easily produces redundant design schemes. We analyze the similar component discrimination method for mechanisms from the perspective of graph theory and apply it to the specialization of topological graphs to solve the problem of redundant design schemes.

Many linkage mechanisms can be broken into components consisting of planar two-revolute (2R) and three-revolute (3R) serial chains, such as the five-, six-, and eight-bar mechanisms. In this study, a new method for the dimensional synthesis of the planar 3R serial chain for motion generation based on CGA is presented. The proposed method provides a new meaning for the motion synthesis of planar serial chains and can be applied to many other types of planar mechanisms.

In the early stage of the creative design of mechanisms, design work was accomplished mainly based on researchers' experience and inspiration, resulting in a low design efficiency. Moreover, the derived mechanism configurations were very limited. An effective mechanism design method is based on the atlas of topological structures of kinematic chains. Our research on the structural synthesis of kinematic chain inversions plays an important role in the improvement of mechanism design efficiency.