Structural synthesis of plane kinematic chain inversions without detecting isomorphism

Abstract

Abstract. A plane kinematic chain inversion refers to a plane kinematic chain with one link fixed (assigned as the ground link). In the creative design of mechanisms, it is important to select proper ground links. The structural synthesis of plane kinematic chain inversions is helpful for improving the efficiency of mechanism design. However, the existing structural synthesis methods involve isomorphism detection, which is cumbersome. This paper proposes a simple and efficient structural synthesis method for plane kinematic chain inversions without detecting isomorphism. The fifth power of the adjacency matrix is applied to recognize similar vertices, and non-isomorphic kinematic chain inversions are directly derived according to non-similar vertices. This method is used to automatically synthesize 6-link 1-degree-of-freedom (DOF), 8-link 1-DOF, 8-link 3-DOF, 9-link 2-DOF, 9-link 4-DOF, 10-link 1-DOF, 10-link 3-DOF and 10-link 5-DOF plane kinematic chain inversions. All the synthesis results are consistent with those reported in literature. Our method is also suitable for other kinds of kinematic chains.

Innovative design method for planar mechanism configuration based on component similarity discrimination

“…Although using kinematic chain configuration synthesis is effective for mechanism innovative design, in practical applications, due to the existence of similar components, this approach can easily produce redundant design schemes and requires a large number of isomorphic discrimination operations (Ravisankar and Mruthyunjaya, 1985;Kim and Kwak, 1990;Shin and Krishnamurthy, 1993;Hsu, 1994;Rao, 2003). However, the problem of isomorphic discrimination has not been effectively solved (Ding, 2009;Yang and Ding, 2018b;Chen et al, 2021;Sun et al, 2021). Therefore, this study examines a method for discriminating between similar components of a mechanism from the perspective of graph theory, applies it to the specialization of a topological map and uses the innovation of the drilling arm mechanism of a rock drilling jumbo as an example to verify it.…”