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The isomorphism identification of the kinematic chain (KC) based on graph theory definition has no advantage in efficiency, especially when the number of links in the KCs is large. The topological characteristic constants for isomorphism identification, such as the power value sequence (PVS), least distance matrix sequence (LDMS), and loop number (LN), are proposed. The fourth PVS, the LDMS, and the LN are compared and arranged in descending order, to form a strong complementary chain, which can identify KCs of at least 15 links with 4 degrees of freedom (DOF). The method is applied to the complete atlas of the following: 8-link 1 DOF, 9-link 2 DOF, 10-link 1 DOF, 12-link 1 DOF, 13-link 2 DOF, and 15-link 4 DOF planar single-joint KCs, 6-link 1 DOF and 7-link 1 DOF planetary gear trains, 8-link 1 DOF planar multiple joint KCs, and contracted graphs with up to six independent loops. All results are in agreement with the reported ones in the literature. Thus, the proposed method possesses good versatility and has been verified as being reliable and efficient.

The similarity recognition of kinematic chains (KCs) is helpful for improving the efficiency of configuration synthesis, which has been paid more and more attention in recent years. The existing recognition methods are divided into the definition method and feature constant method. Among them, the definition method is difficult to adopt in practice because of its long operation time, especially when the number of similar vertices in KCs is large. In this paper, the new concepts of a loop tree (LT) and a loop tree matrix (LTM) have been proposed, which improve the efficiency of similarity recognition. This method is applied on the complete structure of the following: 8-link with 1 DOF (degree of freedom), 9-link with 2 DOF, 10-link with 1 DOF, 12-link with 1 DOF, 13-link with 2 DOF, 14-link with 3 DOF, 15-link with 4 DOF planar single-joint KCs, and contracted graphs with up to six independent loops. All results are verified by the definition method to prove the good applicability, reliability, and efficiency of the proposed method. Simultaneously, the application case of the similarity recognition in a mechanism creation is given to provide a reference for an innovative design.

Obtaining new models of mechanical equipment to conduct mechanical innovative design through kinematic chain configuration synthesis is an effective method. However, in practice, due to the existence of similar components, existing innovative design methods easily produce redundant design schemes, which require extensive isomorphic discrimination operations, and the design process is complex. In view of existing problems, this study analyzes a method for discriminating between similar components of mechanisms from the perspective of graph theory and then applies it to the specialization of topological graphs to solve the problem of redundant design schemes. Finally, using the innovation of a drilling rig drilling arm mechanism as an example, 52 feasible schemes without redundancy are obtained. This paper provides a reference for the innovation of the configuration of planar mechanisms without design redundancy.

Supplemental material, sj-pdf-1-pic-10.1177_0954406221998399 for Synthesis method for planetary gear trains without using rotation graphs by Rongjiang Cui, Zhizheng Ye, Liang Sun, Guanghui Zheng and Chuanyu Wu in Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science

How to realize the garlic seed direction control is the bottleneck problem of the garlic mechanical sowing in our country. Proposed garlic direction control method by using water based on the theory of fluid coupling, and its controlling mechanism is analyzed and tested. Through theory analysis, suitable water control rules to the body shape is on the tip of a coarse, left and right side symmetry, dorsal flap is lanceolate; Design test device, test the performances of the water control method, 98.5% rule body can erect in control the direction cup, satisfy the garlic planting requirements. This study provides reference for the design of the garlic direction controller.

First, considering the characteristics of parallel mechanisms themselves, variable topology mechanism theory was introduced. The definition, determine method and basic variable topology means of variable topology parallel mechanism were given. Also some basic mechanisms evaluation criteria were introduced. Then, taking 3-UPU mechanism as ideal mechanism and topology synthesis was carried out. The introduction of variable topology mechanism theory provided a theoretical basis and innovative approaches for the synthesis of parallel mechanisms.