Automatic synthesis of plane kinematic chains with prismatic pairs and up to 14 links - Yang, Wenjian; Ding, Huafeng; Kecskeméthy, Andrés (Mechanism and machine theory, 2019)
•This paper presents an automatic method to synthesize kinematic chains with prismatic pairs (RP-chains).•A new algorithm based on the vertex degree and edge weight is developed to detect isomorphism.•The synthesis results of RP-chains with 6–14 links are provided, and results with more than 8 links are new.•Our results are reliable, while counterexamples have been found by us when using the existing methods.•Our work is helpful to create mechanisms with prismatic pairs and other types of mechanisms. Mechanisms that contain prismatic pairs (P-pairs) are widely used in industry. Synthesizing kinematic chains with P-pairs is a pivotal step in the conceptual design of mechanisms with P-pairs. However, most synthesis methods for plane kinematic chains in the literature focused on the chains with only revolute pairs (R-pairs), those chains with P-pairs were less discussed. This paper presents a fully automatic method for the structural synthesis of plane kinematic chains with P-pairs. A new algorithm based on the parameters of degree, weight, degree-sequence and weight-sequence is developed to detect isomorphism. The algorithm is simple, efficient, reliable and decodable. The synthesis results of kinematic chains with up to four P-pairs and up to 14 links are provided. Except for the results of 6- and 8-link 1-DOF kinematic chains, others are new and have not been reported in the literature. Our results are extremely reliable, while counterexamples have been found by us when using the existing methods. The present work is helpful to design mechanisms with P-pairs, and can be extended to mechanisms with other types of kinematic pairs.