Type synthesis of planar linkage mechanisms with rotoidal and prismatic joints

MARTÍN PUCHETA; ALBERTO CARDONA

Buenos Aires

Congreso; 8 Congreso Argentino de Mecánica Computacional, MECOM 2005; 2005

Asociación Argentina de Mecánica Computacional

We present a method to enumerate and codify the solutions of type synthesis of linkage mechanisms with rotoidal and prismatic joints. The essence of mechanism synthesis is to find the mechanism for a given motion. Type Synthesis is the first stage of conceptual design of mechanisms, where the number, type and connectivity of links and joints are determined. It is followed by the Dimensional Synthesis stage, where the link lengths and pivot positions are computed to fulfill a given kinematic task. The latter and the subsequent stages of detailing design are very costly. Therefore, the aim is to propose all “non-isomorphic topologies” without repetitions satisfying structural requirements. We use an enumeration of one-degree of freedom topologies developed by Tsai to form an Atlas of kinematic chains. We have developed a method based on the construction of an “initial graph” taking into account prescribed parts (such as fixations, bodies to move, joints, and their interconnections) and the kinematic constraints imposed on them. Then, we use this graph as a pattern to search inside the atlas. This search also involves an isomorphism detection between subgraphs occurrences inside a kinematic chain of the atlas. We develop a classification of the occurrences by the Degree Code of the edge-induced subgraph produced by the pattern edges. After selection of a non-isomorphic topology, there follows a step of specialization where joint types are assigned. We also developed a method to enumerate all possibilities of joint assignments in a non-isomorphic way for a maximum number of prismatic joints given by the user. The method is illustrated with examples for typical aeronautical test problems. The program was written in C++ language under the OOFELIE environment.C++ language under the OOFELIE environment.