Type Synthesis Of Planar Linkage Mechanisms With Rotoidal And Prismatic Joints.

Abstract

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.