Kinematic analysis of geared linkage mechanisms

A general approach to the kinematic analysis of planar geared linkage mechanisms (GLMs) is presented based on their structural topological characteristics. Firstly, a systematic method for decomposing a GLM into a series of sequential independent kinematic units, such as the simple links and the dyad link groups is proposed. The concept of tricolored graph and its mathematic expressions are introduced to describe the topological relationship between the kinematic pairs and the links in a GLM. The criteria and process for the structural decomposition and for choosing circuits using the theory of type transformation are established. Then the kinematic equations and the analytic solutions for the kinematic units are derived, and the method for the kinematic analysis of position, velocity and acceleration of GLMs is obtained in an algorithmic fashion. Finally, an application program has been developed, by which the whole work from the structural decomposition to the kinematic analysis can be accomplished automatically for any one of the GLMs. Some examples are used to illustrate the procedures. (c) 2005 Elsevier Ltd. All rights reserved.