Dynamic analysis of planar elastic mechanisms using the dyad method

Abstract

Based on graph representation of planar linkages, a new algorithm has been developed to identify the different dyads of a mechanism. A dyad, or class II group, is composed of two binary links connected by either a revolute (1) or a slider (0) pair, with provision for attachment of other links by lower pair connectors located at the end of each link. There are five types of dyad: D111, D101, D011, D001 and D010. The dyad analysis of a mechanism is predicated on the ability to construct the system from one or more of the five binary structure groups or class II groups. If the mechanism is complicated and several dyads are involved, the task of identifying these dyads, by inspection, can be difficult and time consuming for the user. This algorithm allows complete automation of this task. It is based on Dijkstra's algorithm for finding the shortest path in a graph. When compared with algorithmic methods, such as the Newton-Raphson method, the dyad method proved to be a very efficient one and requires as little as one-tenth of the time needed by the method using the Newton-Raphson algorithm. The second part of this work presents an extension of the dyad method to non-rigid or elastic mechanisms. Here also, this method is predicated on the ability to subdivide the elastic mechanism into elastic dyads. The solution for each type of elastic dyad is derived and can be applied to each dyad in the mechanism. Therefore, a solution of the complete elastic mechanism is possible when the mechanism is made of dyads only. This method makes a powerful and simple tool for analysing complex elastic mechanisms. Moreover, the complexity of the model does not increase as the mechanism becomes more complex. The D111 dyad is taken as an example to demonstrate this method. A finite element (FE) analysis was made for this type of dyad, and an experimental set-up was built to validate the analysis. The dyad-FE results were in good agreement with the experimental ones.