A NEW APPROACH TO PLANAR ANALYSIS OF MECHANISMS

Kinematic chain analysis is viewed as consisting of a data structure, kinematic analysis, dynamic analysis, and internal force analysis. In designing an algorithm for kinematic chain analysis the emphasis is put on reducing the space required to solve a problem. To accomplish this, a data structure is designed which uses fewer pieces of information to describe a given kinematic chain. A new form for the topological entities relevant to the kinematic and dynamic analysis is introduced. In dynamic analysis the system parameters are divided into dependent and independent system parameters. The constraint equations are used to eliminate the dependent system parameters implicitly in the Lagrange equations. The proposed method generates the same number of differential equations as degrees of freedom of the kinematic chain. The procedure is extended to calculate the Lagrange multipliers corresponding to the vector loop equations. It is shown that these multipliers are related to the reaction forces at the joints whose corresponding edges in the graph are selected as chords. This information and the successive applications of Newton\u27s law to the links become the basis of the algorithm for the force analysis. The result of a comparative study on the performance of the proposed algorithm MAP (Mechanism Analysis Procedure) and DRAM is also reported