Abstract

The structural and positional analysis of planar linkage mechanisms containing higher-class Assur groups requires the generation and solution of systems of algebraic kinematic equations. This paper presents algorithms for the automated analysis of such mechanisms based on an information matrix model. The proposed representation describes a mechanism as a system of material points connected by geometric constraints and provides a unified framework for algorithmic processing of mechanism structure and parameters. A square-matrix information model is developed to store structural and geometric information of a mechanism. Based on this model, three algorithms are proposed: (i) an algorithm for structural analysis and determination of mechanism mobility, (ii) an algorithm for automatic generation of kinematic equations, and (iii) an algorithm for automatic construction of a positional analysis procedure for solving the generated system of algebraic equations. For mechanisms containing higher-class Assur groups, the developed approach automatically generates an ordered sequence of two-link kinematic chains. When direct decomposition is not possible, conditional driving links are introduced by selecting conditionally disconnected links and defining corresponding driving coordinates. The proposed algorithms have been implemented in the SAPRM system. The applicability of the approach is demonstrated through positional analysis of three planar linkage mechanisms containing higher-class Assur groups.

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