Improved Approximation Approach for Folding Analyses of Structures with Kinematic Indeterminacy

Abstract

The kinematic analysis method based on generalized inverse theory has been used in the engineering field. However, the traditional numerical procedure is found to be extraordinarily time consuming when the number of unknowns increases. This paper presents an improved approximation approach (IAA) of the kinematic analysis method to trace the rigid motion of mechanisms with both high accuracy and efficiency. It simplifies the procedure of obtaining the generalized inverse into the process of solving linear equations. Accordingly, the whole calculation can be executed with sparse matrix format. To demonstrate the progress of the IAA, the numerical examples are examined through a comparison with the conventional methods. The results indicate that IAA shows distinct improvements in precision and efficiency. The improvements are found to be clear and effective, especially for systems with multiple DOFs.