A Dependable Method for Solving Matrix Loop Equations for the General Three-Dimensional Mechanism

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Abstract
A new method of generating solutions for the matrix method of linkage analysis is considered. Optimization techniques are used to close the matrix loop equations iteratively until they are sufficiently close to closure to allow a solution by Newton’s method. The method is especially applicable for generating the initial closed position of a general three-dimensional mechanism. This technique is demonstrated on several three-dimensional mechanism examples.

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