Abstract

This paper presents a new approach for mechanism synthesis using exact gradients in optimization. Currently, finite difference methods or similar approximate techniques are used to evaluate the derivatives that are necessary for performing mechanism optimization using gradient-based methods. Typical mechanism synthesis problems involve highly nonlinear functional relationship, and the use of finite difference methods in such problems often leads to an excessive number of function evaluations, algorithm failures, and inaccurate results. Instead, an alternative approach using exact gradients will completely eliminate all of the above problems, and will result in a faster and efficient convergence. This paper also discusses the identification of an appropriate optimization method, namely, the generalized reduced gradient method for mechanisms synthesis based on its good convergence properties, reliability, intermediate feasibility, and efficiency. Numerical examples are included to illustrate the advantages of using exact gradients and the results are discussed.

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