Improved GRG method for the optimal synthesis of linkages in function generation problems

This paper presents a novel approach for optimizing the dimensions of linkages for application to function-generation problems. The main goal is to minimize the objective function formulated as the difference between the desired and generated functional parameters using the Generalized Reduced Gradient (GRG) method. Although this optimization approach is well-known by mathematicians and researchers in optimal design, the formulation developed by the author reveals that it has not been sufficiently explored in dimensional synthesis. Indeed, the examples presented in this paper show that it can be easily formulated and applied to obtain the optimal dimensions of complex linkages with large numbers of prescribed positions. The main contribution of this approach is to demonstrate that the suitable formulation of this approach (denominated improved GRG method) leads to an algorithm that is general, robust, accurate and efficient for synthesizing linkages in function generation problems.