Optimum synthesis of planar linkages using a strain–energy error function under geometric constraints

This paper presents an improved approach to the optimum dimensional synthesis of planar linkages based on an elastic strain–energy error function, according to which the optimum link dimensions are those which result in the minimum energy when the linkage is forced to comply with the synthesis data. This method is suitable for any kind of kinematic synthesis for any planar linkage. New features include geometric constraints in the links, and an effective way of modelling the position of frame joints. In addition, an overall improvement of convergence has been achieved through a new formulation of the error function and its minimization using two stages in the iterative process.