Modified Shadow Robot Control method for optimal path synthesis of mechanisms: Application to five-link mechanism

Abstract

For optimal path synthesis of a mechanism with a single degree of freedom (DOF), a powerful method called Shadow Robot Control (SRC) has been recently proposed in the literature. However, this method is restricted to synthesis problems with prescribed timing (i.e. problems in which a particular input crank angle is associated with each point of the desired trajectory). In this paper, the SRC method was elaborated and modified to be capable of synthesizing both prescribed and nonprescribed timing problems. For this purpose, a new structure of contour error and objective function estimation was presented. As a result, there is no need to consider the input angles (crank angles) corresponding to desired path points as optimization parameters, even for non-prescribed timing problems. This prevents unnecessarily enlarging the search space, providing a more effective and robust optimization method (with respect to initial guess). The synthesis of a geared five-link mechanism was used to detail the proposed algorithm as a case study. Despite the five-link mechanism capability and simplicity of generating a complicated trajectory, this single DOF path generator seems less investigated in the literature. Few existing numerical problems of the five-link mechanism in the literature were solved. The comparison of the results shows the effective performance of the proposed algorithm in synthesizing the mechanism.