Optimum path synthesis of a four-link mechanism with rolling contacts

Kinematic synthesis problems of a four-link mechanism with rolling contacts have been studied in the literature. One may imagine a very difficult synthesis problem, which is much more difficult to solve for a seven-target-point problem. In fact, the kinematic synthesis formulation for a four-link mechanism with rolling contacts discussed in the literature is complicated by the improper selection of the design variables, which leads to simultaneous increases in the number of design variables and in the number of synthesis equations. Thus, in this work, an improved formulation for the kinematic synthesis of the four-link mechanism with rolling contacts is proposed where the GA–DE hybrid evolutionary algorithm is applied to solve the optimum path synthesis problem. Three examples are studied to demonstrate the effectiveness of the proposed model. The findings show that the present formulation can reduce the number of design variables for a seven-target-points synthesis problem by 10 when compared with that using the previous formulation discussed in the literature. This reduces the difficulty of a seven-target-point synthesis problem. More accurate results for all examples can be obtained only with the GA–DE algorithm. Thus, the proposed formulation is superior to the previous one discussed in the literature.