Optimized five-bar linkages with non-circular gears for exact path generation

In this paper, a five-bar linkage with non-circular gears is proposed as a mechanism capable of precisely moving a coupler point along a prescribed trajectory. The first step of the proposed methodology is the inverse kinematic analysis of the linkage, whose mobility, without geared bodies, is two. Therefore, by imposing the required configuration of the coupler at any instant, the rotation of the two inputs is evaluated. A pair of non-circular gears is then synthesized on the basis of the relation between these two angular inputs, thus reducing the mobility to one. The final combined mechanism is able to exactly perform a specific task of path generation.In the design of non-circular gears, a basic requirement is that the non-circularity of the pitch curves is kept as low as possible. Such non-circularity affects both the feasibility of gear manufacture and the dynamic behaviour of the output non-circular gear. For this reason, an optimization of the five-bar linkage with non-circular gears is also proposed, by defining the objective function on the basis of proper dimensional and kinematic criteria. A penalty method is used to manage a set of constraints to which both the linkage and the gears are subjected, while a genetic algorithm is employed to search for a global optimum solution.