A GRAPHICAL-ANALYTICAL TECHNIQUE FOR THE SYNTHESIS OF NON-CIRCULAR GEARS IN PATH-GENERATING GEARED FIVE-BAR MECHANISMS

The paper presents a graphical-analytical technique for the synthesis of non-circular gears in path-generating geared five-bar mechanisms. In such mechanisms, a two degree-of-freedom (dof) five-bar linkage is integrated by a pair of non-circular gears to precisely guide a coupler point along a prescribed planar trajectory. The synthesis method proposed here considers the most general case, where the prescribed trajectory consists of a series of open curves. Each segment of the prescribed path identifies a phase of the mechanism motion that is referred to as requested motion branch.. In each of these phases, for any prescribed position of the coupler point, the inverse kinematic analysis of the linkage and the Aronhold-Kennedy theorem are used to identify the actual configuration of the system and locate the instantaneous centre of the relative motion between the two cranks of the linkage. The regions of the gear's centrodes, corresponding to the requested motion branches, are thus synthesized. These regions are connected to each other by using proper polynomial functions, as to guarantee a continuous and cyclic motion of the mechanism. An example is illustrated where the requested coupler point trajectory consists of a series of straight line segments.