On the kinematics and synthesis of a geared five-bar slider-crank mechanism

The geared five-bar mechanism possesses kinematic abilities that qualify its utility in various industrial applications. Small changes to the mechanism topology or dimensions create new designs with different motion characteristics. This article presents design-orientated kinematical insights and mathematical treatments for the embodiment of the mechanism in which the end gear is eccentrically pivoted to a sliding element. For its synthesis, a kinematic classification is introduced and approximate curves are used to guide the motion of the slider. A gradient-based Levenberg-Marquardt formulation is employed for the optimization procedure. Geometric, mobility, and dimensional constraints are utilized together with numerical position equations for the analysis. Two case studies are presented at the end of this article to highlight the versatility of the mechanism and prove the validity of the presented mathematical model