Optimization of Kinematics of Inclined Swinging Pin

The inclined swinging pin simply transforms the rotary motion into a rotational oscillation. It consists of three components, a rotating inclined tenon, a crossbeam, and a stirrup. The pitch angle of the inclined tenon relative to the x -axis of its rotation is decisive for the kinematics of this joint. Too small inclination angle will result in small amplitude of oscillation; too much inclination will lead to an impulse dynamic stress that can damage the pin. The optimal angle of inclination can be determined from the mathematical model, created in the Maple environment, which uses linear algebra resources to describe the behavior of the joint. Vectors of coordinates of the critical points are created for each joint component. Further-more, transformation matrices are created which describe the behavior of the corresponding kinematic chain in relation to the inclination angle of the inclined tenon and time.