Kinematics of Bennett Mechanism, Negative Angular Velocity

Abstract

This article provides reasoning and research of spatial mechanisms. The creation of the first simple Bennett mechanism obtained through the pyramid of its base and sides is described. In the pyramid, the angles of inclination and heights of the sides are determined to obtain standard equalities. Thanks to all the parameters, the theoretical link lengths that have practical values are determined. All parameters of length and angles are presented on the structural diagram for each received mechanism. On the basis of two identical, but mirrored mechanisms, a five-bar Bennett mechanism is synthesized. The five-link mechanism is obtained by mutual integration of two identical links, for which the calculation method is described. The article contains a calculation to determine the length and angle of the frame. The frame is obtained by the specified parameters of the ghost angle, the parameters of the two mirrored links derived into one expression. The specified inequality is used for a five-link mechanism in which it is obtained by a driving and a driven full-turn link. The text defines the main kinematic parameters of the links that make a complete turn around its axis without contact. All parameters of the mechanism are metered intuitively. Principle kinematic parameters of the mechanism: angular displacement, angular velocity and angular acceleration are determined. The kinematics is determined with respect to the driving and driven link, taking into account the angular displacement, speed and acceleration. For a more accurate calculation, the dependence of the additional ghost angle of the mechanism on the kinematic parameters is considered. The obtained data are visualized using diagrams of relationships of the rotation of the input link to the output using the Maple application. In trigonometric functions, there is a negative and a positive value determined by the quadrants on the sectors of the circle. Diagrams of angular displacement and angular velocity according to the calculations show negative numerical values. The angular acceleration of the driven link during the rotation of a full turn of the driving link of the mechanism changes its acceleration 4 times. The analysis of the data obtained allows us to conclude that the driven link will rotate jerkily, at these moments there is a possibility of destruction of the mechanism and an increase in the load on the driven link and imbalance of the mechanism.