Mathematical model of kinematic calculation of flat lever mechanisms

Kinematic calculation is a mandatory part of the design of the flat lever mechanisms. This operation is very time-consuming and always need many calculations. Therefore, it is important to develop mathematical models for calculating the kinematic characteristics of the flat lever mechanisms, containing at least one double-leash Assur group. The article is devoted to mathematical modeling of five types of the Assur groups. The initial pin joint position and the driving ring kinematic characteristics used as an input for the further calculations. For the selected Assur group created the equation of motion in plane coordinates axis for the pin joints. With double differentiating the equations of motion were derived equations for determining velocity and acceleration of the pin joints in the global axes projections. The result of several transformations in matrix forms is the equations for the kinematic characteristics of the slave units in the selected Assur group. Finally, mathematical procedures for the kinematic characteristics of each double-leash Assur group were calculated. In a structural analysis of the complex planar mechanisms with a leading link and several double-leash Assur groups it is possible to determine the kinematic characteristics of all parts by consistently addressing the appropriate procedure. All suggested algorithms implemented as a software library that will speed up the designing of the complex planar mechanisms.