Calculation of velocities and accelerations of points of a crank mechanism

Abstract

In this article, presented is an analytical method of determining linear and angular velocities and accelerations of links of a crank mechanism on the basis of a grapho-analytical method (without the construction of displacement, velocity, and acceleration diagrams) with the use of angles, which form between vectors on velocity and acceleration diagrams, as well as between links on the mechanism diagram. Pointed out is the role of analytical methods (with the help of which the research of kinematics of mechanisms can be conducted with high degree of accuracy), which has especially increased in recent years due to the fact that by having analytical expressions that link the main kinematic and structural mechanism parameters with each other, it is possible to compile a calculation program for a counting machine at any moment, and with the help of such a machine all the necessary results can be obtained. Given are the results of the implementation of the proposed calculation algorithm on computer equipment, a comparative analysis of the obtained data and an estimation of the relative error of the calculation. A justification for the suitability of the developed algorithm of calculating velocities and accelerations of points of the mechanism is provided. The proposed calculation algorithm of kinematic parameters of a crank mechanisms allows to automate the process of calculating the velocities and accelerations, significantly reduces the amount of labor needed for the calculation, ensures a high degree of accuracy.