Analysis of the third class mechanism using the modeling method in the mathcad software environment

Abstract

Purpose. To carry out a kinematic analysis of a flat twelve-link hinged mechanism with three leading links, the basis of which is a structural group of links of the third class of the fourth order with rotational kinematic pairs, which is used in technological equipment.Methodology. The kinematic study of a flat complex mechanism of the third class with three leading links was performed using the mathematical modeling method in the Mathcad software environment. Findings. Using the method of mathematical modeling, the mechanism was presented in the form of free vectors built on its links, for which, taking into account the presence of three leading links, three vector contours were selected, which made it pos sible to draw up a system of vector equations of their closedness with further solving by a numerical method in the Mathcad soft ware environment. The functions of the rotation angles of the mechanism links, their angular velocities and accelerations were obtained in analytical and graphical form depending on the rotation angle of the first driving crank of the mechanism, the calcula tion of the angular velocities and accelerations of all the driven links of the mechanism was performed. Originality. A sequence was developed and a kinematic study of a complex planar mechanism of the third class with three lead ing links was done, the basis of which is a structural group of links of the third class of the fourth order. Schematic modeling of the mechanism with three leading links was performed, a visualization schedule of its kinematic scheme was built, and a valid version of its assembly was obtained from many possible ones, for which the values of kinematic parameters of all its links were determined. Practical value. An analysis of the effect of the kinematic parameters of the three leading links of the third-class mechanism on the movement of the working body of the technological equipment was carried out. From the analysis of the obtained research results for the cycle of the mechanism the reason was found for the incomplete technological stoppage of the link, which should provide the working body of the machine for the required period of time. Recommendations of the elimination were made to identify the deficiency and proposals for the need to improve the drive of this equipment.