GRAPHOANALYTICAL METHOD FOR CALCULATING KINEMATIC PARAMETERS OF A HINGES FOUR-LINK MECHANISM

Abstract

The purpose of the work is to develop an algorithm and determine the necessary formulas for calculating the kinematic parameters of the hinged four-link rod mechanism using the grapho-analytical method of determining the current positions of the mechanism links and standard PMK calculation programs while simplifying the calculation method itself and obtaining the necessary and high-quality research results. Research results. A new method of calculating the kinematic parameters of the hinged four-link rod mechanism has been developed using the grapho-analytical method of analyzing the kinematic diagram of the mechanism in the current position of its links and calculation formulas for using the standard MathCAD program to determine the kinematic parameters of the hinged four-link rod mechanism. The scientific novelty of the research is determined by a new method for calculating the kinematic parameters of mechanism links, based on determining the projections of the linear peripheral velocities of the crank and connecting rod on the axis Cartesian coordinate systems that do not directly affect the change in the positions of the mechanism links when the position of the leading link - the crank changes relative to the fixed axis, but only allow one to determine the linear speed of the center of mass of the connecting rod depending on the location of the center of mass on the connecting rod. TIn turn, the magnitudes and directions of angular velocities and accelerations of all links of the mechanism are directly determined by the angular functions of rotation of these links depending on the angle of rotation of the driving link. The reliability of the obtained research results. The calculations of kinematic parameters based on the formulas obtained in the work using the standard MathCAD application program completely coincide with the determination of the same parameters for a similar articulated four-link rod mechanism, obtained by the traditional graphic method of constructing the mechanism plans, the speed plan and the acceleration plan. Practical implementation of the obtained results. The developed grapho-analytical method simplifies the determination and analysis of kinematic parameters of hinged four-link rod mechanisms when changing their layout and linear dimensions of links, which creates a basis for further development and improvement of analytical methods of kinetostatic and dynamic calculations. for any hinged four-link rod mechanism.

Keywords: kinematic scheme, rod mechanism, center of mass, geometric modeling, analytical modeling; kinematic parameters, velocity projections, acceleration projections, angular velocity, angular acceleration.