Synthesis of Four-Bar Linkages by Four Infinitely Close Relative Positions and Pressure Angle

Abstract

A computer-applicable linear mathematical model has been developed to determine Burmester’s curves for infinitely close relative positions (cubic of stationary curvature), which indirectly uses Carter-Hall’s circle. By varying a free parameter and using elements of kinematic and analytical geometry, an incomparably simpler solution is achieved than that obtained by the third-degree equations of the Burmester's curves for stationary curvature. The mathematical model for the synthesis of four-bar linkages includes and a condition for the pressure angle, whereupon is uniquely defined the kinematic diagram of the mechanism. Of the pressure angle, the reactions of the forces in the kinematic pairs and the force sizing of the mechanism depend. The model would facilitate the engineers in the synthesis of four-bar linkages by generating a function approximating a given function in the vicinity of a given position, where the two functions have four infinitely close common points (3rd-order approximation). An example of the synthesis of a four-bar linkage illustrates the application of the model, which is linear - it includes only equations of straight lines written in Cartesian coordinates, which is why it is convenient for computer calculations.