Optimization kinematic synthesis of four-link linkage mechanism in two preset positions

Abstract

The widespread use of flat articulated four-link mechanisms in various automatic devices and devices requires the further development of automated kinematic synthesis methods, which, based on modern mathematical approaches, will reduce the required amount of a priori information and obtain an exact solution. The approach of the best quadratic approximation of functions used in the article made it possible to formulate both the optimality criterion and the conditions for its achievement on the basis of the equation of closure of a vector contour. The analysis of the model showed that on its basis it is possible to evaluate the presence of singular positions of the links at which a spontaneous change in the law of motion of the output link is possible. A numerical experiment in the MathCAD package made it possible to verify the synthesis methodology based on the results of solving the kinematic analysis problem and the graphical representation of the connecting rod curves.

Keywords

• flat connecting rod mechanism
• kinematic synthesis
• quadratic approximation of functions
• modeling