DefinePK

Abstract

In this paper the use of natural coordinates for the analytical determination of the center of rotation of four-bar mechanisms is proposed. The natural coordinates are mostly Cartesian coordinates located in the kinematic pairs or in points of interest of the mechanism, where the main advantage of their use is that angular parameters and trigonometric functions can be disregarded, which facilitates the understanding of the modeling, in addition it is not necessary to use trigonometric functions. This technique allow to reduce the computational cost in a great way, optimizing problems where the rotation center has to be calculated many times. To achieve this goal, the problem is described and formulated in a robust way using natural coordinates and operating within the body of complex numbers. Then, to deal with the present problem, the mechanism’s kinematics position in natural coordinates is modeled and computing and with the obtained equations, a program is implemented in MATLAB® to show the curve described by the rotation centers of links, which is fundamental for the optimal design of polycentric mechanisms.