ANALYSIS OF A FOUR-BAR MECHANISM USING THE COMPLEX NUMBER METHOD WITH MATLAB PROGRAMMING

Abstract

This study aims to analyze the kinematic characteristics of a four-bar linkage mechanism applied to an automotive wiper system using the complex number method implemented through MATLAB programming. The four-bar mechanism is modeled based on actual geometric parameters obtained from AutoCAD drawings, consisting of a crank, a connecting rod, and a rocker with two fixed pivot points. The complex number method is used to formulate the loop-closure equations so that the relationships of position, angular velocity, angular acceleration, as well as linear velocity and acceleration at key points of the mechanism can be systematically analyzed. Numerical simulations are performed by applying a constant angular velocity to the crank. The analysis results show that the connecting rod rotates counterclockwise, while the rocker rotates clockwise, in accordance with the motion characteristics of the wiper mechanism. The magnitudes of velocity and acceleration in each link and at critical points are significantly influenced by the link length configuration and the input angular velocity. Validation of the calculation results using a parallel numerical method shows a very small relative difference, thereby confirming the reliability of the developed model. The MATLAB based complex number method is proven to be effective and accurate for the kinematic analysis of four-bar mechanisms and can serve as a reference for the design and development of wiper mechanisms and similar planar mechanisms.