Software modeling of multi-degree-of-freedom motion system using matrices

Abstract

This paper presents the results of the research of multi-degree-of-freedom robot motion with multiple degrees of freedom by using a mechanical model of transformation of the matrix that can be used in solving the kinematics of the robots whose internal structure of the joints allows only the rotation. The matrices of rotation transformations and their application in different cases of robot motion, such as the first step, the second, third, and fourth steps, are set out. The research which was conducted in this work is a part of the development of mechatronic systems, and the results obtained by this method are suitable to solve problems of the anthropomorphic of robots and can be used for other purposes in various areas of mechanical engineering. Mechanism with multiple degrees of freedom, such as a mechanical robot system, occupies a number of positions necessary to carry out the task. Thus the position of the mechanical system is determined by a set of internal coordinates that determine the movement of the joints. It is understood that the movement is a requirement that each of the coordinates governed by its law determines the position of the robot movement, through the so-called internal and external coordinates. It also determines the way of conversion of coordinates from one movement to another, or the application of equations to solve the kinematics problems of robots (robots determine the vector segments, segment positioning, angle and line speed, angle and line acceleration). The movement of the joints is achieved with the use of an motor, which allows only rotation movement. By applying the static equilibrium of the centrer of gravity of the robots, a part of the research of an anthropomorphic robot with 18 degrees of freedom, allowing the development of a mechatronic system, whose results allow the movement of the robot position in stages, is carried out. The largest part of the investigation described in the paper was performed on a computer, applying powerful software.