Kinematics study for a spatial manipulator

Emperor Alexander I St. Petersburg State Transport University, 9, Moskovsky pr., 190031 Saint Petersburg, Russia

^* Corresponding author: sirayaekaterina@mail.ru

Abstract

For industrial robot design and control problems, it is necessary to determine both the positions of its parts relative to the stationary coordinate system, absolute positions of the parts, and their relative positions, generalised coordinates. The first problem is called the forward problem, and the second is the inverse problem for manipulator positions. The purpose of the paper is to solve the direct problem on manipulator positions, i.e., to determine and study positions of manipulator sections with known generalised coordinates. In the paper a spatial manipulator with four degrees of freedom is considered. Kinematic characteristics of the last link of the manipulator - grabber are defined. The kinematic characteristics are the coordinates of current position, velocity, and acceleration of the grip. Kinematic characteristics are found by applying the vector matrix method, based on the application of transition matrices from one reference system to another and rotation vector matrices. The vector matrix method belongs to the universal methods and is designed for use in mathematical computer simulation systems. Keywords: Vector matrix method, spatial manipulator, kinematic characteristics, mechanics of industrial robots.