Forward Kinematics Analysis of a 4-DOF Robotic Manipulator

Abstract

The development of science and technology has significantly changed the approach to industrial operations, especially in the field of automation. The growing demand for high-quality products has led to the transition toward automated systems that use robots to replace humans in performing repetitive tasks. Industrial robotic manipulators are widely used in manufacturing processes such as welding, painting, assembly, cutting, and others.

This work presents a mathematical description of solving the forward kinematics problem for the educational robotic manipulator with four degrees of freedom. The algorithm is proposed for the procedure of forming a sequence of consistent coordinate systems associated with the manipulator’s links. An orthonormal coordinate system has been established for each of the four links.

During the task execution, the structure of the manipulator was described. The external appearance of the manipulator is presented, along with its 3D-model and structural-kinematic diagram. Based on the obtained parameters and the matrix-based method of coordinate representation using the Denavit–Hartenberg convention, transformation matrices were constructed, which mathematically represent the spatial positions of each manipulator link. The use of the Denavit–Hartenberg transformation made it possible to determine the spatial position of each of the four kinematic pairs of the robotic manipulator.

Based on the proposed algorithm, a computer program was developed using Visual C#, which allows for automatically obtaining the spatial coordinates of each kinematic pair as well as the trajectory of the end effector from the initial to the target point. In this way, the planned movement is first tested in a virtual simulation environment and executed on the physical robot only after verification.

The proposed method and software are universal and can be used for simulating any robotic manipulator in the educational process.

The functioning of the developed software is described in detail, including code fragments that perform the calculation of the coordinates of the respective kinematic pairs within the manipulator’s working area, as well as the end effector’s movement trajectory in space. As a result of the calculations and the schematic representation of the 3D-model, the spatial positions of the manipulator links fully match the predefined target positions, confirming the adequacy of the developed model and its software implementation. In the future, based on this model, it is planned to synthesize a control system for the educational robotic manipulator and to implement the inverse kinematics solution.