Investigation of the kinematic characteristics of a delta robot in forward and inverse kinematics problems

Юрій Вячеславович Широкий, Юрій Олександрович Сисоєв, Юрій Олександрович Семененко, Ольга Діонісівна Семененко, Анастасія Сергіївна Сорока, Микита Павлович Ковальов

Abstract


The article is devoted to the kinematic analysis of a delta robot, with a focus on solving the forward and inverse kinematics problems. The kinematic analysis of a delta robot primarily examines the relationship between the input angles of the servo-driven actuator arms and the spatial position of the end effector, which determines the accuracy and efficiency of the entire robotic system. Such analysis covers two key aspects: the solution of forward kinematics and the solution of inverse kinematics. The forward kinematics problem of a delta robot involves determining the coordinates of the end effector when the rotation angles of each actuated joint are known. This task is mathematically complex due to the nonlinearity of the equations and the geometric features of the parallel mechanism structure. Conversely, the inverse kinematics problem consists in calculating the rotation angles of all actuators required to achieve a predefined position of the end effector, which is critically important for tasks requiring precise positioning, manipulation, and high-speed movements.

The article provides a detailed examination of the geometric model of the delta robot, presents the mathematical description of the kinematic equations for both forward and inverse kinematics, and analyzes the structural configuration features that affect the workspace, stiffness, and positioning accuracy. The issue of structural deformability becomes especially relevant in cases where the robot operates with high accelerations or under varying loads. Even small deviations in the geometry of the links may lead to accumulated errors, complicating the achievement of stable and repeatable positioning. To minimize the impact of such factors, thorough analysis of the kinematic model, refinement of stiffness parameters, and the application of compensation methods in control systems are required. The obtained results contribute to improving the accuracy of delta-robot control and optimizing its performance under high dynamic loads, making the presented research valuable for engineers, developers of robotic systems, and researchers in the field of mechatronics.

Keywords


Delta robot, parallel mechanisms, kinematic analysis, forward kinematics, inverse kinematics, mathematical modeling

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