Analysis of Distributed Dynamic Loads Induced by the Own Mass of Manipulator Links and Their Visualization on Interactive 3D Computer Models

Abstract

This study proposes an approach to 3D modeling of spatial manipulators in the Maple 2023 software environment. Algorithms and program codes have been developed to create computer 3D models of manipulators controlled by generalized coordinates. The implementation of these algorithms and program codes has enabled the creation of three-dimensional computer models of manipulators with clear visual representations of links, their cross-sections, kinematic pairs, grippers, and loads, differing in structure and degrees of freedom while ensuring a comprehensive view from all spatial perspectives. During the motion of the manipulator, complex distributed dynamic loads arise in its links due to their intrinsic masses. These dynamic loads create several challenges: for instance, excessive dynamic loads or significant deformation of the links may lead to failure of the manipulator or a loss of precision in the positioning of the gripper. Such loads significantly impact the design, operation, and reliability of manipulators. The study and understanding of dynamic loads in manipulators are crucial areas in mechanics and robotics, enabling the development of more reliable and efficient systems. The Denavit–Hartenberg method was applied to control the motion of the created computer 3D models of manipulators using generalized coordinates. Using the recursive Newton–Euler equations, the necessary kinematic characteristics of the manipulator’s links were determined for calculating the distributed dynamic loads arising from the intrinsic masses of the links at each cross-section, relative to the local coordinate systems rigidly attached to the links. Algorithms and program codes were developed for controlling the motion of 3D models of manipulators, as well as for constructing visual diagrams of distributed dynamic loads in mutually perpendicular planes, formed by the principal axes of the link cross-sections and the axes passing along the longitudinal axes of the links. The implementation of these algorithms and program codes enabled the generation of distribution diagrams of all dynamic loads in all links of the moving manipulator. These diagrams visually illustrate the changes in direction and magnitude of the distributed dynamic loads in all cross-sections of the links throughout the full cycle of the manipulator’s operation. This allows for the consideration of the identified dynamic loads in the strength and stiffness calculations of the manipulator links, which is essential for the design of new innovative manipulators.