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.
