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.

In recent years, the utilization of 3D modeling for various robotic systems has gained significant traction, serving educational, research, and diverse applications. Presently, there are a multitude of 3D modeling tools tailored to different facets of robotic research, each possessing distinct advantages and limitations. This paper presents the development of novel algorithms and software aimed at constructing 3D representations of robotic arms that have enabled the visualization of the manipulator and its links’ motion. These algorithms allow for the depiction of forward kinematic outcomes through spatial 3D graphs. Consequently, these graphical representations provide a tangible means to observe the changes in module components and parameter orientations as the manipulator assumes different spatial configurations. Within the Maple environment, a comprehensive 3D model of robotic arms was constructed, and the forward kinematic problem was solved for a manipulator that had five degrees of freedom (DoF). This endeavor was achieved by implementing the Denavit-Hartenberg method to elucidate kinematic characteristics and the Newton-Euler method to ascertain the velocity and acceleration of the robot manipulator’s links. The newly created algorithms and software are expected to be widely used in 3D modeling of robotic manipulators as scientific research in industries and other complex mechanical systems.

Three-dimensional (3D) modeling and visualization are important tools for the analysis and development of robotic systems. This paper presents a Maple-based unified framework for 3D motion modeling and visualization of kinematic characteristics of spatial robot manipulators. The framework integrates analytical kinematic modeling, automated generation of three-dimensional manipulator models, and graphical representation of their motion within a single computational environment. The Denavit–Hartenberg convention is used to define the geometric and kinematic parameters, while recursive analytical formulations determine the spatial position, orientation, linear velocity, and linear acceleration of the manipulator links. The proposed algorithms enable the construction of interactive 3D models and visualization of the calculated kinematic characteristics for different manipulator configurations. The methodology is demonstrated using a five-degree-of-freedom spatial RRRRP manipulator in the Maple environment. The results provide three-dimensional representations of manipulator motion, end-effector trajectory, and selected kinematic characteristics. The proposed framework offers an integrated approach for analytical kinematic analysis and 3D visualization and can support robotics research, engineering education, virtual prototyping, and computer-aided development of robotic manipulators.