A Unified Maple-Based Framework for 3D Motion Modeling and Visualization of Kinematic Characteristics of Spatial Robot Manipulators

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.