КІНЕМАТИЧНИЙ РОЗРАХУНОК ПОЛОЖЕННЯ ТА ОРІЄНТАЦІЇ ЗАХОПЛЮВАЛЬНОГО ПРИСТРОЮ РОБОТА ANNIN ROBOTICS AR3

This paper presents a comprehensive analysis and practical solution to the direct kinematics problem of the six-axis manipulator Annin Robotics AR3 – an open-source robotic platform widely used in educational, laboratory, and industrial environments. Considering the structural features of the AR3, a classical approach based on Denavit-Hartenberg parameters was chosen for kinematic modeling. The process of constructing specific coordinate systems for each manipulator link is described in detail, taking into account their placement and rotational axes. Based on the kinematic diagram, a table of link transition parameters is compiled and used to form the corresponding homogeneous transformation matrices. The study sequentially constructs six homogeneous transformation matrices that describe the position and orientation of the end effector in the base coordinate frame. A complete mathematical procedure for matrix multiplication and extraction of geometric characteristics – direction cosines and spatial coordinates of the gripper—is presented. To verify the calculations, plots of the end effector’s position and orientation over time were generated for a given sequence of joint angles. As a result of the computations, the spatial dynamics of the gripper’s movement were obtained with an accuracy that corresponds to the AR3 robot’s technical specifications. The article also reviews recent scientific publications addressing similar problems. In particular, it examines hybrid approaches combining analytical models with machine learning, real-time sensor adaptation of kinematic models, and the use of digital twins to simulate manipulator operation in virtual environments. The results confirm the feasibility of using classical analytical methods for both educational and applied purposes and serve as a foundation for future developments in inverse kinematics algorithms, adaptive control, and embedded motion planning.