Analytical Inverse Kinematic Solution for Original Robotic Manipulator Construction

During robot development, one of the main problems is the problem of more weight transfer to the greatest distance. The article discusses the robot kinematics, where all the movers are located as close as possible to the carrier link axis. All link engines perform rotational movements. This can significantly increase the payload of the robot. Due to kinematic relationships, the motion of one robot link is difficult to describe both in the Cartesian coordinate system and in the spherical one. The article proposes the solution to the problem of the robot intermediate link position determination, with a known position of the end unit. We analyzed such options for the problem solution as the inverse transformation method, the analytical method, the interval method, the finite rotation and displacement method, the biquaternion solution, Mesh-based Inverse Kinematics, and FABRIK. The analytical method was optimal for the kinematics of the manipulator under consideration. Mathematical formulas are obtained that allow one to obtain the position of the intermediate links after the method application. The resulting mathematical models will allow you to get the position of the manipulator intermediate links, to create a virtual manipulator and debug a control program on stationary computing systems. The resulting mathematical models are quite simple. Their calculation can be entrusted to a low-power computing system. This will allow the creation of autonomous adaptive systems using artificial intelligence.