Motion Performance Study of 2UPR-1RPS/2R Hybrid Robot based on Kinematics, Dynamics and Stiffness Modeling

The unique structural characteristics of hybrid robots, such as few-DOF and redundant constraints, lead to a series of challenges in the establishment of theoretical models. However, these theoretical models are indispensable parts of motion control. Therefore, this paper focus on establishing the kinematics, dynamics and stiffness models for an Exechon-like hybrid robot, which are then used for error compensation and velocity planning to improve the robot motion performance. Firstly, the kinematic model is derived through intermediate parameters and the kinematics equivalent chains. By analyzing the parasitic motion due to few-DOF, the redundant equations in the model are eliminated to obtain the solution of inverse kinematics. Secondly, based on the beam element, the optimal equivalent configuration of the moving platform which connects the parallel part and serial part is determined and then an entire equivalent structure of the robot is formed. It helps establish the stiffness model by using the Matrix Structure Analysis method. Next, the dynamic model is established by combining the Newton Euler method with co-deformation theory to solve the underdetermined dynamic equations caused by redundant constraints. Finally, the compensation method is designed based on the stiffness model and kinematic model to improve the end positioning accuracy of the robot; the velocity planning algorithm is designed based on the dynamic model and kinematic model to enhance the smoothness of the robot motion. The methods proposed in this paper are also of referential significance to other Exechon-like hybrid robots.