Stiffness modeling of an industrial robot with a gravity compensator considering link weights

In the robotic machining process, the external force due to cutter-workpiece interactions and gravity force due to link weights can cause considerable deviations of the desired trajectory. Besides, gravity compensators can be found in many heavy-duty industrial robots to balance the gravity force. However, the effects of gravity force and balancing force are rarely considered in the deflection analysis. This paper proposes an effective method for the stiffness modeling of heavy-duty industrial robots by taking account of the joint/link compliances, link weights and gravity compensator. Firstly, the static equilibrium equations of each substructure are formulated to derive the expressions of reaction force exerted on each joint. Secondly, a linear map of linear/angular deflections between the joints/links and the end-effector is developed. Finally, the stiffness model of the whole robot is formulated by integrating the joint/link compliances. The robot deflections at several configurations are analyzed, and the deflection distributions throughout the workspace are demonstrated. With this model, it is possible to analytically evaluate the contributions of external force, link weights and gravity compensator to the total deflections. The correctness of the proposed model is also experimentally verified by comparing the calculated and the measured deflections under the same conditions.