Motion Modelling of a 5-Axis Delta Robot with Telescopic Shafts

This paper deals with motion modelling of a 5-axis industrial Delta robot. The robot has extra rotational 2-DoF realised with a wrist arm driven through two co-axial telescopic shafts as compared to the basic 3-DoF Delta robot. The kinematic model is derived with fully symbolic Jacobian matrices. Using the derived Jacobians, a novel simplified dynamic model is proposed based on the virtual work principle and the trajectory dependent artificial mass distribution. As compared to the existing literature, the proposed dynamic model does not require Lagrangian multiplier calculation or recursive and parallel computing so that it provides advantage for model-based control design. Also a linear regression model is provided to identify the dynamic parameters. The presented models are suitable to be employed for basic Delta and the extended Delta robots with parallel telescopic shafts as well. The derived models are verified through a Simulink model where the 3D CAD files of robot bodies having the information of real dimensions, masses and moments of inertia are used. The adequate agreement of the proposed dynamic model with the simulation results are illustrated via performing three different generated trajectory profiles. We also demonstrate the better accuracy of the proposed dynamic model as compared to a simplified and widely-employed model for basic Delta robot. The simulation model is shared online to serve as a research and test platform for performing tasks such as motion planning, model prototyping and control design.