Control-orientated dynamic modeling of forging manipulators with multi-closed kinematic chains

• Control-orientated dynamic modeling was proposed for multi-closed-loop manipulators.
• The reduced system and screw theory were combined for the manipulator modeling.
• Suitable selection of generalized coordinates can simplify the dynamics calculation.
• A full dynamics of the main motion mechanisms in a forging manipulator is modeled.
• The proposed method was validated by simulations and experiments.

The dynamic model, particularly with reference to controller design, is an important issue in mechanical control and design. However, this model is often difficult to achieve in complex multi-closed-loop mechanisms, such as parallel mechanisms or forging manipulators. A new approach on the dynamic modeling of a multi closed-chain mechanism in a forging manipulator, which applies screw theory and the reduced system model, is proposed in this paper. The proposed method not only allows a straightforward calculation of actuator forces but also obtains the dynamic equation of the multi-closed-loop mechanism easily. The structure of dynamic model obtained is similar to that of standard Lagrangian formulations, which can extend vast control strategies developed for serial robots to complex multi-closed-loop mechanisms. A complex multi-closed-loop mechanism on a forging manipulator is decomposed into several serial mechanisms or simpler subsystems. The Lagrangian equations associated with each subsystem are directly derived from the local generalized coordinates of the sub-mechanisms. Jacobian matrices are used to interpret the differential equations of the sub-mechanisms into the generalized coordinate or the actuated pairs according to the D’Alembert principle. Hessian matrices are also applied to form a standard Lagrangian formulation. The screw theory is introduced to overcome the difficulties of solving transformed Jacobian matrices, thereby simplifying the calculation of the matrices. Computation difficulties of transformation matrices may decrease considerably by choosing suitable generalized coordinates instead of direct actuator variables. The full dynamics of the complex multi-closed-loop mechanism in a forging manipulator is presented. Simulations and experiments illustrate the reliability of the proposed method and the correctness of the dynamic model of the forging manipulator.