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The Tricept is a novel industrial robot characterized by a hybrid kinematic design featuring a three-degrees-of-freedom (3-DOF) structure of parallel type and a 3-DOF spherical wrist. In this work the authors focus on the derivation of a dynamic model to be used for both simulation and control purposes. Two different approaches are discussed and compared in terms of inverse dynamics computation. Then, a model-based control is derived aimed at enforcing a 6-DOF impedance behavior at the end effector to manage interaction with the environment. Simulation results are presented to evaluate the accuracy of an approximate dynamic model computation as well as to test the effectiveness of the proposed impedance control strategy.