Coupled kinematic and dynamic analysis of parallel mechanism flying in space

Parallel mechanism with two rotational degree-of-freedoms (DoFs) has been widely applied in driving antenna to track moving targets in space, where its base is moveable and its kinematic performances including position, velocity and acceleration are involved with its dynamic properties. This leads an unsolved coupled kinematic and dynamic problem. In light of this, this paper proposes a novel approach to solve this problem. Firstly, the position, velocity and acceleration of the base are modeled by employing the laws of centroid conservation and momentum conservation. Then, these kinematic properties of the other parts of the mechanism are derived by using superposition principle. For the convenience of dynamic analysis, velocity relationships between the moving platform and the other parts are expressed as Jacobian matrixes. Secondly, the inertial forces of all parts of the mechanism are calculated, and the corresponding virtual displacements are expressed by the displacements of the actuated joints. Finally, the actuated torques of mechanism are solved in a theoretical form by applying virtual work principle for the first time and the validity of this approach is verified by numerical simulation.