3D Dynamic Analysis of a Flexible Deploying Arm Subjected to Base Angular Motions

Problems related to the three-dimensional (3D) dynamics of the deploying flexible arms subjected to base angular motions are studied with simulated tip payloads and actual deployment trajectories. To facilitate the solution, an equivalent dynamical system is developed by introducing the inertial reaction forces on the arm, while the equations of motion are derived in the non-Newtonian reference frame attached to the arm. The dynamic behavior of the arm is investigated both by the finite element and assumed Modes methods for the purpose of verification. This study reveals that base angular motions lead to considerable couplings between the two lateral displacements and axial motions. Meanwhile, the induced loadings on the flexible arm due to the base angular motions are obtained, which are useful for the design of more efficient arms. Furthermore, one may use the resulting arm–tip position envelop to predict the antenna positioning accuracy, which paves the way for possible control systems to limit undesirable motions.