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Abstract. This paper presents a novel deployable hexagonal prism module for parabolic cylinder antennas that exhibit characteristics of geometric scalability. The hexagonal prism module consists of six basic rib mechanisms distributed along the axis and parabolic directions of the parabolic cylinder. The basic rib mechanism along the axis direction is designed, and the position of each member in the deployed state is calculated according to the geometric relationships at the folded state. The basic rib mechanism along the parabolic direction is designed to ensure that the mechanism can be fully folded. The degree of freedom of basic loop mechanisms consisting of four basic rib mechanisms due to the splice of multiple modules is analyzed. The degree of freedom of the proposed hexagonal prism module is verified through simulations and experiments of a deployable mechanism composed of three hexagonal prism modules. The simulation and experiment results show that the proposed hexagonal prism module can offer synchronized and coordinated movement during the deployment process.

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Due to kinematic function requirements, deployable structures inevitably have many clearance joints. The existence of clearance joints not only reduces the structural stiffness, but also leads to complex nonlinear dynamic characteristics. This paper proposed a general numerical method based on the wave motion theory which is able to analyze these complex nonlinear dynamic characteristics of frame structures with clearance Joints. The dynamic model of frame structures with clearance joints is derived on the basis of continuous wave equations. The clearance joint is modeling by combining Lankarani and Nikravesh contact model with the Ambrósio friction model. The established dynamic model of frame structures is solved by the finite difference time domain method. A triangular frame structure with two clearance joints is taken as the numerical example for the verification of the proposed numerical method. Numerical results show that the longitudinal wave affects the distribution direction of contact positions and the transverse wave mainly affects the distribution range of contact positions. It has been also found that the introduction of torsional springs with reasonable pre-tension torque is able to significantly improve the distribution of contact positions and reduce state uncertainties of clearance joints in structural vibrations.