Study On Type Synthesis And Shape Design Methods For Space Deployable Mesh Antennas

Space deployable mesh antennas are the key components of mobile communications, environment explorations, manned spaceflights and moon-landing projects. In order to design space deployable mesh antennas with the features of large aperture, light weight and high accuracy, the degree of freedom (DOF) analysis and type synthesis for generalized mechanisms are systematically studied, some methods for geometry design, pretension design and cable net design under uncertainties are also proposed in the paper and detailed as follows.(1) The DOFs of generalized mechanisms are firstly analyzed. Generalized mechanisms contain both the rigid links and pairs, and the generalized links and kinematic pairs. Generalized links consist of flexible links, springs, cables etc. Generalized kinematic pairs consist of pre-tensioned prismatic and re volute joints etc. Based on screw algebra, motion spaces of generalized links and constraint spaces of generalized kinematic pairs are derived to obtain the minimal/maximal mobilities of generalized links and the minimal/maximal constraints of generalized kinematic pairs. Considering the common constraints, redundant constraints and the passive DOFs, three formulas for calculating the DOF of generalized mechanisms are established. The analytical results show that the DOF of a generalized mechanism is not unique but an interval value. The specific DOF depends on the links’ materials, the magnitude and direction of external loads.(2) An inverse-kinematics type synthesis method is proposed for generalized mechanism. Based on screw descriptions of generalized links and kinematic pairs, the screw systems of the kinematical chains are constructed. The kinematical characteristic of the mechanism is obtained by combing the screw systems. An analytical method for kinematical characteristics of generalized mechanisms is thus established. By inversing analysis, an inverse-kinematics type synthesis method is proposed for generalized mechanisms. When given some motion requirements, constraint screws are obtained according to the reciprocal theory. By further decomposition and reciprocally operation, the set of generalized links and generalized kinematic pairs is obtained to form the limb kinematic chains. Finally, some generalized mechanisms which satisfy the given motion requirements are obtained by the permutation and combination of the limb kinematic chains.(3) A method is proposed for designing geodesic cable net of deployable antennas. Based on the geodesic theory in differential geometry, the general geodesic differential equation between arbitrary two points on the paraboloidal surface is derived by the analysis of geodesic curvatures. By combining the relaxation method with the quadratically convergent Newton’s method, the general geodesic differential equation is solved numerically. In order to design the geodesic cable net with the generated geodesies and prescribed topology, an optimization model is established, and the dynamic boundary adjustment method for geometry design of geodesic cable net is thus built. The geodesic cable nets have shorter cable length and larger efficient area than other cable nets.(4) A plane projection method and an equal tension method are studied for pretension design of cable nets. For spatial cable net structures with known nodal coordinates, a plane projection method is researched. By projecting the cable net onto the aperture plane, an optimization model is established to obtain the cable tensions of the plane cable net. Then, the spatial pretensions are calculated by projected the obtained cable tensions back to the spatial cable net, which improves the efficiency of the pretension calculating. For cable net structures with unknown nodal coordinates and pretensions, the equal tension method is established. Based on the fixed point theory which is used to solve nonlinear equations, the cable tensions are set identically. According to the coupling relationship among the force density, the cable length and the cable tension, the iteration model for equal tension is established with force densities as iteration variables. The analytical results show that the geodesic cable nets which calculate cable tensions with the plane projection method have good tension uniformity and high surface accuracy, and the internal cable tensions in the cable nets designed by the equal tension method are completely equal.(5) Pretension design methods are studied for cable net structures under uncertainties. By analyzing the influences of uncertainties resulted from structures, material and environment on the cable tensions, these multi-source uncertainties are equivalent to the tension uncertainties in cables. For cable net structures with known nodal coordinates, the anti-optimization strategy is introduced to establish the optimization model for cable net structures under the tension uncertainties. Then, the optimally cable tensions are calculated, and the influences of uncertainties on the surface accuracy are minimized. For cable net structures with unknown nodal coordinates and pretensions, the concept of interval force density is proposed. The surface accuracy interval under cable tension uncertainties is thus derived. An optimization model with interval force density is established, which effectively reduces the influences uncertainties on the surface accuracy.