Mobility Discriminant And Movement Study Of The Paraboloidal Rigid Deployable Structure

Recently, with the development of aerospace industry and the increase of people’s demands for information, the information transmission ability of satellites are becoming more and more important, which poses new requests for the caliber of satellites. Then the rigid deployable antenna structure obtains more and more wide application for its simple mechanism and high-precision.In consideration of research achievements in pin-bar mechanisms domestic and oversea, this paper presents a method for the judgment of mobility based on constraint equations of the structure, which contain abundant information of the structure. With the solution of these equations by Wu elimination method or numerical method, the necessary and sufficient condition of mobility could be obtained, which means the system is movable if the solutions exist and continuous and vice versa. If the system is immobile, infinitesimal mobility and stable structure can be differentiated with the first-order of constraint equations. Then finite mechanism, infinitesimal mobility, stable structure and be distinguished integrallty.For the finite mechanism, the kinetic bifurcation is analyzed with the tracking of motion curves.. Meanwhile, the limit point in kinematic path is analyzed in this paper. It can be obtained the iterative error increase sharply when the mechanism moves to the configuration around the limit point. Then limited iterative step is selected to guarantee that the mechanism would not move to infeasible paths. System with infinitesimal mobility is a special type of structure area. In this paper, we analyze the order of infinitesimal mechanisms with the high-order expansion of constraint equations in time domain. And linear equations can be obtained instead of solving nonlinear equations. Then all types of structures can be taken into consideration with infinitesimal analysis. The structure is immovable if its infinitesimal mobility is equal to 0, and it comes to be the infinitesimal mechanism if its infinitesimal mobility is more than 0. The finite mechanism can be considered as a exception of infinitesimal systems as its infinitesimal mobility is infinite. In addition, the trend of the stiffness of infinitesimal mechanisms changing with their infinitesimal orders is studied. It can be obtained that stiffness is weakened gradually with the increase of the mechanism order. When the order is high enough, slight disturbing force will make the structure move with low stress. And this is defined as the movable range of infinitesimal mechanisms. Then the structures turn to be flexible mechanisms corresponding to finite mechanisms. Such mechanisms can be designed without extra stabilization equipment with the same working principle as finite mechanisms.The movement of the rigid deployable antenna structure is analyzed based on the research of pin-bar mechanisms in the paper. Constraint equations of triangular plate elements and rectangular plate elements which is common in plate structures are given based on those of pin-bar mechanisms. Then the condition of multiple motion paths existing in mechanisms is considered by obtaining all solutions of constraint equations. Different solutions represent different motion configuration. As these equations ate nonlinear, their solution process is much more complicated than that of linear equations. Simplex Method and Global General Algorithm are applied in this paper to solve all solutions of constraint equations using the mathematic software lstOpt. As to multiple kinematic paths of mechanisms, three ways of increasing constraints and increasing drive as well as symmetric control are put forward to ensure the unique kinematic path. Kinematic bifurcation and mechanisms with multiple mobility are hard to control their kinematic paths, so mechanisms are turned into those with unique path and the kinematic simulation software ProE are used to check the validity of this method.The last part of this paper is focused on the optimization and design of the paraboloidal rigid deploy able structure. The topology-of 4-creases model and 5-crease model are adopted with the analysis of their mobility, and geometric parameters of them are optimized. The optimization method is also the Simplex Method and Global General Algorithm In the design, the offset of joints ensures the simplification of joint manufacture. By choosing the proper position of reflectors and rotation axes as well as offsetting the reflectors cut, the crash of curved slabs would be avoided. In the final,4-creases and 5-creases paraboloidal rigid deployable structures are designed.