Approximated Completion Conditions of Kinematic Couplings for Precise Deployable Structures

Abstract

In this paper, the completion conditions for a latch mechanism with a kinematic coupling, which consists of three v-groove/sphere pairs (Maxwell type), are approximately derived as a relationship between the slope angle of v-grooves and friction coefficient. The kinematic coupling is an economical and suitable method for attaining high repeatability in fixtures. Therefore, the kinematic coupling is used in various types of deployable space structures, such as the James Webb Space Telescope and the extensible optical bench of ASTRO-H (Hitomi). In previous studies, numerical simulations were carried out to determine the amount of additional force that should be applied to complete the latch from the incomplete state. However, it is difficult to use such numerical solutions as general design criteria. In this paper, approximated completion conditions are described using analytic functions. As a result, the derived completion conditions are intuitively clear and usable as design guidelines. The most severe condition, where two v-groove/sphere pairs are latched and only one pair remains unlatched, is clarified. It is shown that there are an optimum slope angle and upper limit of the friction coefficient for latch completion. Finally, the most severe completion condition is verified through experiments.