Stiffness and Stability Characteristics of Small Satellite Deployables With Integrated Tape-Spring Booms

Currently, the small satellite mechanisms that are used to deploy sensors and antennae in space have been restricted to simple one arm pin jointed members or telescopic mechanisms. This means, to deploy multiple sensors, multiple actuators and controllers are required. However, simple rigid link mechanisms, like the 6-bar hexagonal mechanism described in this paper, give the freedom to incorporate a greater number of sensor platforms in one deployable structure and also helps reduce the number of actuators. In fact, by the use of boom technology, the entire mechanism can be deployed by a single tape-spring boom. Further, to make these structures more robust and stiffer at the joints, rotational springs can be used. In this paper, an attempt is made to study the stiffness and stability of such mechanisms at their equilibrium points. Also since the positions and orientations of the sensor platforms are critical, it is shown through a few examples how these parameters can be adjusted just by tweaking the preloads of the rotational springs. The tape-spring boom — which is bi-stable in nature — offers further stiffness to the structure in its deployed state. It is well known now and also well established by the theory of mechanics of materials that by arranging multiple tape springs in certain orientations within the boom; a boom can be obtained with significant axial and flexural stiffness in its deployed state. Through modal analyses at equilibrium and by looking at the characteristics of the Hessian of the potential energy function, it is also shown how this significantly rigid boom affects the stiffness and stability of the structure. Herein, the force method of matrix analysis for deployable structures is used for analyses. This paper also discusses the possibilities of the system failing due to insufficient actuation force by the boom — the condition where the boom does not reach its second stable position.