[Univ of Cambridge] [Dept of Engineering]

Kinematic bifurcations and deployment simulation of foldable space structures

P Kumar


Deployable structures are structural assemblies with internal mechanisms that can be mobilised to transform the shape of the structure. Their primary use is for space applications, due to the severe payload volume constraints of most space transportation systems. From an initially folded configuration at launch, the structure is deployed in space into its final working configuration. The high cost involved in space transportation necessitates rigorous ground testing and analysis of the structure, in order to reduce the possibility of failure during deployment in space. The micro-gravity conditions and the harsh space environment make the design of such structures a difficult task.

This dissertation investigates two aspects of the behaviour during deployment of foldable structures. The first part of the dissertation deals with deployable structures which possess special, singular configurations at which the number of degrees of freedom of the structure may change. Computational methods are developed to simulate the motion of an idealised pin-jointed bar assembly through points of kinematic bifurcation, in general; and a particular application to a space sail concept is investigated. At a bifurcation point the number of infinitesimal degrees-of-freedom increases, even though the number of overall large displacement mechanisms is one in most configurations. Thus, there arises the possibility of motion along a number of different kinematic paths. The computational scheme, based upon the singular value decomposition of the equilibrium matrix of the structure, follows the motion of the structure until a bifurcation point is reached. At this point, the algorithm identifies the available kinematic paths and follows a chosen path to move out of the bifurcation. The algorithm has been tested by applying it to a number of simple structural assemblies. The folding and unfolding of a space sail has been examined.

The second part of the dissertation deals with the deployment and retraction behaviour of a real structure. Deployment tests are carried out on a 2.3 m cable-driven retractable Rigid-Panel Solar Array. The model array is operated by a cable attached to a drum driven by a stepper motor. The deployment profile is precisely controlled from a computer which operates the stepper motor through a micro-stepping device. The variation in cable tensions and the vibration characteristics of the array during deployment and retraction are investigated. A quasi-static model of the deployment process is validated through experiments. The interaction with gravity cancellation system is studied. Modal testing and vibration analysis are carried out to estimate the vibrations during deployment of the array and the end-of-deployment shocks. A non-linear deployment profile that reduces the deployment shocks is identified.

Keywords: Foldable space structure, kinematically indeterminate assembly, mechanism, rigidity, kinematic bifurcation, deployable, retractable, cable-driven, rigid-panel, solar array, deployment simulation.

[Cambridge University | CUED | Division D | Structures Group ]

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