Polynomial continuation in the design of deployable structures

Polynomial continuation, a branch of numerical continuation, has been applied to several primary problems in kinematic geometry. The objective of the research presented in this document was to explore the possible extensions of the application of polynomial continuation, especially in the field of deployable structure design. The power of polynomial continuation as a design tool lies in its ability to find all solutions of a system of polynomial equations (even positive dimensional solution sets). A linkage design problem posed in polynomial form can be made to yield every possible feasible outcome, many of which may never otherwise have been found. Methods of polynomial continuation based design are illustrated here by way of various examples. In particular, the types of deployable structures which form planar rings, or frames, in their deployed configurations are used as design cases. Polynomial continuation is shown to be a powerful component of an equation-based design process. A polyhedral homotopy method, particularly suited to solving problems in kinematics, was synthesised from several researchers’ published continuation techniques, and augmented with modern, freely available mathematical computing algorithms. Special adaptations were made in the areas of level-k subface identification, lifting value balancing, and path-following. Techniques of forming closure/compatibility equations by direct use of symmetry, or by use of transfer matrices to enforce loop closure, were developed as appropriate for each example. The geometry of a plane symmetric (rectangular) 6R foldable frame was examined and classified in terms of Denavit-Hartenberg Parameters. Its design parameters were then grouped into feasible and non-feasible regions, before continuation was used as a design tool; generating the design parameters required to build a foldable frame which meets certain configurational specifications. iv Two further deployable ring/frame classes were then used as design cases: (a) rings which form (planar) regular polygons when deployed, and (b) rings which are doubly plane symmetric and planar when deployed. The governing equations used in the continuation design process are based on symmetry compatibility and transfer matrices respectively. Finally, the 6, 7 and 8-link versions of N-loops were subjected to a witness set analysis, illustrating the way in which continuation can reveal the nature of the mobility of an unknown linkage. Key features of the results are that polynomial continuation was able to provide complete sets of feasible options to a number of practical design problems, and also to reveal the nature of the mobility of a real overconstrained linkage

Viscoelastic Effects in Metal-Polymer Laminate Inflatable Structures

A 1 m long inflatable-rigidizable mast was developed as a payload for InflateSail: a 3U CubeSat technology demonstration mission. The thin-walled cylindrical mast consists of an aluminum-polymer laminate, and long-term structural performance is ensured through strain-rigidization: the packaging creases are removed through plastic deformation of the aluminum plies. During ground tests it was observed that after rigidization the internal pressure dropped more rapidly than could be accounted for by leakage of inflation gas alone. It was hypothesized that viscoelastic behaviour of the laminate material causes a further, time-dependent (order of seconds), increase in cylinder diameter, with a corresponding drop in internal pressure. Additional experiments revealed an increase in diameter, including large visco-elastic shear in the adhesive of the lap joint. This was not found to be sufficient to fully account for the observed reduction in pressure. An increase in temperature of the gas during inflation, with subsequent cooling down to ambient is thought to cause the additional pressure drop

Flight Results of the InflateSail Spacecraft and Future Applications of DragSails

The InflateSail CubeSat, designed and built at the Surrey Space Centre (SSC) at the University of Surrey, UK, for the Von Karman Institute (VKI), Belgium, is one of the technology demonstrators for the QB50 programme. The 3.2 kilogram InflateSail is “3U” in size and is equipped with a 1 metre long inflatable boom and a 10 square metre deployable drag sail. InflateSail\u27s primary goal is to demonstrate the effectiveness of using a drag sail in Low Earth Orbit (LEO) to dramatically increase the rate at which satellites lose altitude and re-enter the Earth\u27s atmosphere. InflateSail was launched on Friday 23rd June 2017 into a 505km Sun-synchronous orbit. Shortly after the satellite was inserted into its orbit, the satellite booted up and automatically started its successful deployment sequence and quickly started its decent. The spacecraft exhibited varying dynamic modes, capturing in-situ attitude data throughout the mission lifetime. The InflateSail spacecraft re-entered 72 days after launch. This paper describes the spacecraft and payload, and analyses the effect of payload deployment on its orbital trajectory. The boom/drag-sail technology developed by SSC will next be used on the RemoveDebris mission, which will demonstrate the applicability of the system to microsat deorbiting

The InflateSail CubeSat Mission:The First European Demonstration of Drag-Sail De-Orbiting

The InflateSail (QB50-UK06) CubeSat, designed and built at the Surrey Space Centre (SSC) at the University of Surrey, UK, for the Von Karman Institute (VKI), Belgium – was one of the technology demonstrators for the QB50 pro-gramme. The 3.2 kilogram 3U CubeSat was equipped with a 1 metre long inflat-able boom and a 10m2 deployable drag sail. InflateSail's primary mission was to demonstrate the effectiveness of using a drag sail in Low Earth Orbit (LEO) to dramatically increase the rate at which satellites lose altitude and re-enter the Earth's atmosphere and it was one of 31 satellites that were launched simultane-ously on the PSLV (polar satellite launch vehicle) C-38 from Sriharikota, India on 23rd June 2017 into a 505km, 97.44o Sun-synchronous orbit (SSO). Shortly after orbital insertion, InflateSail booted-up, and, once safely clear of the other satellites on the launch, it automatically activated its payload – firstly, deploying a 1 metre long inflatable boom comprising a metal-polymer laminate tube, using a cool gas generator (CGG) to provide the inflation gas, and secondly, using a brushless DC motor at the end of the boom to extend four lightweight bistable rigid composite (BRC) booms to draw out the 3.1m x 3.1m square, 12 micron thick polymer drag-sail. As intended, the satellite immediately began to lose alti-tude, and re-entered the atmosphere just 72 days later – thus demonstrating for the first time the de-orbiting of a spacecraft using European inflatable and drag-sail technologies. The boom/drag-sail technology developed by SSC will next be used on the RemoveDebris mission, due for launch in 2018, which will demon-strate the capturing and de-orbiting of artificial space debris targets using a net and harpoon system

InflateSail de-orbit flight demonstration results and follow-on drag-sail applications

The InflateSail (QB50-UK06) CubeSat, designed and built at the Surrey Space Centre (SSC) for the Von Karman Institute (VKI), Belgium, was one of the technology demonstrators for the European Commission’s QB50 programme. The 3.2 kg 3U CubeSat was equipped with a 1 metre long inflatable mast and a 10m2 deployable drag sail. InflateSail's primary mission was to demonstrate the effectiveness of using a drag sail in Low Earth Orbit (LEO) to dramatically increase the rate at which satellites lose altitude and re-enter the Earth's atmosphere and it was one of 31 satellites that were launched simultaneously on the PSLV (polar satellite launch vehicle) C-38 from Sriharikota, India on 23rd June 2017 into a 505km, 97.44o Sun-synchronous orbit. Shortly after safe deployment in orbit, InflateSail automatically activated its payload. Firstly, it inflated its metrelong metal-polymer laminate tubular mast, and then activated a stepper motor to extend four lightweight bi-stable rigid composite (BRC) booms from the end of the mast, so as to draw out the 3.1m x 3.1m square, 12m thick polyethylene naphthalate (PEN) drag-sail. As intended, the satellite immediately began to lose altitude, causing it to re-enter the atmosphere just 72 days later – thus successfully demonstrating for the first time the de-orbiting of a spacecraft using European inflatable and drag-sail technologies. The InflateSail project was funded by two European Commission Framework Program Seven (FP7) projects: DEPLOYTECH and QB50. DEPLOYTECH had eight European partners including DLR, Airbus France, RolaTube, Cambridge University, and was assisted by NASA Marshall Space Flight Center. DEPLOYTECH’s objectives were to advance the technological capabilities of three different space deployable technologies by qualifying their concepts for space use. QB50 was a programme, led by VKI, for launching a network of 50 CubeSats built mainly by university teams all over the world to perform first-class science in the largely unexplored lower thermosphere. The boom/drag-sail technology developed by SSC will next be used on a third FP7 Project: RemoveDebris, launched in 2018, which will demonstrate the capturing and de-orbiting of artificial space debris targets using a net and harpoon system. This paper describes the results of the InflateSail mission, including the observed effects of atmospheric density and solar activity on its trajectory and body dynamics. It also describes the application of the technology to RemoveDebris and its potential as a commercial de-orbiting add-on package for future space missions

A continuation-based method for finding laminated composite stacking sequences

A method of recovering laminate ply stacking sequences from a set of up to twelve lamination parameters using polynomial homotopy continuation techniques is presented. The ply angles are treated as continuous variables, and are allowed to take any value between -90 and +90 degrees. The individual plies are assumed to be orthotropic and have constant stiffness. The method is fully deterministic, and does not rely on an optimisation process to establish the stacking sequence. Polyhedral continuation methods are used to limit the solution space in which the stacking sequences are sought. The method can reliably find every stacking sequence solution that exists to achieve a precisely specified set of lamination parameter "targets", with the number of real solutions to a feasible combination of target properties found to vary from 1 to over 100. The same method is also demonstrated to be able to find stacking sequences to satisfy a set of specified ABD stiffness matrix terms, as might be required following a direct-stiffness modelling design process

Curved bistable composite slit tubes with positive Gaussian curvature

An investigation into the bistability of positively curved laminated composite slit tubes is presented, establishing a natural extension in this area that has previously been focused on straight tubes. Curved slit tubes are modeled as the surface segments of a torus. The design space is explored through a parametric study to investigate the effect on the second stable state, representing a small coil. This includes the effects of longitudinal curvature, cross-section subtending angles, nonuniform transverse curvature, and spatially varying laminate properties. The second equilibrium state is determined through strain energy minimization using the Rayleigh–Ritz method. To verify the model, samples are manufactured from glass-fiber braid and polypropylene resin. This investigation finds 1) the initial curvature along the length of the tube has little effect on coil radius, however, the coil has a distinct barrel shape; 2) highly enclosed and 3) highly curved cross-sections result in higher edge strains of the second equilibrium, enabling identification of practical bistable tubes; and 4) conversely, the greater the initial curvature along the length of the tube, the lower the second equilibrium strain

Helical bistable composite slit tubes

Bistability in doubly curved and twisted (helical) composite slit tubes is investigated for the first time. This work establishes a natural extension in this area which has been focused on straight and until more recently, doubly curved (toroidal) tubes with positive Gaussian curvature. The model developed introduces longitudinal and transverse curvature, and twist into strips of laminated composite material. The composite is engineered to be bistable and the second stable state determined via strain energy minimisation using the Rayleigh-Ritz method. The strain energy is formulated as a function of curvature strains, longitudinal stretching and a variable middle ply fibre angle of the laminate. The second stable state forms a compact and untwisted cylindrical coil with the latter engineered by tailoring the middle ply fibre angle. A new manufacturing process capable of producing helically curved tubes using glass-fibre/polypropylene-matrix composite is presented to verify the hypothesis of this work. An untwisted coil enables the efficient stowage and deployment of new forms of bistable composite tube which adhere to similar form factors as straight and toroidal ones. By embedding electrical conductors, helical bistable composites enable new lightweight, compact and multifunctional structures for communication and sensing applications