The purpose of this research is to develop fundamentals of compliant mechanisms in deployable space systems. The scope was limited to creating methods for thick origami, developing compliant deployable solar arrays, and developing methods for stowing and deploying the arrays. The research on actuation methods was focused on a one-time deployment of the array. Concepts for both passive and active actuation were considered. The primary objective of this work was to develop approaches to accommodate thickness in origami-based deployable arrays with a high ratio of deployed-to-stowed diameter. The HanaFlex design was derived from the origami flasher model and is developed as a deployable solar array for large arrays (150 kW or greater) and CubeSat arrays (60 W). The origami folding concept enables compact stowage of the array, which would be deployed from a hexagonal prism into a flat array with about a 10-times increase in deployed diameter as compared to stowed diameter. The work on the origami pattern for the solar array was also applied to the folding of 80-100 m2 solar sails for two NASA CubeSat missions, NEA-Scout and Lunar Flashlight. The CubeSat program is a promising avenue to put the solar array or solar sails into space for testing and proving their functionality. The deployable array concept is easily scalable, although application to CubeSats changes some of the design constraints. The thickness-to-diameter ratio is larger, making the issues of thickness more pronounced. Methods of actuation are also limited on CubeSats because of the rigorous size and weight constraints. This dissertation also includes the development of a compact, self-deploying array based on a tapered map fold design. The tapered map fold was modified by applying an elastic membrane to one side of the array and adequately spacing the panels adjacent to valley folds. Through this approach, the array can be folded into a fully dense stowed volume. Potential applications for the array include a collapsible solar array for military or backpacking applications. Additional compliant mechanism design was done in support of the HanaFlex array. This included a serpentine flexure to attach the array to the perimeter truss for deployment, and a bistable mechanism that may be used in the deployment of the array or sail.

The unique environment of CubeSat and small satellite missions allows certain accepted paradigms of the larger satellite world to be investigated in order to trade performance for simplicity, mass, and volume. Peak Power Tracking technologies for solar arrays are generally implemented in order to meet the End-of-Life power requirements for satellite missions given radiation degradation over time. The short lifetime of the generic satellite mission removes the need to compensate for this degradation. While Peak Power Tracking implementations can give increased power by taking advantage and compensating for the temperature cycles that solar cells experience, this comes at the expense of system complexity and, given smart system design, this increased performance is negligible and possibly detrimental. This thesis investigates different Peak Power Tracking implementations and compares them to two Fixed Point implementations as well as a Direct Energy Transfer system in terms of performance and system complexity using computer simulation. This work demonstrates that, though Peak Power Tracking systems work as designed, under most circumstances Direct Energy Transfer systems should be used in small satellite applications as it gives the same or better performance with less complexity.

L’estimation de la charge d’un satellite et du risque de décharge nécessite dans certains cas la prise en compte dans les modèles numériques d’échelles spatiales très différentes. En particulier, les interconnecteurs présents à la surface des générateurs solaires d’un satellite sont susceptibles de modifier son équilibre électrostatique lors de missions spatiales rencontrant un environnement plasma dense. Une modélisation classique de cet effet nécessiterait le maillage d’éléments à des échelles submillimétriques,sur un satellite de plusieurs dizaines de mètres d’envergure, ce qui rendrait la simulation extrêmement onéreuse en temps de calcul. De plus, ces interconnecteurs sont parfois fortement chargés positivement par rapport à l’environnement, ce qui empêche l’application du modèle de Maxwell-Boltzmann classiquement utilisé pour les populations d’électrons. Dans une première partie, nous avons développé une méthode itérative de type Patch adaptée à la résolution du problème non-linéaire de Poisson-Boltzmann pour la simulation du plasma spatial. Cette méthode numérique multigrille permet la simulation de l’impact d’éléments de petite taille à la surface d’un satellite complet. Dans une seconde partie, nous avons développé un schéma correctif permettant d’utiliser le modèle de Maxwell-Boltzmann pour la population d’électrons, malgré la présence de surfaces satellites chargées positivement, en y ajoutant un terme de correction calculé à l’aide de la méthode Particle-in-Cell. Nous avons montré que ce schéma permet, tout en limitant le coût en calculs, de déterminer avec précision les courants collectés par les surfaces du satellites, qu’elles soient chargées négativement ou positivement. / The numerical simulation of spacecraft charging can require to resolve widely different geometrical scales. In particular, solar array interconnects on the surface of solar panels have a major impact ona satellite electrostatic equilibrium. A classical model of this effect would require a mesh refined tosub-millimetre scales, on a spacecraft spanning several dozen metres, which would make the simulation computationally expensive. Moreover, the solar array interconnects can have a large positive potentialrelative to the space plasma, preventing the use of the classical Maxwell-Boltzmann model for theelectrons in the plasma. In a first part, we have developed an iterative patch method to solve thenonlinear Poisson-Boltzmann equation used in plasma simulations. This multigrid numerical scheme allows to resolve the impact of small-scale components on the surface of a complete spacecraft. In asecond part, we have developed a corrective scheme for the Maxwell-Boltzmann model to account for the presence of charged surfaces in the simulation. We have shown that this simple model is able to precisely compute the currents collected by the spacecraft surfaces.