A six-sided foldable frame

Abstract

Deployable structures have applications in many industries. This thesis presents a detailed analysis of the kinematics, analytical geometry and deployment of a six-sided mechanism.  This is done using both computer algorithms and physical models.  The six-sided mechanism has two distinct stable configurations.  It can either be an expanded quadrilateral frame or a folded up compact bundle.  This mechanism has special characteristics that allow it to violate the mobility constraints, mainly the placement of joints along a plane of symmetry within the structure.  It is possible to construct various different kinds of six-sided foldable mechanisms by varying their construction parameters and then to categorize them into families which have similar properties. The various relationships between the construction variables of the mechanism are mapped using a computer program based on describing rotations using hyper complex numbers,  specifically hyper complex numbers of rank four called quarternions.  It is also possible to create larger deployable structures using the six-sided mechanism as a basic unit.  A new construction technique is developed which allows this task to be done in a more efficient and easy manner so that the mechanism can be specifically tailored for a particular application.