A structure is a combination of resistant bodies made to bear loads. In general no internal mobility or relative motions among its members are allowed. However, there exists a family of unconventional structures, found in many places from common household items such as umbrellas and foldable chairs to solar panels of spacecrafts and retractable roofs, that are capable of large shape changes. These structures are commonly known as deployable structures. The purpose of adopting deployable structures is to have convenience in transportation or storage, but some, e.g. the retract able roofs, are concerned primarily with provision of instant coverage or shelter to create a desirable environment. In accordance with the deploy ment process, they fall into two categories. The first category is the deform able structure characterised by the fact that the overall strain energy of the structure varies during geometrical transformation. Typical examples include the inflatable structures such as balloons and cardiovascular stents, a type of medical device placed via minimum invasive surgery for treat ment of blockage in blood vessels. The other category is essentially mech anism. The deployment is executed by activation of one or a number of carefully designed internal mechanisms. Retractable roofs for sports facili ties and a toy called the Hoberman sphere belong to the second category. This book focuses on the second category. The term Motion Structures is adopted to represent this branch of the deployable structure family owing to the existence of internal mechanisms. A mechanism in machine theory, which is referred to as a conventional mechanism hereafter, is commonly identified as a set of moving or working parts used essentially as a means of transmitting motions or controlling movement of one part relative to another. It is often assembled from gears, cams and linkages, though it may also contain other specialised com ponents, e.g. springs, ratchets, brakes, and clutches, etc. There are close similarities as well as distinct differences between a motion structure and a conventional mechanism. First, the primary function of a motion structure is to have shape alteration essential to practical requirements, rather than transmitting or controlling motions. Second, as a structure, a motion struc ture is usually composed of far more parts than a conventional mechanism.