Deployable mechanisms

Among the many deployable mechanisms currently available on the market, the most famous one is the Hoberman sphere. This mechanism which is mainly used as a toy, can be deployed from 24 to 75 cm (9.5 to 30 inches), thus increasing its volume by more than 30 times.

Fig. 1: A Hoberman Sphere used as a toy.

Since deployable mechanisms do not all function in the same manner, each mechanism has its own advantages and disadvantages. Several deployable mechanisms have been developed in the laboratory, their main characteristics being the following:

the mechanisms have only 1 DOF;
the mechanisms always keep the same gemometric shape;
the mechanisms always have an empty centre;
the mechanisms are based on the five Platonic solids.

Fig. 2: The five Platonic solids: tetrahedron (pyramid), hexahedron (cube), octahedron, dodecahedron and icosahedron. The name of each figure is derived from its number of faces: respectively 4, 6, 8, 12 and 20.

The design was achieved in paying special attention to mechanical interferences, which were eliminated, and to the optimization of the mechanism as a function of its expansion ratio.

An example of a tetrahedron deployable mechanism is given below. As shown, the centre of the mechanism is always empty, no matter what position of elongation the mechanism takes on. Moreover, the geometric shape of each of its faces, which are triangles in this case, is always maintained, if for example the face is clearly illustrated by connecting a cloth to the three vertices. In addition, the mechanism requires only one single motor to allow it to expand or contract. Only a single mobile polygon located on each face has to be actuated. The other faces automatically follow the movement as a result of the architecture of the system.

Fig. 3: CAD Model and simulation of the deployable tetrahedron.

Prototypes were also built using rapid prototyping. The figure below shows the cube, whose expansion ratio of 2.8 increases its volume by almost 22 times. Moreover, the expansion ratio can easily be increased by adding one or more additional parallelograms on each face.