Multi-Stable Hoop Structures

The concept of multi-stability hoop structures originated with the 4B4S. The idea was to connect several hoops together, thereby constructing an articulated arm with a limited number of distinct, stable states. Such an arm would require an input of energy to change from one configuration to another but would not consume any energy to remain in any of its stable states.

The most interesting hoop studied was one that contained 5 sides. These hoops each have five discrete stable states. Both the five sided hoop and a diagram showing each of its stable states are shown below. Each state is defined by three variables. The displaced distance, the direction of the displacement (alpha) and the final orientation (beta).

It is not very useful in itself to have one five sided hoop on its own. However, if they are connected together one achieves a useful workspace that resembles that of an analogue arm. Below, the workspace of an articulated constructed from 8 five sided hoops is shown. One can vary how the hoops are connected to each other and thereby control the shape of the workspace. In general, an arm of n hoops will have a workspace of n^5 points.

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Last updated on the 8th of February, 2003

T. Schioler - ts229@cam.ac.uk