  The plate trick or belt trick is a striking physical demonstration of
properties of the double cover of the three-dimensional rotation group by the
sphere of unit quaternions or spinors. The two ends of a flexible object are
continuously rotated with respect to each other. Surprisingly, the object can
be manipulated so as to avoid accumulating twists. We present a new mechanical
linkage that implements this task. It consists of a sequence of rigid bodies
connected by hinge joints, together with a purely mechanical control mechanism.
It has one degree of freedom, and the motion is generated by simply turning a
handle.
