This is a planar mechanism. The white vertices are pinned, so cannot
move. Its position is determined by 6 of the vertices which do move,
each having a pair of coordinates, so abstractly the mechanism moves in
12 dimensional Euclidean space. The configuration space is the subset
of 12 dimensional Euclidean space which satisfies the constraints imposed
by the bars and pins, and so corresponds to the realizable positions of
the mechanism. The configuration space of this mechanism is homeomorphic
to a circle, which we see in the animation loop. The actual curve
can be shown to have a cusp at the position when the background of the
animation flashes red. This mechanism, discovered in 1993,
was the first example of a cusp mechanism . For details see
the following.
Authors: Robert Connelly and Herman Servatius
Reference: J. Discrete and Computational Geometry 11, 2 193-199, 1994.
Abstract: We exhibit a bar--and--joint framework G(p) which has a configuration p in the plane such that the component of p in the space of all planar configurations of G is a 1 dimensional curve with a cusp at p.
At the cusp point, the mechanism G(p) is third order rigid in the sense that every third order flex must have a trivial first order component. The existence of a third order rigid framework that is not rigid calls into question the whole notion of higher order rigidity.
