Thin Red Thread, a mechanical sculpture by Jennifer Townley

This kinetic wall sculpture consists of twelve white gears that drive each other. As they all have the same amount of teeth, they rotate at the same speed. Small rods are attached to the edges of the gears and help form a symmetrical figure constructed from a thin red thread. When the sculpture is in motion the thread exposes the compositional changes of the gears. Gradually the figure formed by the thread moves and transforms fluently in accordance with the turning of the gears. See See
Investigate the length of the two thin red threads. Is there a way that to make a construction is such a way that the length of these thin red thread is constant?