I just came across the lovely and unreal set of gear constructions – that seem to work when you watch the videos. At first I thought this was a one-off project by a student but there seems to be more science behind the geometries of these paradoxical gear sets.
From Jacques Maurel’s explanation on his website:
“…This gear pair has been invented by Mr. Mercier of Renault automobile company, and has been patented in 1988 – it was to be used in a special differential providing “torque transfer” This model below shows 2 pulleys with a crossed belt – a knot giving a point on the belt. With a felt pen, it is possible to point out the trajectory of this point on a disc locked by a pin to the left pulley (red spots) and afterward, on a disc locked to the right pulley (green spots). These spotted lines are the involute curves, which will give the profile of the teeth. The pulleys are turning in opposite directions. But look at photo 4, showing a straight (non-crossed) pulleys and belt mechanism, the 2 same involute curves are still meshing together, but the pulleys are now turning in the same direction – This gives the paradoxical gear pair.”