In traditional gears the tooth from one gear must go in between two teeth in the second gear — in order to work the two gears must spin in opposite directions. In paradoxical gears the tooth of one gear must pass in front of the second gear without meeting any of the second gear's teeth or this mechanism will lock.
Paradoxical gears were apparently patented back in 1988 by a "Mr. Mercier," who worked for Renault. The purpose of the gears then was for a special differential using "torque transfer." Or in other words, equalizing the torque on all the wheels of a car in cases where one wheel might have low torque adherence — such as on ice — and the other wheels don't. The gears on the low torque wheels are essentially slipping and can't move the car.
Because paradoxical gears start with low efficiency gearing where there is little contact between the gears in the first place, they offer a simple solution to the differences encountered in torque presented by things like snow and ice.
Source: dvice.comAdded: 13 November 2012