A continuously variable transmission includes: (a) at least one external, three-dimensional cam; (b) at least four follower assemblies, each including a planet pulley, a roller shaft, and at least one follower roller, the roller shaft being mounted on the planet pulley, the roller shaft being connected to the follower roller; (c) at least two sun assemblies, each including a sun pulley, at least one sprag clutch, and a differential pulley, the differential pulley being mounted to the sun pulley, the sun pulley driving the sprag clutch; (d) an input assembly including a sun pulley shaft, the sun pulley shaft being connected to the at least two sun pulley assemblies through the respective sprag clutches; and (e) at least one differential mechanism connecting each of the sun pulleys to at least two of the planet pulleys; wherein the cam is external to the follower assemblies.