Shifting mechanisms for split-pulley variable transmissions

A transmission having a controllable transmission ratio for more rapid or more controllable shifting, the transmission comprising:

• a first conical split pulley having a first half-pulley and a second half-pulley;
• a first input member;
• a second input member, wherein the first input member and the second input member are capable of rotating relative to each other;
• a differential, wherein the differential is coupled to the first and second input members and the first and second half-pulleys such that a torque difference between the first input member and the second input member causes an axial force to be applied, via the differential, between the first half-pulley and the second half-pulley, thus allowing an axial distance between the first half-pulley and the second half-pulley to increase or decrease, which thereby enables a change in an effective diameter of the first conical split pulley resulting in the controllable transmission ratio of the transmission;
• a second conical split pulley having a third half-pulley and a fourth half-pulley, wherein the first conical split pulley is nested within the second conical split pulley;
• and
• a belt that couples the first conical split pulley to the second conical split pulley;
• wherein the differential is coupled to the first and second input members and the first and second half-pulleys of the first conical split pulley such that a net torque of the first input member and the second input member causes a torque to be transmitted, via the differential, from the first conical split pulley to the second conical split pulley via the belt.