Shifting mechanisms for split-pulley variable transmissions

A variety of shifter mechanisms are provided for controlling the axial distance between half-pulleys of a split pulley variable transmission, thus controlling the transmission ratio of the variable transmission. Some of these embodiments include a differential such that a variable transmission can be driven and shifted differentially by two inputs. A torque or rotation difference between the inputs results in a change in the transmission ratio and in-common torque or rotation is transmitted through the transmission to an output. The same motors used to drive the output of the transmission are thus also able to effect shifts in the transmission ratio. Accordingly, motor mass that is not being used to effect high-speed shifts may be used to drive the transmission output, and vice versa. The provided shifter embodiments are well-suited to application to nested-pulley variable transmissions, including nested-pulley infinitely variable transmissions.