In this letter, we proposed a variable radius pulley (VRP) to linearize input-output behavior of twisted string actuators (TSAs). With the help of a VRP, it is possible to make the inherently nonlinear transmission ratio of twisted string constant. This enables design of bidirectional transmission systems driven by a single motor, much like is done in conventional belt transmissions. Herein, we analyze the limitations on employing constant-radius pulleys in bidirectional twisted string transmission systems and propose a VRP design methodology based on TSA kinematics. We manufactured the pulley and evaluated its performance experimentally in a series of unidirectional and bidirectional actuations. The experiments demonstrated that the resultant transmission ratio from motor to load remained nearly constant as expected from the simulation results. Different statistical measures for error between the experimental and simulated results were also calculated.