A stationary conical sheave member is fixed on the output shaft of an engine to rotate therewith. A movable conical sheave member faces said stationary half pulley member and is made slidable in the direction of its axis. A weight is pivoted on the output shaft, to control the shifting of the movable conical sheave member by a pawl portion; the contact plane of the movable conical sheave member along which the pawl portion of the weight slides has a convex curvature in the direction in which the pawl portion of the weight slides along said contact plane, so as to vary the speed-torque characteristics of the sheave drive to match it to the speed-torque characteristics of internal combustion engines.