Abstract: A continuously variable all speed transmission apparatus employs a conically-shaped driven surface which is frictionally contacted by a taut endless compliant transmission member that extends to a circular power source such as the pedal hub of a bicycle. The driven surface is centered upon an axis upon which an axle is disposed that causes rotation of a wheel such as a bicycle wheel. A shifting mechanism moves the contact site of the transmission member axially along the driven surface, thereby producing variation in the rotational speed of the wheel. The transmission member includes a central wire and a series of rollers disposed upon the wire in a manner to rotate about the wire without moving longitudinally thereupon.