The present invention relates to transmission systems and changing gear ratios within power transmission systems. In particular, the present invention relates to a positive displacement variable speed transmission. The transmission includes one or more drive gears which orbit, rotate, and which translate radially to change the size of the orbital path. The change in the orbital path increases or decreases the linear velocity of the drive gears which engage one or more driven gears and transfer the changed linear velocity in the form of a gear ratio change. The driven gears are also radially movable and movement of the driven gears is synchronized with the radial movement of the drive gears to maintain substantially constant engagement between gear ratios change. Thus, as the drive and driven gears can slide or step radially to any location within a range of positions, gear ratio changes can be made in very small increments.