The sliding velocity plays an important role on the energetic efficiency and longer life of cam mechanisms with flat-faced translating followers. In this work, an optimization procedure published recently and based in the Bézier curves, is adapted to minimize the sliding velocities in this kind of cam mechanisms. Specifically, when the maximum lift of the follower, h, the total rise angle, β, and the angular velocity of the cam, ·, are given, it is found the minimum prime circle radius, Ra*, that minimizes the sliding velocity avoiding the undercutting.