A continuously variable transmission has a number of tiltable ball-leg assemblies configured angularly about a longitudinal axis. Each ball-leg assembly is in contact with, and guided through a tilting motion by an axially translating shift cam having a convex shape. The convex shape of the shift cam can have a profile defined by a set of parametric equations. The profile of the shift cam can vary according to the location of the contact point between an idler and the ball-leg assembly as well as the amount of relative axial motion between the ball-leg assembly and the idler. The profile of the shift cam can be configured to control the axial translation of the idler relative to the change in tilt angle of the ball-leg assembly. A roll-slide factor can be used to characterize the axial translation of the idler relative to the tilt angle of the ball-leg assembly.