This paper introduces an analytical approach for the design of variable stiffness mechanisms. The basis of this approach is a general model - representing the potential energy function and the physical constraints - covering the design space of variable stiffness mechanisms. Using this model, we present a systematic procedure to analytically define classes of variable stiffness mechanisms from first principles. Consequently, we identify mechanisms capable of infinite range stiffness modulation using bounded motor forces, and define the simplest mathematical model representing mechanisms in this class. A prototype mechanism consistent with this canonical model is designed, fabricated and experimentally tested. The experimental data are consistent with our theoretical predictions showing constant motor force independent of the output deflection and output stiffness when the mechanism is subject to external load.