Antagonistically actuated variable stiffness actuators (VSAs) take inspiration from biological muscle structures to control both the stiffness and positioning of a joint. This paper presents the design of an elastic mechanism that utilizes a cable running through a set of three pulleys to displace a linear spring, yielding quadratic spring behavior in each actuator. A joint antagonistically actuated by two such mechanisms yields a linear relationship between force and deflection from a selectable equilibrium position. A quasi-static model is used to optimize the mechanism. Testing of the fabricated prototype yielded a good match to the desired elastic behavior.