Biological systems are able to perform movements in unpredictable environments more elegantly than traditionally engineered robotic systems. A current limitation of robotic systems is their inability to simultaneously and independently control both joint angle and joint stiffness without electromechanical feedback loops, which can reduce system stability. In this paper, we describe the development and physical implementation of a servo-actuated robotic joint that uses antagonistic, series-elastic actuation with novel nonlinear spring mechanisms. These mechanisms form a real-time mechanical feedback loop that provides the joint with angle and stiffness control through differential and common-mode actuation of the servos, respectively. This approach to joint control emulates the mechanics of antagonistic muscle groups used by animals, and we experimentally show that it is capable of independently controlling both joint angle and joint stiffness using a simple open-loop control algorithm.