Recently we proposed a novel principle to design variable stiffness actuators [1]. For a single actuated joint, the principle adopts two motors in agonist-antagonist configuration coupled to the joint via nonlinear springs. Co-activation (the simultaneous activation of both motors) increases both the joint stiffness and the joint passive noise rejection, which is the ability to reduce the effect of noise without relying on explicit feedback loops. In this paper we further explore the properties of this actuator modeling the effect of static frictions (also known as stiction) on the joint equilibrium configuration. In the proposed framework, it is observed that static friction might result in multiple equilibrium configurations for a constant actuation level; this possibility is undesirable given the characteristics of the proposed actuator.We therefore characterize how stiction acting on the two motors influences the equilibrium configurations of the actuated joint. The analysis is conducted without specifying the characteristics of the non-linear springs. This procedural choice allows to give sufficient analytical conditions to guarantee that an increased level of co-activation reduces the effects of stiction on the joint equilibrium. Analytical conditions are then verified on a prototype of the actuator.