When I started looking into this problem I thought it would be rather easy. As I got into it further I found it getting more difficult. I will explain the image first. These components are circular, but I have unwrapped them for simplification. The block on the top is a complete ring. Force F1 is a force due to torque. The lower section can be considered ground. The wedge has a small preload that is applied toward the top portion(the ring). What I am trying to solve for is the angle of the wedge. When a force(due to torque) is applied to the top portion(the ring), what angle will keep any component from sliding when F1 is applied?