Abstract <p>This article investigates the motion of a heavy rigid body constrained to a vertical plane, where its displacements occur within a fixed region bounded by a rough surface. When the body is in contact with the boundary of this region, its motion is constrained by the reaction force exerted at the point(s) of contact. The analysis is limited to configurations involving no more than two contact points. The body is modeled as a homogeneous rod, and the region within which it moves is represented by a circular domain. The problem is characterized by three key parameters: two distinct friction coefficients at the rod’s endpoints and the ratio of the rod’s length to the circle’s diameter. For the mechanical system under consideration, non-isolated equilibrium sets are identified, and their dependence on these parameters is explored. A comprehensive description of the possible constraint reaction values is provided, with respect to the rod’s position on the circle and the governing system parameters.</p>