Sliding-frame mobile robots used for autonomously inspecting metallic structures consist of two bodies connected by few joints. They move by alternately adhering one body to the structure while moving the other body to the next position. Sliding-frame robots are simpler and offer safer adhesion than legged and wheeled robots, and their control can be simplified using binary actuators that adopt only two stable states. However, most existing sliding-frame robots require continuous actuators to reach targets with precision, since binary actuators impose steps of fixed length. To solve this, this paper presents a new sliding-frame robot consisting of two bodies connected through a 2RPR-PR kinematic chain driven by two binary actuators. The 2RPR-PR chain can perform nonsingular transitions, which is the ability of many parallel robots to switch between different poses corresponding to the same state of its actuators, without crossing singularities. Thanks to this, the poses reachable by the proposed robot are doubled, granting it a denser workspace and more accuracy than similar robots, using only two binary actuators. The feasibility of the proposed robot is shown through a prototype.