Robots have been researched and developed for cleaning or inspecting buildings with vertical walls. However, robots that target buildings with convex surfaces are a necessity. This paper describes a robot that can move on a convex surface using two ropes and analyzed its feasibility. A spur gear differential mechanism was implemented to reduce the weight of the robot targeting the Gocheok Sky Dome in Seoul, South Korea. The accessible area of the two-rope driven system was derived through static and manipulability analyses. In addition, an algorithm for maneuvering a robot using instantaneous kinematics was proposed. A dome-shaped test bench was built to verify the accessible area of the robot and performance of the maneuvering algorithm.