Climbing robots are expected to be utilized for tasks in high places. Particularly, climbing widely installed fences enables them to significantly expand their workspace. However, when climbing fences using arms, they can only climb fences with fine meshes due to their restricted range of motion. In addition, motor overheating caused by gravitational loads remains a major challenge. Furthermore, transitioning between horizontal and vertical fence surfaces, as well as low manipulability in environments with limited footholds, are also problems. To address these issues, this study developed a three-limbed wheeled climbing robot equipped with a feed screw mechanism acting as a prismatic joint. This robot enables climbing on fences with vertically large meshes while suppressing the load on the motors. Additionally, by implementing mutual transition with the horizontal plane using wheels and an unlocking motion, the robot successfully achieved the task of opening a fence gate.