A mobile mechanism with four tracked-units for a missing miner search robot (MMSR) is presented, with a design based on the terrain features and atrocious environment of an underground mine. Its structure and working principle is discussed. The four tracked-units are controlled independently and driven cooperatively. By means of two DC motors being controlled respectively, one tracked-unit can accomplish two types of driving mode: tracked travel and integral unit legged rotation (IULR), forming a track-legged compound function mechanism. Its capabilities of surmounting obstacles and its toppling stability in underground mines have also been analyzed. The results show that the mobile mechanism can directly surmount an obstacle of the height less than the length of one tracked-unit and get across a raceway with a span less than the length of one tracked-unit by using tracked travel and IULR. Its unstable slope angle is 51.3°. Toppling stability is determined by its structural size, moving direction and slope angle. IULR of four tracked-units can adjust the robot's posture and then enhance toppling stability or assist in surmounting obstacles. Its track-legged compound function mechanism makes it suitable for working in underground mines.