Various in-pipe robots used for inspection have been developed as a preventive measure against leakage. To expand the use of these robots in small pipelines, high environmental adaptability via a simple structure must be achieved. One solution, using the screw drive mechanism, has been focused on because it requires only one motor. However, the screw drive mechanism cannot achieve complex motion because of its 1-d.o.f. Therefore, existing screw drive in-pipe robots cannot pass through curved pipes with a small curvature radius. To overcome this problem, the kinematic analysis of the screw drive mechanism has been conducted on the basis of the basic principle of helical motion in curved pipes. From the analysis, the relationship among the spring stiffness, motor torque, robot length and static friction on the inner pipe wall is established for the design of stiffness of the supporting springs. The optimal spring stiffness is, thus, derived for the robot to pass through the curved pipe and to climb up in the vertical pipe. The experimental test has been used to verify the validity of the design.