Worm-like robots have been widely designed for applications including maintenance of small pipes and medical procedures in biological vessels such as the lungs, intestines, urethra and blood vessels. The robots must be small, reliable, energy efficient and capable of carrying cargos such as cameras, biosensors, and drugs. Earthworm and inchworm robots have been traditionally designed with three or more cells and clamps and a corresponding number of actuators. The use of multiple actuators complicates the design, makes the system more cumbersome, reduces power efficiency and requires more control for coordination. In the present study, we analyze the worm locomotion, in terms of the distance between the cells and clamping modes, and model it as a cyclic function of the time. That is, the worm locomotion can be represented by a single degree of freedom. Consequently, multi-cells worm-like robots actuated by a single motor were designed. The robots employ a rotating screw-like shaft that mechanically coordinates the sequencing of the cell displacement as well as the clamping modes with no external control for each separate cell. This design allows for significant miniaturization and reduces complexity and cost of the system. Two prototypes of earthworm and inchworm robots for locomotion within 20mm and 70mm wide tubes were manufactured. The robots demonstrated high reliability and strong grip. They can crawl vertically while carrying a payload at a rate of few cm/s for the larger robots and roughly 1cm/s for the smaller ones. Furthermore, the low power consumption enables the robots to crawl wirelessly for hundreds of meters using standard off the shelf batteries.