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Abstract The diverse and heterogeneous terrains in the Arctic, consisting of snow, melting ice, permafrost, ice-covered lakes, sea ice and open ocean, pose serious challenges to locomotion and autonomous navigation capabilities of rovers deployed in the region for data collection and experimentation. The Multi-terrain Amphibious ARCtic explOrer or MAARCO rover is a proposed screw-propelled vehicle that uses helical drives (similar to Archimedes’ screws) to move seamlessly across the diverse terrains in the Arctic. The motion of a pair of helical drives operating in soft or fluid terrain is dictated by the response of the surrounding substrate to the stresses exerted by the rotating helical drives. If the substrate under the rover does not fail when it is moving in a straight line, the linear displacement of the rover (x) and the number of rotations of the helical drives (n) are related through x = P · n, where P is the pitch length of the helical drives. However, when the substrate fails, the linear displacement of the rover is less than P · n, i.e., x < P · n. Thus, “x = P · n” motion represents the optimal mode of operation for the rover when moving in a straight line. This paper represents the first ever attempt, to the best of author’s knowledge, to derive the conditions necessary for the application of the holonomic constraint x = P · n to the dynamics of a helical drives-based rover.