Solar sailing is a flight-proven low-thrust propulsion technology with strong potential for innovative scientific missions. The heliogyro is promising sailcraft design that utilizes a set of long slender blades which are deployed and flattened by spin-induced tension and whose orientations can be individually controlled. The main advantages of such a design are the easier stowage and deployment, and potentially lower structural mass. The heliogyro’s translational and rotational motions are strongly coupled, with non-trivial relationships between the control inputs and the forces and moments produced by the sail. The purpose of this research is to investigate, for the first time, the coupled roto-translational motion of the heliogyro. Two dynamical models of the heliogyro motion are developed and applied to design Earth-to-Mars stopover cycler trajectories. The resulting heliogyro trajectories are then compared to those of a traditional fixed-area and flat sail-system design demonstrating potential advantages of the heliogyro.