In this work, four key design parameters of cycloidal rotors, namely the airfoil section, number of blades, chord-to-radius ratio, and pitching axis location, are addressed. The four parameters, which have a strong effect on rotor aerodynamic efficiency, are analyzed with an analytical model and a numerical approach. The numerical method, which is based on a finite-volume discretization of two-dimensional unsteady Reynolds averaged Navier-Stokes equations on a multiple sliding mesh, is proposed and validated against experimental data. A parametric analysis is then carried out considering a large-scale cyclogyro, suitable for payloads above 100 kg, in hovering conditions. Results demonstrate that the airfoil thickness significantly affects the rotor performance; such a result is partly in contrast with previous findings for small-scale and microscale configurations. Moreover, it will be shown that increasing the number of blades could result in a decrease of the rotor efficiency. The effect of chord-to-radius will demonstrate that values of around 0.5 result in higher efficiency. Finally it is found out that for these large systems, in contrast with microscale cyclogyros, the generated thrust increases as the pitching axis is located away from the leading edge, up to 35% of chord length. Furthermore, the shortcomings of using simplified analytical tools in the prediction of thrust and power in nonideal flow conditions are discussed