An investigation of the dimensionless torque in the newly developed cone drum twister texturing mechanism is reported. The cone drum twister is one of the outer surface contacting friction-twisting devices in false-twist texturing. In this cone drum twister, a filament yam passes over the surface of the cone drum that rotates by the passing yarn without a special driving device. This research is composed of the theoretical analysis of the false twisting mechanism and the experimental analysis at room temperature. The equations have been derived which shows interrelationship of the conical angle of cone drum, the wrapping angle, the drag angle, and the yam helix angle. Theoretical values of dimensionless torque were calculated and were compared with the experimental results. It is shown that, as the conical angle and the projected wrapping angle increased, the dimensionless torque also increased. But the conical angle was reached to ${30.75}^{circ}C$, the dimensionless torque decreased.