Pulling Illusion Based on the Phase Difference of the Frequency Components of Asymmetric Vibrations

When presented with asymmetric vibrations, humans experience an illusory force, similar to the sensation of being pulled in a particular direction. A pulling illusion has also been used in new display elements for a virtual reality content and a pedestrian navigation system. However, the basic design of asymmetric vibration stimuli that can induce this illusion has not yet been determined. In particular, it is unclear as to which part of the vibration waveform should be asymmetric to induce an illusion. To better understand the design of asymmetric vibration stimuli that can induce a pulling illusion, we evaluated the effect of the illusion corresponding to the waveform deformation due to a change in phase difference of asymmetric-vibration frequency components. The results of a psychophysical experiment demonstrate that when the phase differences of the fundamental and second harmonic waves of the asymmetric vibration are close to 0^\circ or -180^\circ, the illusion is more likely to occur. This result implies that the difference in the rate by which the acceleration changes at each polarity contributes to the illusion.