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

Abstract

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 • or −180 • , 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.

Effects of Asymmetric Vibration Frequency on Pulling Illusions

“…We confirmed that the illusion can be induced by presenting the asymmetric vibrations that consists of two frequency components [18]. The basic model of the asymmetric vibration based on this finding is as follows:ẍ…”

“…In addition, in the basic model of the asymmetric vibration (Equation 1), we confirmed the effects of the phase difference at 75 Hz [18]. Thus, the main frequencies at which the illusion occurred were 40 Hz [6,8] and 75 Hz [9,18]. In this experiment, the fundamental frequency f was 40 Hz and 75 Hz (2 levels) because the illusion occurred at these frequencies.…”

“…On the other hand, we confirmed that the asymmetry of the vibration waveform (an acceleration profile per cycle) affects the illusion [18]. Specifically, the illusion occurred when the differences in the rates of change of the acceleration per unit time between the positive and negative directions were maximized, as shown in Figure 1a.…”

“…In this study, this basic model was used for asymmetric vibration stimuli because the illusion occurred at minimal levels. More details of the basic model of asymmetric vibration can be found in [18]. According to Equation (1), the waveform changes by changing the phase difference φ 0 ( Figure 2).…”

“…To measure the gripping force of the participant during the psychophysical experiment, a pressure sensor (SingleTact S8-10N, Pressure Profile Systems, Inc., LA, CA, USA) was attached between the thumb and the device. Since more details of the control method of asymmetric vibration can be found in [18], they are omitted. Figure 3 shows the experimental setup.…”