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The kinesthetic illusion induced by tendon vibration has the potential to be applied to virtual reality because it can provide the sensation of motion without the need to actually move the body. The psychophysical and neurophysiological properties of this phenomenon have been studied for a long time, and more recently, research has been conducted to realize the presentation of complex motion. However, there is still a lack of knowledge that quantitatively relates time-varying vibratory stimuli to the resulting kinesthesia. In response to this situation, we experimentally quantify the relationship between the time-varying frequency of the vibratory stimuli and the perceived joint angle, as a transfer function which is directly applicable to the presentation of kinesthetic illusions. To minimize temporal error, we presented vibration stimuli to one arm and a physical motion to the other arm, and asked participants to adjust the amplitude and phase of the physical motion so that the sensations of the two stimuli matched. The transfer function obtained from the experiment was nearly constant between the presented reciprocating frequencies of 0.05 Hz and 0.30 Hz, with a flat amplitude response and a phase advance of approximately 180 degrees. This transfer function represents motion in the opposite direction to that expected from existing knowledge. Possible reasons for this could be the induction of motion in the opposite direction by the tonic vibration reflex, misunderstanding by the participants, or the generation of an illusory force sensation due to the activation of the Golgi tendon organs.

Measurement of the Transfer Function of Kinesthetic Illusion Induced by Antagonistic Tendon Vibration