Effects of Mechanical Parameters on Hardness Experienced by Damped Natural Vibration Stimulation

Humans can perceive the hardness of an object from the damped natural vibration produced by tapping its surface. This damped natural vibration can be used in hap tic rendering to effectively present a sense of the hardness of an object. Although its frequency is known to influence the subjective hardness, the effects of the viscosity or decay rate have yet to be studied. We researched the contributions of the mass, viscosity, and stiffness to the hardness perception using a commercial force display and psychophysical experiments, where only the vibratory displacement was presented. As a result, the stiffness was found to have a positive effect on the subjective hardness, similar to the usual hap tic rendering of an object. The mass of the object was negatively correlated with the subjective hardness. These results indicated that the vibratory frequency was the dominant parameter in determining the perceived hardness, which agreed with the previous reports on the perceptual effect of damped natural vibration. In contrast, the perceptual effect of the viscosity depended on the individual. For approximately half the participants, the viscosity did not directly influence the subjective hardness of an object. Some participants felt that a damped natural vibration with greater viscosity was harder. However, the other participants felt that it was harder with a smaller viscosity, which suggested that the decay rate of the mechanical system was used as a criterion to judge the hardness of an object. Therefore, the results indicated that the vibratory frequency is a general parameter that can be used to specify the subjective hardness, whereas the perceptual influence of the viscosity or decay rate depends on the individual.