The physical stimuli provided by ultrasonic mid-air haptic interfaces are relatively limited in their ability to represent compliance and stiffness. In our previous research, we proposed to apply spatiotemporal modulation (STM) for the ultrasonic focus to simulate the contact process between a finger and a virtual surface, extending the perceived range of softness by varying the rate of contact area change and focal point speed. In the present study, we proposed to combine STM with amplitude modulation (AM), further investigating the effects of two aforementioned factors and output power variation, on perceived softness by simulating the contact process between a palm and a virtual small sphere. Based on the results of psychophysical experiments, we found that haptic stimuli with a high contact area change rate, fast focal point speed, and low output power amplitude were perceived as softer. Consequently, we covered a wide perception range, i.e., 5.3-fold softer and 4-fold harder than the modulus by altering the parameters. Our research contributes to the understanding and design of soft object simulation, and thus extends the rendering capabilities of ultrasound haptic displays in VR and AR.

Humans evaluate material softness not only by pressing but also through stroking or rubbing motions. While previous studies have primarily focused on pressing to investigate compliance-related softness perception, the present study investigates softness perception during sliding, focusing on the ‘‘curved surface softness illusion,’’ in which slightly wavy surfaces feel softer than flat ones during fingertip sliding, despite being made of the same material. The objective of this study is to identify the surface features of sinusoidal surfaces that enhance the softness perceived in this illusion, using an optimal designing approach. A set of hard plastic specimens with varying wavelengths and amplitudes was manufactured based on a central composite design. Then, their perceived softness was evaluated in an experiment involving 32 participants. Results showed that perceived softness during sliding exhibited an inverted U-shaped function of both macroscopic sinusoidal wavelength and amplitude. A response surface method was then used to determine the design parameters that would maximize perceived softness. In a post-hoc experiment, the optimally designed specimen was rated as soft as the softest specimen in the initial experiment. The specimen judged as softest exhibited the surface wavelength of approximately 70 mm and amplitude of 0.40 mm. The findings of this study will enable the manipulation of softness perception through surface design, which will potentially be applied to consumer products. However, the mechanism of this perceptual phenomenon remains unknown and should be further investigated.

The objective of this study was to investigate the influence of roughened surface features on the perceived hardness of various materials. Thirteen participants used a visual analog scale to evaluate the hardness of ten 3D-printed specimens by sliding a fingertip on them. The specimens had two types of surface features: flat and smooth, or with microscopic rectangular gratings. They were fabricated from two types of plastic with different Young's moduli—2.46 and 9.35 MPa. We found that both surface pattern and mechanical hardness significantly contributed to the perceived hardness of a material individually and without interaction. The roughened surfaces with rectangular gratings were judged to be harder than the flat and smooth surfaces of the same material. Among the parameters of the rectangular gratings, the groove width or periodic surface wavelength significantly contributed to the perceived hardness. Although the root cause of this phenomenon is unknown, friction caused by surface roughness is considered a potential mediator that influences the perceived hardness. The findings of this study can facilitate the manipulation of softness perception through surface design.