Lever Mechanism for Diaphragm-Type Vibrators to Enhance Vibrotactile Intensity

Thin and light vibrators that leverage the inverse piezoelectric effect with a diaphragm mechanism are promising vibrotactile actuators owing to their form factors and high temporal and frequency response. However, generating perceptually sufficient displacement in the low-frequency domain is challenging. This study presents a lever mechanism mounted on a diaphragm vibrator to enhance the vibrotactile intensity of low-frequency vibrotactile stimuli. The lever mechanism is inspired by the tactile contact lens consisting of an array of cylinders held against the skin on a sheet that enhances micro-bump tactile detection. We built an experimental apparatus including our previously developed thin-film diaphragm-type vibrator, which reproduced the common characteristic of piezoelectric vibrators: near-threshold displacement (10 to 20 μm) at low frequency. Experiments demonstrated enhanced vibrotactile intensity at frequencies less than 100 Hz with the lever mechanism. Although the arrangement and material of the mechanism can be improved, our findings can help improve the expressiveness of diaphragm-type vibrators.

Fig. 1.Illustration of the lever mechanism (tactile contact lens) that enhances (a) tactile detection of a micro-bump [20], [21] and (b) vibrotactile intensity of a diaphragm-type vibrator (see also Fig. 2(a)) in this study.The lever mechanism converts and amplifies the normal displacement of the sheet into tangential strain on the fingertip skin.skins of users [2], [3] to provide various spatiotemporal patterns of sensation [4].Because conventional rigid materials make arranging large arrays on the skin challenging, researchers and designers of tactile displays have explored smart materials that are compliant and flexible, such as shape-memory alloys [5], [6], [7], electroactive polymers [8], [9], [10], piezoelectric materials (lead zirconate titanate, polyvinylidene fluoride, etc.), functional rheological fluids [11], [12], [13] and so on.These materials transduce input (commonly electrical) energy into mechanical energy to generate a displacement or force to the skin.See [14], [15], [16] for an overview of smart materials and the details of the actuation mechanism.
Thin film actuators that leverage the inverse piezoelectric effect are promising owing to their form factors.We recently reported a few micrometer-thick piezoelectric thin-film vibrators that use microelectromechanical systems [17], [18], [19].This enables attaching and arranging arrays of multiple vibrators to curved surfaces, such as a human body.Although the piezoelectric effect generates a large force, generating perceptually sufficient displacement in the low-frequency (∼100 Hz) domain is challenging.
This study presents a lever mechanism mounted on the diaphragmtype vibrator to enhance the vibrotactile intensity for the low-frequency vibrotactile stimuli.The lever mechanism, inspired by the tactile contact lens [20], [21] consisting of an array of cylinders on a flexible sheet, converts and amplifies a normal displacement on the sheet into a shear strain at the tip of the pins and enhances tactile detection of a micro-bump (Fig. 1(a)).We apply this mechanism to a piezoelectric actuator with a diaphragm (Fig. 2  The remainder of this paper is organized as follows.First, we review the literature on tactile actuators and sensors that use shear displacement including tactile contact lenses to show the contributions of this study.Next, we describe the experiments to demonstrate enhanced vibrotactile intensity with the present approach.Finally, we conclude the study and discuss directions for future research.

II. RELATED WORK
The inverse piezoelectric effect is a major approach to generating vibrotactile stimuli as opposed to electromagnetic approaches such as eccentric rotating masses and linear actuators.A piezoelectric material, such as a ceramic, mechanically deforms or strains when an electric field is applied.Fixing the piezoelectric material on the diaphragm center and driving using an alternating voltage pushes the diaphragm and generates vibrotactile stimuli (Fig. 2(a)).Compared to electromagnetic vibrators, piezoelectric vibrators are thin, temporally responsive to input signals, and produce a flat displacement frequency response (have no resonant frequency).However, generating perceptually sufficient displacement on the skin in the low-frequency domain is challenging.
In this study, we employ a piezoelectric vibrator that we developed [19].As shown in Fig. 2(b), the vibrator employs lead zirconate titanate (PZT) as the piezoelectric material and a polyethylene terephthalate (PET) film as the diaphragm (Fig. 2(c)).We previously reported that the vibrator behaves as a diaphragm (peak displacement found on the center) [17], as illustrated in Fig. 2(a).In addition to other piezoceramics, such as lead titanate and quartz, synthetic polymers are also used as piezoelectric materials [22], [23], [24] instead of the ceramics we used, and behave as diaphragms when an alternating voltage is applied.The lever mechanism presented in this study can also be applied to such diaphragm-type vibrators.
Neural systems affect tactile detection and intensity in several ways.A certain level of noise boosts the sensitivity of neurons, enhancing weak tactile signal detection, known as stochastic resonance in tactile perception [25], [26].Besides, tactile detection and intensity are improved with spatial summation over larger surface areas of the skin [27], [28], [29] and temporal summation over time [30], [31].These effects enhance neural sensitivity or input to the neurons.
In contrast, a tactile contact lens, presented by Kikuuwe et al. [20], [21], is a mechanical structure that amplifies tactile signals.It consists of an array of cylinders held against a fingertip on a flexible sheet sliding surface, as illustrated in Fig. 1(a).The user feels a magnified bump when the sheet slides over a micro-bump, which a bare fingertip might not detect.Mathematical analysis suggests two possible explanations for the enhanced tactile detection.One is that the cylinders work as levers, converting and amplifying the normal sheet displacement into shear strain at the tips of the cylinders where the fingertip contacts (Fig. 1(a)).The other is increased spatial frequency on the skin due to the discrete contact.
The mechanism is applied to developing tactile sensors, where strains on tips of the cylinders of the tactile contact lenses are measured using a strain gauge and camera [32], [33], [34].For example, Ando et al. installed a strain gauge between a fingertip and tips of the cylinders of a tactile contact lens to measure the strain generated on the skin during active exploration on a surface [32], [33].They also investigated the effect of the length of cylinders on amplifications when sliding a bump whose height and width were 100 μm and 160 mm, respectively [32].The amplification ratio was relatively greater when the length was 5 to 15 mm.Generally, these sensors were designed and evaluated to obtain static tactile events, such as a contact between an object and a human/robot finger, leveraging spatial frequency modulated by the mechanism of tactile contact lenses.However, no studies focused on the effect of the mechanism on dynamic tactile (vibrotactile) events.
Based on prior literature that reports humans to be sensitive to shear displacement or strain [35], [36], tactile displays that provide shear stimuli were developed [37], [38], [39].Wang et al. reported the shear displacement frequency response of their developed device that deflects beam arrays using the piezoelectric effect [38].At higher applied voltages, the displacement decreases except around its resonant frequency, which may be attributed to the internal dissipation in the piezoelectric material and losses in the hinges.Similar characteristics are expected in the lever mechanism in this study.

III. EXPERIMENTS
The experiments aim to demonstrate enhanced vibrotactile intensity with the lever mechanism.A resonant frequency change due to mounting the mechanism and applying load on the vibrator might also enhance vibrotactile intensity at its frequency.Although we confirmed that the vibrators we developed had no resonance within the vibrotactile bandwidth (∼500 Hz), with no load applied to the vibrator [18], it is insightful to measure the resonant frequency with a load considering that the skin is pressed against the vibrator.Therefore, Experiment 1 measures the displacement frequency response of the vibrator with and without the lever mechanism.However, the process is significantly challenging because a more sophisticated apparatus that captures the three-dimensional displacement or strain of the numerous tips of the cylinders is required.Such an evaluation is an opportunity for our future study.In Experiment 2, we evaluate whether the lever mechanism enhances vibrotactile intensity.

A. Experiment 1: Displacement Frequency Response 1) Apparatus:
The apparatus comprised a vibrotactile display, laser displacement sensor (Panasonic, Laser Sensor HL-C2) monitored by an oscilloscope (Yokogawa Test & Measurement, DLM5058), loading mechanism, and computer.As shown in Fig. 3, the display was mechanically coupled with a jig on an anti-vibration table.The sensor was installed under the display on the table to measure the displacement of the center of the display.
As shown in Fig. 4(a) and (b), the vibrotactile display consists of our developed film vibrator [19] of 10-μm thickness (Fig. 2(c)) fixed with epoxy adhesive (Cemedine, CA-193) onto the vibrator jig modeled with acrylic resin (Keyence, AR-M2) from a 3D printer (Keyence, Aglista-3200).The vibrator is electrically connected to a voltage output module (National Instruments, NI-9269).We designed two vibrator jig  surfaces that come in contact with the fingers of participants.One is a 24 × 16 × 0.4-mm plane surface with a lever mechanism (Fig. 4(c)) and the other without a lever mechanism (Fig. 4(d)).We implemented the lever mechanism by arraying cylinders whose diameter, height, and interval were 1.0, 4.2, and 1.5 mm, respectively.Although the optimization of the arrangement and material is outside the scope of this study, these parameters were empirically determined as mentioned in Section II.
The loading mechanism consists of a medical phantom (Navis, Training Model (Navitre) Skin Suture Model II with a three-layer sheet and stand), a load weight, and a counterweight mechanism.The loading mechanism made the phantom contact the vibrotactile display with 50 gf (approximately 0.5 N).
A computer program outputs the sinusoidal voltage V 1 to the vibrotactile display via the voltage output module: where , and V 0 is the offset voltage [V].In this experiment, V A and V 0 were set to 20 V while f was set to {10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 200, or 300} Hz.When driving the vibrotactile display, the oscilloscope recorded the peak-to-peak displacement of each frequency.We obtained data from five samples for each vibrotactile display to overcome inconsistent vibrator characteristics.We also obtained data without load to observe the effect of the medical Fig. 5. Displacement of the vibrotactile displays against frequency: on xand y-axes are the frequency and displacement, respectively.Error bars stand for the standard error of displacement.The black and gray lines show the results obtained using vibrotactile displays with and without the lever mechanism, respectively.The solid and dash lines show the results obtained with load and without load, respectively.For reference, the white line shows the vibrotactile threshold curve obtained in [40] with a contactor diameter of 6 mm.
phantom on the displacement frequency response.We computed means and standard errors of the displacements at each frequency for each vibrotactile display.
2) Results and Discussion: As shown in Fig. 5, the displacement spanned from 10 to 20 μm.Although piezoelectric vibrators are generally flat in displacement frequency response without loads, the resonant frequency is observed at around 20 Hz for both vibrotactile displays with and without the lever mechanism.One explanation should be that applying a load can change the vibration system.The vibrators have similar displacement frequency response characteristics regardless of the lever mechanism over the bandwidth of interest.In addition, the standard errors were less than 10% of the mean displacement except for that with the lever mechanism with a load at 30 Hz (13%), which we consider negligible in this study.Therefore, the following experiment using a similar apparatus allows for studying the effect of the lever mechanism on enhanced vibrotactile intensity.
According to studies on vibrotactile thresholds at fingertips [40], [41], the order of magnitude is from several hundred nanometers (more than 40 Hz; Pacinian channel) to several tens of micrometers (less than 40 Hz; non-Pacinian channel).Although a direct comparison is not feasible owing to differences in the experimental setups, for reference, Fig. 5 shows the vibrotactile threshold curve obtained in the previous study [40] with a contactor diameter of 6 mm.The vibrator generated perceptually sufficient displacement at the Pacinian channel domain while generating near-threshold displacement at the non-Pacinian channel domain.Therefore, our developed vibrators reproduced the common characteristic of piezoelectric vibrators: near-threshold displacement (10 to 20 μm) at low frequency, as mentioned in Section I, even though the resonant frequency was 20 Hz.

B. Experiment 2: Perceptual Evaluation 1) Participants:
The experiment involved eleven participants from the same institution as the authors, comprising seven males and four females, with a mean age of 25.2 years.The experimental protocol was approved by the Institutional Review Board of the University of Tsukuba (Protocol Number: 2022R673).Before the experiment, informed consent was obtained after explaining the purpose and procedures of the experiment.Participants were paid 1000 JPY for an at most 90-min session.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.2) Apparatus: The apparatus comprised a vibrotactile display, an even balance mechanism, and a computer.The vibrotactile displays were the same as that used in the preceding experiment, except that we used a piezo driver (Texas Instruments, DRV2667EVM-CT) instead of the voltage output module, considering the future form factor attaching the numerous devices on the skin of users as in [2], [3].We informally confirmed that there was no significant difference in the performance of the vibrators due to this change.
Isogawa's Lego brick model [42]-based balance built on an antivibration table was used to control the contact force between a finger and the vibrotactile display by putting a weight (50 gf) on the side opposite to the vibrotactile display (Fig. 6).
The computer program outputs the sinusoidal voltage V 2 to the vibrotactile display via the audio interface and piezo driver: where w(t) is the Hanning window and T is the stimulus duration.The Hanning window produces a continuous change in displacement at the start and end of the stimulus.In this experiment, V A , f , and V 0 were the same as those in the preceding experiment, while T was set to 1 s.The program used a graphical user interface (GUI) that let participants play the stimuli and rate the vibrotactile intensity via a visual analog scale (VAS) with a 10-bit resolution whose left and right ends were labeled "No Vibration" and "Strongest Imaginable," respectively.
3) Procedure: In each trial, participants rated the vibrotactile intensity of the stimulus.The participants were instructed to use the left index fingertip to touch the vibrotactile display while maintaining the 50 gf contact force on the display using the balance.The right hand was used to interact with the GUI using a mouse.The GUI allowed participants to play the vibration, rate their perceived vibrotactile intensity via VAS, and enter the rating.VAS was activated after playing the vibration at least once.The participants could play each vibration as many times as necessary before rating.There were 24 conditions (12 frequencies × 2 vibrotactile displays).
The experimental design was a within-participants randomized block design, where each participant completed 96 test trials of each vibrotactile display condition (with and without the lever mechanism) with eight repetitions.Six participants first completed the trials with the lever mechanism, while the others first completed the trials without the lever mechanism.Participants completed 12 practice trials (12 frequency conditions) before the test trials of each vibrotactile display condition to familiarize themselves with the GUI and the range of the stimuli.Participants had a one-minute break between the vibrotactile display conditions while the experimenter changed the display configuration.Participants were instructed to avoid rating the initial stimulus too low and double the large rating if a stimulus felt twice as intense as another.During the test trials, participants wore earplugs and headphones playing white noise to mask mechanical sounds generated by the vibrotactile displays.After all the trials, participants completed a short survey recording their gender and age, as well as comments on the experiment.The data obtained in the practice trials were excluded from the analysis.

4) Analysis:
First, the ratings from each participant were transformed into z-scores.Next, mean z-scores for vibrotactile intensity were computed for each condition.Then, means and standard errors of the mean z-scores for all participants were analyzed as frequency functions for each vibrotactile display condition.
A two-way repeated analysis of variance (ANOVA) was used to evaluate the significance of differences between conditions.The withinparticipants factors were Lever and Frequency.The criterion for significance was set to α = 0.05.Where significance was found, its effect size, η 2 G , for the ANOVA was computed.

5)
Results and Discussion: Significant interaction effects were found for Lever × Frequency (p = 0.049, η 2 G = 0.053).Also, a significant main effect was found for Frequency (p < 0.001, η 2 G = 0.883) while not for Lever (p = 0.422, η 2 G = 0.020).As shown in Fig. 7, enhanced vibrotactile intensity was observed at less than 100 Hz, except at 10 Hz.In contrast, no enhancement or reduction was observed at more than 100 Hz.Moreover, the vibrators in both vibrotactile displays had similar displacement frequency responses, as shown in Section III-A2, attributable to the lever mechanism.That is, enhancement is attributable to the conversion and amplification of a normal vibrator displacement into a greater shear strain on the skin, while lack of enhancement is attributable to internal dissipation of the vibration energy in the cylinders as discussed in [38].
Some participants commented on detecting more low-frequency vibrations with the lever mechanism.As mentioned in Section III-A2, the normal vibrator displacements were near-threshold at the non-Pacinian channel domain (∼40 Hz).The displacement was reflected in the lowest vibrotactile intensity scores at 10 to 30 Hz under the vibrotactile display without the lever mechanism, where the participants could feel no vibrations.In contrast, increased scores were observed from 20 Hz with the lever mechanism, whereas the intensity of the 10-Hz stimuli remains insufficient for perception.
The curves in Fig. 7 are similar to the inverse of the thresholdfrequency [40], [41] and the equal-intensity curves [43].In addition, the standard errors represented by the error bars in Fig. 7 are less than 0.2, suggesting the design validity of this experiment.

IV. DISCUSSION AND CONCLUSION
This study presents a lever mechanism mounted on a diaphragm-type vibrator to enhance the vibrotactile intensity for low-frequency vibrotactile stimuli with insufficient perceived displacement.The inspiration for the lever mechanism is the tactile contact lens consisting of an array of cylinders held against the skin on a sheet that enhances the tactile detection of a micro-bump.Experiments demonstrated vibrotactile intensity enhancement at less than 100 Hz.Our findings can help improve the expressiveness of diaphragm-type vibrators.
The results of this study suggest several opportunities for further investigation.First, further research is needed to investigate the effect of the mechanism on superthreshold stimuli.While the lever mechanism enhanced the vibrotactile intensity at lower frequency stimuli with near-threshold displacements [40], [41], no enhancement or reduction was found at higher-frequency (more than 100 Hz) stimuli with superthreshold displacements.It would be insightful to study the mechanism of superthreshold stimuli and draw equal-intensity curves for various superthreshold stimuli, similar to those reported in [43].
Second, design improvement is possible for the optimal arrangement and materials of cylinders and sheets (the jig in this study) to efficiently convert, amplify, and transmit the stimuli to the skin.One explanation for the lack of enhancement and reduction of vibrotactile intensity at higher frequencies might be internal dissipation in the cylinders.Although long cylinders induce greater tangential strain [20], [21], exceedingly long cylinders decrease the amplification ratio [32], probably due to their damping characteristics.In addition, the impedance of materials also affects vibration transmission [44], [45] as well as the individual differences in mechanical properties of the skin.Simulation and mechanical evaluations of three-dimensional strains generated in the skin could optimize the mechanism.
Finally, we foresee two directions for designing and developing a vibrotactile display with multiple vibrators attached to a human body to create various spatiotemporal patterns of haptic experience.One is to investigate the enhancement effect on other body parts.Due to the mechanical and neurological differences, perceptual characteristics resulting from the mechanism should depend upon the body parts.The other is to explore the form factors of the display, including wearable and mobile devices.A key challenge would be to spatially arrange and mount the vibrators on the skin for the user to feel the vibrations [1], [14], [15].

Fig. 3 .
Fig. 3. Configuration of the apparatus for measuring displacement frequency response: (a) illustration of the apparatus; (b) overview of the apparatus; and (c) contact between the vibrotactile display and medical phantom.

Fig. 4 .
Fig. 4. Configuration of the vibrotactile display: (a) cross-section of the vibrotactile display with the lever mechanism; (b) illustration of fixation of the vibrator and jig; overview of the vibrotactile display.(c) with lever mechanism and (d) without lever mechanism.

Fig. 7 .
Fig. 7. Vibrotactile intensity against frequency: xand y-axes represent the frequency and mean vibrotactile intensity (z-score), respectively.Error bars stand for the standard error of vibrotactile intensity.The black and gray lines show the results obtained using vibrotactile displays with and without the lever mechanism, respectively.