Vibrotactile Actuators Research Articles

Smart Tactile Gloves for Haptic Interaction, Communication, and Rehabilitation

Wearable human machine interfaces (HMI) such as smart gloves have attracted considerable interest in recent years. The quality of the interactive experience with the real and virtual world using wearable HMI technologies depends on the intuitive two‐way haptic interfaces they offer and the real‐time touch‐based information they send and receive. Herein, various smart glove solutions and their application in interaction, rehabilitation, virtual (VR) and augmented reality (AR), and augmentative and alternative communication (AAC) tasks are reviewed. While the early variants of such systems were based on commercial touch sensors and displays integrated (e.g., stitched) on wearables, electronic skin (e‐skin)‐type technologies with multifunctional capabilities are being explored nowadays for rich user experience and comfort. In this regard, instead of using separate touch sensors and actuators, miniaturized integrated devices providing both touch sensing and vibrotactile actuation have also been reported recently. Such advances, the associated challenges, and the advantages they offer for users to enjoy the full characteristic benefits of VR/ARs for interaction, immersion, and imagination are discussed. Finally, the huge potential the smart‐glove‐type solutions hold for advances in various application areas such as robotics, health care, sensorial augmentation for nondisabled and tactile Internet is also discussed.

Tactile spatial discrimination on the torso using vibrotactile and force stimulation

There is a steadily growing number of mobile communication systems that provide spatially encoded tactile information to the humans’ torso. However, the increased use of such hands-off displays is currently not matched with or supported by systematic perceptual characterization of tactile spatial discrimination on the torso. Furthermore, there are currently no data testing spatial discrimination for dynamic force stimuli applied to the torso. In the present study, we measured tactile point localization (LOC) and tactile direction discrimination (DIR) on the thoracic spine using two unisex torso-worn tactile vests realized with arrays of 3 × 3 vibrotactile or force feedback actuators. We aimed to, first, evaluate and compare the spatial discrimination of vibrotactile and force stimulations on the thoracic spine and, second, to investigate the relationship between the LOC and DIR results across stimulations. Thirty-four healthy participants performed both tasks with both vests. Tactile accuracies for vibrotactile and force stimulations were 60.7% and 54.6% for the LOC task; 71.0% and 67.7% for the DIR task, respectively. Performance correlated positively with both stimulations, although accuracies were higher for the vibrotactile than for the force stimulation across tasks, arguably due to specific properties of vibrotactile stimulations. We observed comparable directional anisotropies in the LOC results for both stimulations; however, anisotropies in the DIR task were only observed with vibrotactile stimulations. We discuss our findings with respect to tactile perception research as well as their implications for the design of high-resolution torso-mounted tactile displays for spatial cueing.

A Feasibility Study of a Vibrotactile System Based on Electrostatic Actuators for Touch Bar Interfaces: Experimental Evaluations

Vibrotactile feedback is a very desirable feature for many touchscreen applications, creating a more engaging and effective user experience. Although it is common in small electronic devices, this feedback is often absent in large touchscreen devices because it is difficult to provide vibration sensations and control the magnitude throughout the display. Because of their long shape (over 20 cm), touch bar displays are susceptible to the same challenges that other large display types face. Thus, there is a need for a vibrotactile actuation system capable of generating a freely positionable and fully controllable point of stimulation with satisfying force output at any point of a touch bar display. This study proposes a new spring boundary condition vibrotactile system as a way to provide such feedback in touch bar interfaces. A prototype system was created using two electrostatic resonant actuators and a thin, narrow aluminum beam to study the effect of different actuator excitation parameters on the beam’s response. By varying the number of actuators excited, magnitude, excitation frequency, and signal duration, a minimum vibration of 24.5 m/s2 could be created in the beam, with the majority of the beam able to exceed 40 m/s2. These results show that a targeted vibrotactile response at a given location in the beam can be achieved and sustained. This demonstrates a promising potential for generating a freely positionable and fully controllable point of vibrotactile stimulation at any point of a touch bar display.

Impact Vibration Source Localization in Two-Dimensional Space Around Hand.

This article investigated the localization ability of an impulse vibration source outside the body in two-dimensional space. We tested whether humans can recognize the direction or distance of an impulse vibration source when using their hand to detect spatiotemporal vibrotactile information provided by the propagated vibrational wave from the source. Specifically, we had users put their hands on a silicone rubber sheet in several postures. We asked users to indicate the position of the vibration source when a location on the sheet was indented. Experimental results suggested that the direction of the impact vibration source can be recognized to some extent, although recognition accuracy depends on hand posture and the position of the vibration source. The best results were achieved when the fingers and palm were grounded and a vibration source was presented around the middle fingertip, and the directional recognition error in this case was 6 °. In contrast, results suggest it is difficult to accurately recognize the distance of the vibration. The results of this study suggest a new possibility for directional display where vibrotactile actuators are embedded at a distance from the user's hand.

Visual Capture of a Tactile Sensation is Influenced by Repeated, Structured Exposure of a Visual Stimulus in Virtual Reality

Phantom limb pain is commonly known as a neurological condition, where an amputee will continue to feel a limb that is no longer present in a painful fashion. Virtual mirror therapy (VMT) has been suggested as a method for alleviating phantom limb pain. The inclusion of tactile sensation in VMT has shown to be beneficial; however, delivering a tactile sensation to a phantom limb, without the use of invasive procedures, can be difficult. The current approach for transferring a tactile sensation to a phantom limb is called visual capture. The ability to establish visual capture has been demonstrated in VMT applications. However, there is little research into whether an established visual capture effect can be relocated to a more distal location for phantom limb pain management. This paper investigates whether a passive vibrotactile sensation can be moved to a distal location from its veridical location using a series of distally located lights presented in either a random or a structured fashion. Eight non-amputee participants were tasked with localising a static tactile sensation on a virtual arm. These vibrotactile sensations were presented simultaneously with a visual light stimulus, either co-located or located distally at three different locations. Findings show that a tactile sensation without a visual stimulus was difficult for participants to localise; however, when a visual stimulus was added, they were better able to locate the veridical tactile position. The structured group exhibited a larger range of tactile relocation responses than the random group. However, this result was unreliable, with the majority of the responses situated at the vibrotactile actuator. There was a significant difference between the random and structured group’s ability to retain a visual capture at the veridical vibrotactile location when the lights were located distally. The random group did not express a visual capture response when the lights were presented distally while the structured group did, suggesting the structured group developed a more robust association between the visual stimulus and the vibrotactile stimulus. Findings may be of use where increasing tactile acuity without significant alteration of a veridical location is a desired therapeutic outcome.

A Light-Driven Vibrotactile Actuator with a Polymer Bimorph Film for Localized Haptic Rendering.

A vibrotactile actuator driven by light energy is developed to produce dynamic stimulations for haptic rendering on a thin-film structure. The actuator is constructed by adopting a thermal bimorph membrane structure of poly(3,4-ethylenedioxythiophene) doped with p-toluenesulfonate (PEDOT-Tos) coated onto a polyethylene terephthalate (PET) film. Upon irradiation of near-infrared (NIR) light, the light energy absorbed at the PEDOT-Tos layer is converted into thermoelastic bending deformation due to the mismatch in coefficient of thermal expansion between PEDOT-Tos and PET. Since the light-induced deformation is reversible, spatially localized, and rapidly controllable with designed light signals, the proposed actuator can produce vibrotactile stimulation over 10 dB at arbitrary areas in the human-sensitive frequency range from 125 to 300 Hz using a low input power of ∼2.6 mW mm-2, as compared with a complex electrical circuit and high input power needed to achieve such actuation performance. Together with its simple structure based on light-driven actuation, the advent of this actuator could open up new ways to achieve substantial advances in rendering textures at a flexible touch interface.

VibroMap

In spite of the great potential of on-body vibrotactile displays for a variety of applications, research lacks an understanding of the spacing between vibrotactile actuators. Through two experiments, we systematically investigate vibrotactile perception on the wrist, forearm, upper arm, back, torso, thigh, and leg, each in transverse and longitudinal body orientation. In the first experiment, we address the maximum distance between vibration motors that still preserves the ability to generate phantom sensations. In the second experiment, we investigate the perceptual accuracy of localizing vibrations in order to establish the minimum distance between vibration motors. Based on the results, we derive VibroMap, a spatial map of the functional range of inter-motor distances across the body. VibroMap supports hardware and interaction designers with design guidelines for constructing body-worn vibrotactile displays.

Body-Mounted Vibrotactile Stimuli: Simultaneous Display of Taps on the Fingertips and Forearm.

In this article, we present a body-mounted tactile display to deliver haptic feedback to the forearm and user-initiated haptic feedback to the fingertips. The display mounts two vibrotactile actuators on the forearm, leaving the user's hands free for manipulation tasks when the hands are not interacting with the tactile display, while also exploiting the tactile sensitivity of the fingertips when needed. We test the effectiveness of the display using paired vibrotactile taps sensed through the forearm and the fingertips, either separately or simultaneously. We measure the ability of participants to identify the vibrotactile taps. The results show that mounting the device on the forearm, so that the participant touches the forearm-mounted device with their fingertips receiving feedback to both locations simultaneously, decreases performance relative to mounting on the fingertips unless large amplitudes are used. We also test the accuracy with which participants identified different numbers of vibration taps (4, 8, 16, and 25 signals). The results show that as the number of signals changes, participant accuracy is not different when stimulating the fingertips alone compared to stimulating the fingertips and forearm together. We conclude with an example of a portable and wearable vibration display, and discuss future use cases of such a display.

Adaptive Equalization of Vibrotactile Actuators.

In order to provide convincing artifical touch sensations, humans should be presented with high quality haptic stimuli. In the vibrotactile domain, signals are usually displayed through mechanical actuators. Current high quality actuators exhibit a high dynamic range and have the ability to display a wide range of frequencies. However, fundamentally all actuators introduce distortions into the displayed signals. These distortions are usually nonlinear with additive noise components and they can be detrimental to some vibrotactile application scenarios that require high signal playback precision. To neutralize these distortions, we propose a signal-based equalization setup with adaptive filtering. Such a setup is very general and can be applied to any actuator in a straightforward manner. We introduce a novel adaptive filter based on Volterra and bilinear filter models that is nonlinear and more robust than previous approaches. In simulations and experiments, we show that our filter model is able to consistently outperform existing adaptive filter models and equalize vibrotactile actuators efficiently.

Wearable multichannel haptic device for encoding proprioception in the upper limb

Objective. We present the design, implementation, and evaluation of a wearable multichannel haptic system. The device is a wireless closed-loop armband driven by surface electromyography (EMG) and provides sensory feedback encoding proprioception. The study is motivated by restoring proprioception information in upper limb prostheses. Approach. The armband comprises eight vibrotactile actuators that generate distributed patterns of mechanical waves around the limb to stimulate perception and to transfer proportional information on the arm motion. An experimental study was conducted to assess: the sensory threshold in eight locations around the forearm, the user adaptation to the sensation provided by the device, the user performance in discriminating multiple stimulation levels, and the device performance in coding proprioception using four spatial patterns of stimulation. Eight able-bodied individuals performed reaching tasks by controlling a cursor with an EMG interface in a virtual environment. Vibrotactile patterns were tested with and without visual information on the cursor position with the addition of a random rotation of the reference control system to disturb the natural control and proprioception. Main results. The sensation threshold depended on the actuator position and increased over time. The maximum resolution for stimuli discrimination was four. Using this resolution, four patterns of vibrotactile activation with different spatial and magnitude properties were generated to evaluate their performance in enhancing proprioception. The optimal vibration pattern varied among the participants. When the feedback was used in closed-loop control with the EMG interface, the task success rate, completion time, execution efficiency, and average target-cursor distance improved for the optimal stimulation pattern compared to the condition without visual or haptic information on the cursor position. Significance. The results indicate that the vibrotactile device enhanced the participants’ perceptual ability, suggesting that the proposed closed-loop system has the potential to code proprioception and enhance user performance in the presence of perceptual perturbation.

Defining a vibrotactile toolkit for digital musical instruments: characterizing voice coil actuators, effects of loading, and equalization of the frequency response

The integration of vibrotactile feedback in digital music instruments (DMIs) is thought to improve the instrument’s response and make it more suitable for expert musical interactions. However, given the extreme requirements of musical performances, there is a need for solutions allowing for independent control of frequency and amplitude over a wide frequency bandwidth (40–1000 Hz) and low harmonic distortion, so that flexible and high-quality vibrotactile feedback can be displayed. In this paper, we evaluate cost-effective and portable solutions that meet these requirements. We first measure the magnitude–frequency and harmonic distortion characteristics of two vibrotactile actuators, where the harmonic distortion is quantified in the form of total harmonic distortion (THD). The magnitude–frequency and THD characteristics in two unloaded cases (actuator suspended freely or placed on a sandbag) are observed to be largely identical, with minor attenuation for actuators placed on the sandbag. Loading the actuator (when placed in a DMI) brings resonant features to its magnitude–frequency characteristics, increasing the output THD and imposing a dampening effect. To equalize the system’s frequency response, an autoregressive method that automatically estimates minimum-phase filter parameters is introduced, which by design, remains stable upon inversion A practical use of this method is demonstrated by implementing vibrotactile feedback in the poly vinyl chloride chassis of an unfinished DMI, the t-Stick. We finally compare the result of equalization by performing sinesweep measurements on the implementation and discuss the degree of equalization achieved using it.

Psychophysical principles of discrete event-driven vibrotactile feedback for prostheses

Purpose/aim of the study: We aimed to establish psychophysical principles for non-invasive vibrotactile feedback signalling discrete transition events (e.g., extension to flexion) during use of prostheses, especially for the upper limbs.Materials and methods: Two vibrotactile actuators were used on both upper arms of 10 able-bodied human participants. Absolute thresholds, psychometric functions, and magnitude estimates were measured to equalize the sensation magnitudes for the tested vibrotactile frequencies and skin sites. Then, same-different and pattern recognition tasks were run to evaluate, respectfully, the discrimination and closed-set identification of stimuli with varying parameters (2 frequencies, 2 magnitudes, 2 sites). Finally, parameters of the left/right stimuli were mapped to hypothetical prosthesis events representing object/force and movement type. The stimuli were applied sequentially in accordance with the discrete event-driven feedback paradigm.Results: Reliable psychophysical models could be established for individual participants as verified by repetitive threshold measurements and relative adjustment of stimulus levels based on sensation magnitudes. Discrimination accuracy was higher for magnitude versus frequency comparisons; and magnitude discrimination accuracy was correlated with magnitude estimate differences. Pattern recognition recall/precision rates decreased from ∼0.7 to ∼0.5 for sequential delivery of two stimulus patterns to one arm versus to two arms. Using the patterns as two and three consecutive prosthesis events yielded statistically similar performance rates not correlated with magnitude estimate differences.Conclusions: By careful calibration of stimuli based on psychophysical principles, discrete event-driven vibrotactile feedback can be used to signal manipulated object and movement information with moderate identification rates as shown by confusion matrices.

Wearable Assistive Tactile Communication Interface Based on Integrated Touch Sensors and Actuators

This paper presents the design and fabrication of a wearable tactile communication interface with vibrotactile feedback for assistive communication. The interface is based on finger Braille, which is a simple and efficient tactile communication method used by deafblind people. It consists of a flexible piezoresistive sensor and a vibrotactile actuator integrated together and positioned at the index, middle and ring fingers of both hands to represent the six dots of Braille. The sensors were made using flexible piezoresistive material whereas the actuator utilizes electromagnetic principle by means of a flexible coil and a tiny NdFeB permanent magnet. Both were integrated to realize a Bluetooth-enabled tactile communication glove which enables deafblind people to communicate using Braille codes. The evaluation with 20 end-users (10 deafblind and 10 sighted and hearing person) of the tactile interface under standardized conditions demonstrated that users can feel and distinguish the vibration at frequencies ranging from 10Hz to 200Hz which is within the perceivable frequency range for the FA-II receptors. The results show that it took non-experts in Braille within 25s and 55s to send and receive words like "BEST" and "JOURNAL", with an accuracy of ~75% and 68% respectively.

Machine Learning Methodology in a System Applying the Adaptive Strategy for Teaching Human Motions.

The teaching of motion activities in rehabilitation, sports, and professional work has great social significance. However, the automatic teaching of these activities, particularly those involving fast motions, requires the use of an adaptive system that can adequately react to the changing stages and conditions of the teaching process. This paper describes a prototype of an automatic system that utilizes the online classification of motion signals to select the proper teaching algorithm. The knowledge necessary to perform the classification process is acquired from experts by the use of the machine learning methodology. The system utilizes multidimensional motion signals that are captured using MEMS (Micro-Electro-Mechanical Systems) sensors. Moreover, an array of vibrotactile actuators is used to provide feedback to the learner. The main goal of the presented article is to prove that the effectiveness of the described teaching system is higher than the system that controls the learning process without the use of signal classification. Statistical tests carried out by the use of a prototype system confirmed that thesis. This is the main outcome of the presented study. An important contribution is also a proposal to standardize the system structure. The standardization facilitates the system configuration and implementation of individual, specialized teaching algorithms.

Flexible Vibrotactile Actuator Based on Soft PVC Gel Embedded Polyaniline/Silicon Dioxide Nanoparticles

Nanocomposite hybrid materials made of inorganic nanoparticles and organic polymers are fascinating to design high performance polymeric materials, customized in electronics and transportation sectors. In this concern, a soft and flexible PVC gel embedded with silicon dioxide nanoparticles (SDNs) coated with polyaniline (PANI) has been proposed as a dielectric interface in vibrotactile actuator. Soft PVC gels were achieved by plasticization using acetyltributylcitrate (ATBC), an ecofriendly green plasticizer. The optimization of plasticizer content to PVC was precisely controlled and the ratio was kept constant throughout the experiment. PANI was coated on SDN by using chemical oxidative polymerization technique in order to tune the dielectric/electronic properties and minimize the leakage current. Various quantities of PANI-SDNs were loaded to PVC; the behavior of nanocomposite PVC gels as soft vibrotactile actuators was investigated. All the composite materials were comprehensively investigated using different physico-chemical techniques and haptic performance of the optimized PANI-SDN-0.2 nanocomposite PVC gel was assessed. The following are available online at http://www.xxx.com/xxx/s1, Figure S1. Pictograph representing PANI-SDN-0.2 nanocomposite PVC gel, (a) a flat PANI-SDN-0.2 nanocomposite PVC gel, (b) demonstrating the flexibility of PANI-SDN-0.2 nanocomposite PVC gel, (c) a wavy-shaped PANI-SDN-0.2 nanocomposite PVC gel for actuator design (d) dimensions of the fabricated wavy-shaped PANI-SDN nanocomposite PVC gels. Figure S2. Illustration to demonstrate the fabrication process of the vibrotactile actuator (a) components of the vibrotactile actuator, (b) lower surface of the top layer, (c) assembled vibrotactile actuator, (d) cross-sectional image of the vibrotactile actuator. Figure S3. Experimental environment demonstrating the measurement of haptic performance of PANI-SDN nanocomposite PVC gels. Description: Instrumentation and Characterization Techniques. Figure S4. EDX spectra of PANI (Scale = 1 μm). Figure S5. EDX spectra of SDNs (Scale = 1 μm). Figure S6. EDX spectra of PANI-SDNs (Scale = 1 μm). Figure S7. EDX spectra of PANI-SDN-0.2 nanocomposite PVC gel (Scale = 1 μm). Figure S8. (a & b) FESEM micrographs of PANI-SDN-0.2 nanocomposite PVC gel with different magnitudes (Scale = 2 μm and 200 nm respectively). Figure S9. Acceleration performance of PANI-SDN-0.01, PANI-SDN-0.05, PANI-SDN-0.1, PANI-SDN-0.3, PANI-SDN-0.4 and PANI-SDN-0.5 nanocomposite PVC gel based actuators.

GAN-Based Fine-Tuning of Vibrotactile Signals to Render Material Surfaces

The design productivity of fine-tuning for vibrotactile stimuli becomes important as consumer devices equipped with vibrotactile actuators will become wide-spread. The fine-tuned vibrotactile stimuli output by vibrotactile actuators allows the end-users to feel the surface of the virtual material. However, there is no suitable tool for fine-tuning while there are existing tools suitable for initial designing. In this paper, we test whether we can use GAN (Generative Adversarial Network)-based vibrotactile signal generator at the tuning phase. The generator provides a material-level interface to designers. Designers can define any intermediate materials among pre-defined 108 materials and obtain corresponding intermediate signals that the generator generates. We showed the applicability of the generator to the fine-tuning of vibrotactile signals from the viewpoints of principal component analysis and a user test.

Power Wheelchair Navigation Assistance Using Wearable Vibrotactile Haptics.

People with severe disabilities often rely on power wheelchairs for moving around. However, if their driving abilities are affected by their condition, driving a power wheelchair can become very dangerous, both for themselves and the surrounding environment. This article proposes the use of wearable vibrotactile haptics for wheelchair navigation assistance. We use one or two haptic armbands, each composed of four evenly-spaced vibrotactile actuators, for providing different navigation information to power wheelchair users. With respect to other available solutions, our approach provides rich navigation information while always leaving the patient in control of the wheelchair motion. Moreover, our armbands can be easily adapted for different limbs and can be used by all those patients who are unable to safely maneuver a kinesthetic interface. The results of two human subjects studies show the viability and effectiveness of the proposed technique with respect to not providing any environmental cue. Collisions were reduced by 49% when using the vibrotactile armbands. Moreover, most subjects expressed a preference for receiving haptic feedback and found the armbands comfortable to wear and use.

Transparent and Soft Haptic Actuator for Interaction With Flexible/Deformable Devices

This study presents a transparent and soft haptic actuator based on an electroactive polymer designed to create abundant haptic sensations in flexible/deformable next-generation devices and to convey them to users. The haptic sensations are created in the form of vibrations and vary depending on the amplitude and frequency of the vibrations. The haptic actuator consists of a transparent and soft dielectric layer and two transparent and soft ionic conductive layers. The dielectric layer is sandwiched between the two ionic conductive layers, and is compressed in the thickness direction when an electric field is applied to the two ionic conductive layers. When the applied electric field is removed, the proposed haptic actuators are rapidly restored to their initial configuration. Owing to this effect, the actuator can easily create vibrations that are sufficiently strong for human perception. In this study, three different dielectric elastomers (silicone rubber, poly urethane, and acrylic polymer) are used for the dielectric layer. Experiments are conducted to investigate the haptic performance of the proposed soft vibrotactile actuators using an accelerometer. In the case of the silicone rubber-based actuator, the measured acceleration at the resonant frequency (80 Hz) is 1.408 g (g = 9.8m/s 2 ) and the response time is approximately 2.8 ms. Furthermore, the perceived intensity of the stimuli generated by the proposed actuator is verified by perceptual experiments. The results indicate that the proposed actuator can selectively stimulate human mechanoreceptors with sufficient perceptual strength.

Evaluation of Optimal Vibrotactile Feedback for Force-Controlled Upper Limb Myoelectric Prostheses.

The main goal of this study is to evaluate how to optimally select the best vibrotactile pattern to be used in a closed loop control of upper limb myoelectric prostheses as a feedback of the exerted force. To that end, we assessed both the selection of actuation patterns and the effects of the selection of frequency and amplitude parameters to discriminate between different feedback levels. A single vibrotactile actuator has been used to deliver the vibrations to subjects participating in the experiments. The results show no difference between pattern shapes in terms of feedback perception. Similarly, changes in amplitude level do not reflect significant improvement compared to changes in frequency. However, decreasing the number of feedback levels increases the accuracy of feedback perception and subject-specific variations are high for particular participants, showing that a fine-tuning of the parameters is necessary in a real-time application to upper limb prosthetics. In future works, the effects of training, location, and number of actuators will be assessed. This optimized selection will be tested in a real-time proportional myocontrol of a prosthetic hand.

Design and fabrication of wearable male-type radio button-shaped vibrotactile actuators

Vibrotactile actuators have been studied in a variety of wearables that require actuation feedback because of their accurate and rapid feedback. To provide robust and reliable feedback to users, wearable vibration actuators must be seamlessly integrated into smart clothing to deliver vibrotactile stimulation of the appropriate intensity. In order to solve the vibration attenuation problem due to clothing fabric, and seamlessly integrate the actuator, wearable male-type radio button-shaped vibrotactile actuators (WMVAs) were designed and fabricated. The WMVAs were designed with a structure in which a linear resonant actuator was housed in a stud, and vibration was passed through the fabric and transferred to the skin through the cap. Three WMVAs were fabricated, one with a cap of standard size and thickness, the second with a thicker cap than the standard, and the third with a wider cap than the standard. In order to investigate the vibration transmission performance of the WMVA, vibration perception experiments were performed on various body parts of the subjects. As a result, the vibration perception of the WMVA was statistically significant in all tested body parts. Using the WMVA, the mean value of vibration perception was 2.743, while that without a cap and stud was 2.062. The mean value of the vibration perception of the actuator with a cap 2.78 times thicker is 2.736, compared with the standard actuator value of 2.512. The average value of vibration perception of an actuator with a 2.78 times larger cap than the standard size is 2.743.