A tuned mass amplifier for enhanced haptic feedback
Sai Sharan Injeti, Ali Israr, Tianshu Liu, Yi?it Mengüç, Daniele Piazza, Dongsuk D. Shin
AA tuned mass amplifier for enhanced haptic feedback
Sai Sharan Injeti ∗1,2 , Ali Israr , Tianshu Liu , Yiğit Mengüç , Daniele Piazza , andDongsuk D. Shin †11 Facebook Reality Labs Research, Redmond, WA, USA Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA, USA
Abstract
Vibro-tactile feedback is, by far the most common haptic interface in wearable ortouchable devices. This feedback can be amplified by controlling the wave propaga-tion characteristics in devices, by utilizing phenomena such as structural resonance.However, much of the work in vibro-tactile haptics has focused on amplifying localdisplacements in a structure by increasing local compliance. In this paper, we showthat engineering the resonance mode shape of a structure with embedded localizedmass amplifies the displacements without compromising on the stiffness or resonancefrequency. The resulting structure, i.e., a tuned mass amplifier , produces higher tac-tile forces (7.7 times) compared to its counterpart without a mass, while maintaininga low frequency. We optimize the proposed design using a combination of a neuralnetwork and sensitivity analysis, and validate the results with experiments on 3-Dprinted structures. We also study the performance of the device on contact with asoft material, to evaluate the interaction with skin. Potential avenues for future workare also presented, including small form factor wearable haptic devices and remotehaptics.Keywords:
Vibration, Haptics, Optimal design, Deep learning, 3-D printing
Interaction between humans and computational devices mainly relies on visual or auditory feed-back. With most interactive devices, the user’s vision are overloaded, which makes utilizinghaptic feedback an important sensory interface. For example, haptic feedback can be used fornavigation when the user is using visual feedback to avoid obstacles [1, 2]. It is also a usefulinterface in applications such as robot assisted minimally invasive surgery [3] and prosthesesfor rehabilitation [4]. Haptic feedback further enables sensing fine textures and shape changesthat may not be visually perceivable [5]. The first type of haptic interface includes touch-basedfeedback, that relies on the high density of mechanoreceptors on fingertips [5, 6]. It is morechallenging to design for the second kind of haptic interface, wearables, as the skin around sucha device tends to have fewer receptors [7].The three main categories of wearable haptic displays are force feedback, electro-tactile feed-back and vibro-tactile feedback devices [8]. A force feedback device typically uses an exoskeleton,which is capable of exerting large forces, but tends to be bulky and often requires user-specific ∗ [email protected] † [email protected] a r X i v : . [ c ond - m a t . m t r l - s c i ] J a n igure 1: (a) A tuned mass amplifier consisting of a stiff primary structure (a cantilever), asecondary compliant structure (a circular region with spiral cut) with an embedded heavy sphericalmass. (b)
A mode of flexural resonance showing the compliant region resonating in-phase withthe rest of the cantilever. (c)
Close up of the compliant region containing the variable designparameters, indicated in red. calibration [9]. Electro-tactile feedback devices rely on surface electrodes that directly stimulatethe muscles themselves to contract, which sometimes causes pain to users and hence requiresa challenging design and calibration to avoid lesions [10]. Vibro-tactile feedback has shownto be an effective way to produce tactile sensations by using low frequency mechanical forces.Carefully arranging vibration actuators within a device allows for a range of tactile spatial res-olutions [11–14]. A fine spatial resolution requires localized vibration on the structure/ deviceto stimulate mechanoreceptors at specific regions.The first way to create local vibrations is by utilizing time-reversal for elastodynamic waves[11, 12]. Such techniques often result in the need for multiple actuators, which can result in abulky device. A second way to induce local vibrations is by utilizing local resonance, where asingle actuator can be vibrated at different frequencies to locally excite compliant regions in thedevice [13, 14]. So far, this mechanism has proven to be effective in amplifying the vibrationdisplacements from thin and weak actuators at locally distinct regions in a structure, leadingto the possibility of low form factor wearable devices. However, achieving large amplificationsin displacements together with high haptic forces at low frequency has remained challenging.Typical methods to amplify local displacements at low frequency rely on softening the structurelocally, and as a result compromise on local stiffness. This is the focus of our work. In this paperwe present a way to amplify local displacements in a structure at low resonance frequencies forhaptics, while still maintaining high structural stiffness, hence demonstrating our tuned massamplifier (TMA).We demonstrate the concept where a structure can be resonated such that a primary andsecondary structure move in-phase to amplify displacements and stiffness, and a local masscan be used to ensure the phenomenon happens at low frequency for haptics. As an exampleof this concept, our proposed device shown in Fig. 1(a) consists of a primary structure (acantilever), with a secondary compliant structure made from an Archimedian spiral cut [13],with an embedded mass that is several times more dense compared to the material used tomake the remaining structure. We tune the parameters describing this geometry such that theresonance mode shape consists of the cantilever and compliant spiral displacing in-phase (Fig.1(b)), hence amplifying both local out-of-plane displacement and stiffness. The embedded massensures that the resonance frequency remains low. This combination of high static stiffnessand large resonance displacements leads to high tactile forces. We design the structure toachieve a desired resonance mode shape, frequency and static stiffness, by utilizing a neuralnetwork to learn the required outputs from finite element analysis and then solve an optimal2esign problem using a sensitivity analysis. We perform dynamic and static experiments on3-D printed structures and validate our analysis with measurements of the resonance frequency,displacements, and local static stiffness. We quantify the force feedback and the effect of skinwith experiments where the device is in contact with a soft material. Note that the design of thebase where the actuator is mounted (Fig. 1(b)) is guided by the actuator we use in experiments,as detailed later in the paper.
We model the dynamic and static response of the structure using finite element analysis inCOMSOL. For a non-dissipative linear elastic medium, let ˜ K (cid:0) ˜ χ (cid:1) and ˜ M (cid:0) ˜ χ (cid:1) represent theassembled stiffness and mass matrices, where ˜ χ is the vector of parameters that describes thetopology of the structure. For a harmonic excitation at the base as indicated in Fig. 1(b), theeigenvalue problem (cid:16) ˜ K (cid:0) ˜ χ (cid:1) − (cid:0) ω (˜ χ ) (cid:1) ˜ M (cid:0) ˜ χ (cid:1)(cid:17) ˜ U (cid:0) ˜ χ (cid:1) = 0 , (1)indicates modes of resonance of the structure [15]. Each mode shape ˜ U (cid:0) ˜ χ (cid:1) represents thenormalized displacements at the nodes of the finite elements in the structure at a resonancefrequency ˜ ω (cid:0) ˜ χ (cid:1) . For a static problem where the base of the structure is fixed and a point loadof magnitude f is applied at the center of the spiral ˜ K (cid:0) ˜ χ (cid:1) ˜ V (cid:0) ˜ χ (cid:1) = ˜ F, (2)where ˜ F (the force vector) contains only one non-zero element of magnitude f corresponding tothe node at the center of the spiral. ˜ V (cid:0) ˜ χ (cid:1) represents the small deformation static displacement inthe structure for the applied load. In vectors ˜ U and ˜ V , let the i th and j th elements represent thedisplacement of the node at the center of the spiral and at the upper-right tip of the cantilever,respectively (Fig. 1(a)). We define three key mechanical properties that can influence haptic feedback. The first propertyis the frequency of excitation (cid:0) ω (˜ χ ) (cid:1) at the base that produces a desired (coupled) mode ofresonance as illustrated in Fig. 1(b). Second, we introduce a property for a measure of modelocalization (cid:0) L (˜ χ ) (cid:1) , which we define as the ratio of displacement at the center of the spiral tothe tip of the cantilever for the coupled mode shape (i.e. L = U i /U j ). Third, we aim to designfor the local stiffness of the structure at small deformations (cid:0) S (˜ χ ) (cid:1) subject to a unit point loadat the center of the spiral ( S = 1 /V j ). A locally stiffer structure would result in higher tactileforces for a given local displacement. We pick the base material to be Nylon 12, which we useto 3-D print these structures. The mass at the center of the spiral is made of tungsten carbide,which is more than 16 times as dense as Nylon 12. The linear elastic material properties for thematerials used are listed in table 1 [16, 17]. We measure the density from the ratio of mass tovolume of a 1 cm side cube. We determine its Poisson’s ratio from analytically verifying the firstresonance frequency of a solid cantilever beam made of Nylon 12, with length 65 mm, breadth15 mm and height 1.5 mm, with finite elements. We obtain the Young’s modulus of elasticityand Poisson’s ratio from the bulk and shear moduli of Tungsten Carbide reported in [17], andits density from the ratio of mass to volume of a spherical ball with a diameter of 3 mm.The optimal design of the structure to yield a desired set of mechanical properties ( ω , S and L ) can be time consuming if we purely rely on the finite element simulation to estimate themat each step of any optimization algorithm. The time taken increases drastically, when thereis a need to design for multiple devices each with a distinct set of mechanical properties. Forexample, if the number of design iterations in one optimization algorithm to design for a set of3able 1: Linear elastic material properties Material Young’s modulus ( E ) Poisson’s ratio ( ν ) Density ( ρ )Nylon 12 1.2 GPa 0.34 983 kg/m Tungsten Carbide 702 GPa 0.20 16,000 kg/m mechanical properties is ∼ ∼ ˜ χ = [ n, t, d, a, r ] T , that do not change the form factor of the device inFig. 1. These are the number of turns in the spiral cut ( n ), thickness of the spiral cut ( t ), depthof the spiral ( d ), smallest outer radius of the spiral ( a ) and the radius of the center mass ( r ),respectively. Note that we fix the length, breadth and height of the cantilever to fix the formfactor of the device. The fixed dimensions and variable design parameters are indicated in blueand red in Fig. 1(a) and (c), respectively. We pick bounds for each variable design parameteras indicated in table 2 and generate 21,000 geometries that are uniformly distributed withinthese bounds. We ensure that each generated point represents a structure where the minimumfeature size is larger than δ = 0 . mm, to aid meshing. We train a deep neural network withthree hidden layers (of 15 nodes, 20 nodes and 15 nodes, respectively) that takes the × designvector as the input and learns the mechanical properties calculated using finite elements. Wetrain 3 such separate networks to estimate each property, ω , S and L . We use 17,000 data pointsfor training, and 2,000 data points each for testing and validation. Each data point represents aninput vector containing the design variables and output containing the frequency of resonance,stiffness or localization. We use MATLAB’s machine learning toolbox, where we minimize themean squared error, using a gradient descent algorithm. The activation function used is therectified linear unit (ReLU). A schematic of the network along with its performance againstFEA is indicated in Fig. 2(a). We formulate the following optimal design problem to calculate the bounds on frequency andstiffness of the device, min ˜ χ γ ω (˜ χ ) + γ S (˜ χ ) s.t. ˜ A ˜ χ ≤ ˜ b,f (˜ χ ) ≥ δ,f (˜ χ ) ≥ δ. (3)Solving problem (3) for several pairs of real numbers γ and γ such that | γ | + | γ | = 1 , and takingthe intersection of all half planes γ ω (˜ χ ) + γ S (˜ χ ) ≥ O min gives us the outer envelope of possiblevalues of ω and S . It is an outer bounds since all attainable values lie within this intersection.Similarly, replacing S with L in problem (3) gives us bounds on frequency versus localization.The linear inequality constraint ˜ A ˜ χ ≤ ˜ b is formulated to satisfy the bounds of parameters intable 2. The constraint f (˜ χ ) ≥ δ limits the minimum solid thickness of the spiral to 0.1 mm.This function can be approximated as f (˜ χ ) = ( a (cid:48) − a ) − ([ n ] + 1) t [ n ] , where a (cid:48) = 5 . mm is thefixed largest outer radius of the spiral and [ n ] is the greatest integer less than or equal to n . Note4igure 2: (a) Architecture of the deep neural network to learn the mechanical properties given thedesign parameters. The table indicates the performance of the network. (b)
Bounds on frequencyand stiffness for design parameters within the range in the table 2. (c)
Structure 1 (TMA withcoupled resonance) and structure 2 (without an embedded mass and localized resonance at thesame frequency) are tested in experiments, and their properties are indicated in (b).
Bounds Minimum Maximum n t d a r f is a conservative estimate of the minimum feature size. The constraint f (˜ χ ) ≥ δ limitsthe maximum radius of the tungsten carbide ball. We have that f (˜ χ ) = a − t − r . We solveproblem (3) using gradient descent optimization. The sensitivities with respect to each designparameter are numerically calculated by perturbing the design variable along each orthogonaldirection and measuring the change in the objective. To avoid local minima, we perform eachoptimization starting from several feasible initial guesses and finalize the best value. The resultsare indicated in Fig. 2(b). The blue shaded area enclosed by the half planes represents theregion within which all attainable values of resonance frequency ω (of the first mode) and localstiffness S lie. A similar approach to calculating the bounds between such highly non-linearproperties can be found in [18]. To illustrate the concept of a TMA, we pick a low frequency of ω =65 Hz and engineer twostructures, one with a coupled mode of resonance and a local mass, and the other without anembedded mass and localized mode of resonance at the spiral. The former yields our tuned-massamplifier (with a design vector ˜ χ ) and possesses high stiffness. The latter yields a representativestructure for the state-of-the-art method that solely maximizes localization and compliance toamplify haptic feedback [13] (with a design vector ˜ χ ). We pick a frequency of 65 Hz as thehuman perception drops over 100 Hz [19]. We formulate the following optimal design problemto solve for the topologies of the two structures min ˜ χ , ˜ χ (cid:16) ω (˜ χ ) − Hz (cid:17) + (cid:16) ω (˜ χ ) − Hz (cid:17) + sin (cid:18) π ˜ χ . ˜ v . mm (cid:19) + sin (cid:18) π ˜ χ . ˜ v . mm (cid:19) + Φ p (cid:16) . − L (˜ χ ) (cid:17) + Φ p (cid:16) L (˜ χ ) − (cid:17) + Φ p (cid:32) − S (˜ χ ) S (˜ χ ) (cid:33) s.t. ˜ A ˜ χ ≤ ˜ b, ˜ A ˜ χ ≤ ˜ b,f (˜ χ ) ≥ δ, f (˜ χ ) ≥ δ,f (˜ χ ) ≥ δ, f (˜ χ ) ≥ δ, ˜ v = (0 0 0 0 1) T . (4)The first two terms in the objective of problem (4) ensure that the resonance frequencies of thetwo optimal designs are close to the desired value. The third and fourth terms ensure that theradius ( r ) of the Tungsten Carbide ball is a multiple of 0.25 mm, due to the availability of preci-sion ball bearings in such denominations. The power of the trigonometric functions are chosen toavoid terms with much smaller sensitivities than others at a local minimum. We define a penaltyfunction Φ p ( x ) = 1 p ( e px − , with p being large (we take p = 50 for our calculations) [20]. Notice6able 3: Properties of the optimal designs from analysis Property Neural Network FEA ω (˜ χ ∗ ) L (˜ χ ∗ ) S (˜ χ ∗ ) ω (˜ χ ∗ ) L (˜ χ ∗ ) S (˜ χ ∗ ) Φ p ( x ) is non-positive and low in magnitude when x ≤ , and is positive and large otherwise.The fifth and sixth terms in the objective ensure that the optimal design for the first structure(indexed by 1) produces a localization between 2.5 and 3, ensuring a coupled mode of resonance.The last term in the objective drives the stiffness of the first structure to be much larger than thesecond, ultimately forcing a localized mode of resonance in the second structure (indexed by 2).This is because lower stiffness occurs when the spiral region is much softer than the cantilever,which also results in a localized mode of resonance. When a point load at the center of thespiral displaces both the spiral and cantilever, this results in higher stiffness as well as a coupledmode of resonance. The optimal values, ˜ χ ∗ = [2 . , . mm , . mm , . mm , . mm ] T and ˜ χ ∗ = [6 . , . mm , . mm , . mm , . mm ] T . Table 3 compares the result predicted forthese optimal designs using the neural network, with FEA. The values of the properties arein agreement, and we clearly notice structure 1 displays a much higher stiffness compared tostructure 2 at the same resonance frequency. We 3-D print the structures using fused depositionmodeling (FDM) with Nylon 12 (Fig. 2(c)). The tungsten carbide ball is press-fit into a cavity instructure 1. The properties of these structures and their mode shapes of resonance are indicatedin Fig.2(b) and (c), respectively. In order to validate the mechanical properties estimated from the analysis, we first measure thedesired resonance frequencies of the two optimal designs. We use a piezoelectric stack actuator(model P-235) as the vibration source, that we attach to our sample at its base using an M-8screw (Fig. 3(a)). Due to the extremely high stiffness of the actuator, the boundary conditionsat the base of our structures resemble our analysis, i.e. displacement boundary conditions.We measure the displacement response at the center of the spiral in each case using a laservibrometer. We perform the experiments on three samples for each structure, to account forvariability in the 3-D printing process. We provide sinusoidal input vibration with a frequencysweep from 40 Hz to 90 Hz, to identify the first resonance frequency in each structure. Toidentify the resonance frequency, we take the Fourier transform of the displacement versus timedata as measured by the vibrometer, and locate the frequency corresponding to the peak indisplacement. The results are indicated in table 4. Notice that the mean values agree very wellwith our analysis from table 3.At their respective measured resonance frequencies, we excite each structure for 15 secondsand measure the displacement versus time response at the center of the spiral. The Fouriertransform of the data is indicated in Fig. 3(b) for representative samples in each topology. The7igure 3: (a)
Setup showing the TMA attached to a piezoelectric stack actuator for vibrationmeasurements. (b)
Displacement response in the two structures excited at their respective reso-nance frequencies. (c)
Setup showing the TMA loaded on an Instron machine. The inset showsthe sharp indenter used. (d)
Force vs displacement response of the two structures for smalldeformation. (e)
Comparison between the properties measured in experiments with the analysis.
Table 4: Properties of the optimal designs from experiments
Property Structure 1 (TMA) Structure 2 (no mass)
Resonance frequency 68.203 ± ± ± ± ± ± ± × − m. Notice that the displacementamplification at the spiral is much larger for the tuned mass amplifier (structure 1), whencompared to structure 2 that does not feature a local mass. This can be attributed to thecoupled resonance that is engineered in structure 1. Structure 2 amplifies displacements solelydue to the high compliance of the spiral. The displacement amplifications at resonance in eachstructure is summarized in table 4.In order to measure the local stiffness of a structure at the center of the spiral, we use thesetup shown in Fig. 3(c). The piezoelectric stack actuator is fixed to a table (stationary) andthe sample is screwed into the actuator at its base. We load the center of the spiral on an Instronmachine, with a sharp indenter that has a tip diameter of 1 mm. We displace the indenter by 1.5mm at a low strain rate of 0.01 mm/s to measure the quasi-static small deformation response.The measured force vs displacement curve for representative samples in each case is shown inFig. 3(d). Notice the linear response of the structure for small deformation, indicating thata linear elastic material model is sufficient to model small deformation vibrations. The localstiffness is measured as the slope of the curve near the origin, and the results are tabulated intable 4. As expected, the tuned mass amplifier displays a much higher stiffness than the otherstructure.Fig. 3(e) compares the experimentally measured stiffness and resonance frequency of thethree samples with either topology, to the values estimated from the neural network. We seegreat agreement between our analysis and experiments and clearly demonstrate the engineeredphenomenon: a large local stiffness and displacement amplification without any change in reso-nance frequency. The device would ultimately be used in contact with skin, and it is important to understandthe vibration response with a contact boundary condition to evaluate its haptic performance.The increase in stiffness and displacement would translate into a higher tactile force when thedevice comes in contact with skin, as felt by the authors. To validate and quantify this, wemeasure the displacements and tactile stresses by repeating the vibration experiments, with thedevice now in contact with a soft material block. We use a platinum-catalyzed silicone block(Ecoflex TM (a) Vibration test setup showing structures 1 and 2 in contact with the soft block. (b)
Displacement response in the structures (structure 1 without and with contact, and structure 2with contact) excited at their respective resonance frequencies. (c)
Close up of (b) showing thecomparison between structures 1 and 2 with contact. (d)
Setup showing the soft block loaded onan Instron machine. (e)
Force vs displacement response of the soft material for small deforma-tion.
This explains why we clearly feel the tuned mass vibrate with our fingertip whereas we hardlyfeel a vibration with the other structure.In order to quantify the force and pressure feedback from each structure, we first measurethe stiffness of soft block on an Instron machine as shown in Fig. 4(d). Here, we utilize alarger indenter that has a circular cross-section with a diameter of 6.75 mm. We choose this toapproximate the contact area of a fingertip with each structure as well as the contact area ofeach structure with the soft block at resonance (estimated from the mode shapes in Fig. 2(c)) .The force versus displacement response from the small deformation quasi-static compression testat 0.01 mm/s is shown in Fig. 4(e). Its small deformation stiffness of 395.20 N/m is measuredas the slope of the curve near the origin. We can approximate the force from each structure incontact with the soft block as the product of peak displacements in Fig. 4(c) with the measuredstiffness of the block. This results in a peak force of 0.0915 N from the TMA (structure 1) anda force of 0.0115 N from the structure without a local mass (structure 2). This translates to apressure of 2.558 KPa and 0.321 KPa in the structures with and without the mass, respectively.
The TMA clearly displays a much higher stiffness when compared to the structure without atuned mass, that resonates at the same frequency, as demonstrated by our analysis and experi-ments. This can be attributed to the spiral having a higher thickness (and stiffness) as well asthe local stiffness contribution from both the spiral and cantilever in the TMA. The structurewithout the mass amplifies displacements purely by maximizing localization and compliance.10mbedding a mass in the structure does not alter the stiffness as the mass is localized, butdrastically drops the resonance frequency, hence allowing us to design high stiffness structuresthat resonate at low frequency. Further, we notice in experiments that the TMA resonates witha much higher displacement amplitude than its no mass counterpart. This can be attributed tothe coupled resonance we design where the cantilever and spiral resonate in-phase at these lowfrequencies in the TMA.The properties of the structures that are designed and tested in this paper lie within thebounds estimated in Fig. 2(b). Similarly, one could design structures with or close to other fre-quencies and stiffness within these bounds by appropriately modifying the objective in problem(4). Note that all attainable properties within the bounds on the design parameters in table 2 liewithin the blue shaded region in Fig. 2(b), but not all values in the region may be attained. Thisis because the bounds represent a convex hull of the possible values. However, all values wherethe tangents meet the shaded region in Fig. 2(b) are attainable, and such extremal propertiesare often of interest.We notice that the resonance frequency of the structures slightly increase when the spiralend of the cantilever is in contact with the soft block. This can be attributed to the stiffnessincrease due to the cantilever and soft block assembly, compared to just the cantilever in air.This increase would need to be taken into account when designing such amplification mechanismsagainst skin. Further, on contact with the soft block, we notice that the displacements dropwhen compared to a case without contact. We observe this due to the resistance to deformationprovided by the silicone block. However, the amplitude at resonance of the TMA in contactwith the block is 7.7 times the value when compared to structure 2, and this can be attributedto the higher stiffness of the TMA. Finally, the forces and pressures from the structure can beamplified by increasing the local stiffness of the TMA. This can be done in a couple of ways.We can increase the thickness of the spiral and place a heavier mass, or we can print the TMAwith a stiffer base material and use a heavier mass to maintain the same resonance frequency.
We present a tuned mass amplifier (TMA), that is capable of enhancing haptic feedback byamplifying local displacements together with local stiffness and low frequencies suitable forhaptics. We amplify the local displacements by utilizing coupled resonance, where a primarystructure (cantilever) resonates in-phase with a secondary structure (compliant spiral cantileverpatch). The embedded mass helps drop the frequency of resonance to low values, while stillmaintaining high structural rigidity. We establish an optimal design framework by first learningthe finite element simulations given the design parameters using a deep neural network. We thencalculate the bounds on attainable mechanical properties using a sensitivity analysis. Withinthese bounds on stiffness and resonance frequency, we design the parameters describing thegeometry to achieve prescribed mechanical properties. We compare two structures- structure1 is a TMA that features a tuned mass and resonates at 65 Hz, and structure 2 does nothave an embedded mass and resonates at the same frequency. We validate the high stiffnessand displacement amplification seen in the TMA through experiments on 3-D printed structuresmade of Nylon-12 with an embedded Tungsten Carbide mass. We also conduct experiments withthe structures in contact with a soft silicone block to quantify the effect of touch in haptics. Thestructures can be made of arbitrary geometries such as a curved cantilever for remote haptics,where the site of vibration actuation is further away from the location of haptic feedback. Also,the spiral patch can be engineered as a network of truss-like connections or a soft continuousmaterial embedding a mass to explore higher amplifications. The proposed designs can be madearbitrarily small to realize such phenomena in wearable haptics.11 ata availability
The data that support the findings of this study can be made available from the correspondingauthor upon reasonable request.
Acknowledgements
We thank Hamzeh Musleh Fahmawi and Joseph Aase for help with conduting the experiments.We also thank Dr. Maurizio Chiaramonte and Dr. Kevin Carlberg for useful discussions.
References [1] Sevgi Ertan, Clare Lee, Abigail Willets, Hong Tan, and Alex Pentland. A wearable hap-tic navigation guidance system. In
Digest of Papers. Second International Symposium onWearable Computers (Cat. No. 98EX215) , pages 164–165. IEEE, 1998.[2] Robert W Lindeman, Yasuyuki Yanagida, Haruo Noma, and Kenichi Hosaka. Wearablevibrotactile systems for virtual contact and information display.
Virtual Reality , 9(2-3):203–213, 2006.[3] Allison M Okamura. Haptic feedback in robot-assisted minimally invasive surgery.
Currentopinion in urology , 19(1):102, 2009.[4] Aaron Plauché, Dario Villarreal, and Robert D Gregg. A haptic feedback system for phase-based sensory restoration in above-knee prosthetic leg users.
IEEE transactions on haptics ,9(3):421–426, 2016.[5] Roland S Johansson and J Randall Flanagan. Coding and use of tactile signals from thefingertips in object manipulation tasks.
Nature Reviews Neuroscience , 10(5):345–359, 2009.[6] Alex Chortos, Jia Liu, and Zhenan Bao. Pursuing prosthetic electronic skin.
Nature mate-rials , 15(9):937–950, 2016.[7] Anusha Withana, Daniel Groeger, and Jürgen Steimle. Tacttoo: A thin and feel-throughtattoo for on-skin tactile output. In
Proceedings of the 31st Annual ACM Symposium onUser Interface Software and Technology , pages 365–378, 2018.[8] Yuichi Kurita. Wearable haptics. In
Wearable Sensors , pages 45–63. Elsevier, 2014.[9] Guilin Yang, Hui Leong Ho, Weihai Chen, Wei Lin, Song Huat Yeo, and Mustafa ShabbirKurbanhusen. A haptic device wearable on a human arm. In
IEEE Conference on Robotics,Automation and Mechatronics, 2004. , volume 1, pages 243–247. IEEE, 2004.[10] Xinge Yu, Zhaoqian Xie, Yang Yu, Jungyup Lee, Abraham Vazquez-Guardado, HaiwenLuan, Jasper Ruban, Xin Ning, Aadeel Akhtar, Dengfeng Li, et al. Skin-integrated wirelesshaptic interfaces for virtual and augmented reality.
Nature , 575(7783):473–479, 2019.[11] Gregory Reardon, Nikolas Kastor, Yitian Shao, and Yon Visell. Elastowave: Localizedtactile feedback in a soft haptic interface via focused elastic waves. In , pages 7–14. IEEE, 2020.[12] Charles Hudin, Jose Lozada, and Vincent Hayward. Localized tactile feedback on a trans-parent surface through time-reversal wave focusing.
IEEE transactions on haptics , 8(2):188–198, 2015. 1213] Osama R Bilal, Vincenzo Costanza, Ali Israr, Antonio Palermo, Paolo Celli, Frances Lau,and Chiara Daraio. A flexible spiraling-metasurface as a versatile haptic interface.
AdvancedMaterials Technologies , 5(8):2000181, 2020.[14] Sabrina Paneels, Margarita Anastassova, Steven Strachan, Sophie Pham Van, Saranya Siva-coumarane, and Christian Bolzmacher. What’s around me? multi-actuator haptic feedbackon the wrist. In , pages 407–412. IEEE, 2013.[15] Thomas JR Hughes.
The finite element method: linear static and dynamic finite elementanalysis . Courier Corporation, 2012.[16] F Knoop, V Schoeppner, FC Knoop, and V Schoeppner. Mechanical and thermal propertiesof fdm parts manufactured with polyamide 12. In
Proceedings of the 26th Annual Inter-national Solid Freeform Fabrication Symposium—An Additive Manufacturing Conference,Austin, TX, USA , pages 10–12, 2015.[17] Zhijun Lin, Lin Wang, Jianzhong Zhang, Ho-kwang Mao, and Yusheng Zhao. Nanocrys-talline tungsten carbide: As incompressible as diamond.
Applied Physics Letters , 95(21):211906, 2009.[18] Sai Sharan Injeti, Chiara Daraio, and Kaushik Bhattacharya. Metamaterials with engi-neered failure load and stiffness.
Proceedings of the National Academy of Sciences , 116(48):23960–23965, 2019.[19] Ali Israr, Seungmoon Choi, and Hong Z Tan. Mechanical impedance of the hand holdinga spherical tool at threshold and suprathreshold stimulation levels. In
Second Joint Eu-roHaptics Conference and Symposium on Haptic Interfaces for Virtual Environment andTeleoperator Systems (WHC’07) , pages 56–60. IEEE, 2007.[20] Anurag Jayswal and Sarita Choudhury. Convergence of exponential penalty functionmethod for multiobjective fractional programming problems.
Ain Shams Engineering Jour-nal , 5(4):1371–1376, 2014.[21] C Pailler-Mattei, S Bec, and H Zahouani. In vivo measurements of the elastic mechanicalproperties of human skin by indentation tests.