Pith. sign in

REVIEW 4 major objections 6 minor 54 references

Continuity Reinforcement Skeleton for Pixel-based Haptic Display

T0 review · 4 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A buckled-beam 'continuity reinforcement skeleton' lets pixel-based haptic displays show smooth moving contact between actuators, without adding pixels.

desk verdict A genuinely new buckling-based interpolation skeleton for haptic pixels, with a sound no-collapse design rule; the perceptual proof is still thin. read the letter →

arxiv 2411.15445 v1 pith:LCDH7U62 submitted 2024-11-23 cs.HC

Xinyuan Wang , Zhiqiang Meng , Chang Qing Chen This is my paper · ORCID
classification cs.HC
keywords continuityreinforcementskeletonhapticdisplayvirtualrealityphysicallydriveninterpolationbeambucklingpositiondistortionshapedigitalimagecorrelation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper introduces a continuity reinforcement skeleton (CRS) for pixel-based haptic displays: thin steel beams span the actuator array, are tied to the pixels, and are compressed at their ends, so the beam's bending and buckling create a smooth surface through the pixels. The central claim is that this physically driven interpolation lets a haptic display show continuous moving contact, such as stroking, gliding, and ripples, between pixel gaps without increasing pixel density. The authors quantify continuity with two distortion metrics, position distortion and shape distortion, and report that the CRS lowers both relative to pixel-only and straight-line-connected displays, with peak position distortion about an order of magnitude lower. This matters because pixel-based haptics face a trade-off between pixel pitch and actuation travel in thin wearables, and simply adding pixels is not a viable fix. If the claim holds, a simple passive beam layer can upgrade ordinary haptic arrays into continuous surfaces and improve VR touch experiences.

What carries the argument

The central object is the continuity reinforcement skeleton (CRS): a layer of thin steel beams spanning the pixel array, tied to each pixel with fishing line, and axially compressed by boundary servos. Pixels prescribe off-plane displacements while the beam's bending and buckling equilibrium fills in the curve between them, which is physically driven interpolation rather than software interpolation. The mechanical model treats the skin surrogate as an elastic foundation with stiffness $\beta$, expands the beam deflection as a trigonometric series, and yields the no-collapse condition $\Delta = 16\pi^4 E I / (27 \beta d^4) > 1$; the phase diagram built from $\Delta$ predicts when the beam collapses between pixels, and experimental markers match it. This machinery converts discrete actuator points into a continuous surface and provides a design rule for beam thickness, pixel spacing, and skin stiffness.

What would settle it

Measure the contact force distribution on a real fingertip while the CRS displays a moving single peak; if the pressure field shows two local maxima at the actuator positions while the Digital Image Correlation displacement field of the cover is smooth, the continuity gain is a property of the cover rather than of the stimulus delivered to the skin.

Watch

Extended reading notes

Core claim

On its own terms, the paper's discovery is that a buckled beam is an analog interpolator for haptic shape: when discrete pixels pull a beam to specified off-plane heights and boundary servos compress its ends, the beam's equilibrium shape is the smooth curve through those points, so the displayed peak can sit at any location between pixels rather than only on actuators. The paper supports this with a beam-on-elastic-foundation model in which the skin surrogate has local stiffness, yielding a no-collapse condition, and with Digital Image Correlation measurements on spandex-covered and silicone-covered devices showing continuous displacement fields. The reported numbers are: position distortion and shape distortion below both pixel-only and linear-connection baselines in one dimension, with position distortion about an order of magnitude lower; roughly half the distortion in two-dimensional square and hexagonal arrays; and a rise in VR digit recognition from 50.3% to 67.8%. The same skeleton is demonstrated in one-dimensional, two-dimensional, and curved prototypes.

Load-bearing premise

The whole continuity argument rests on treating the measured deformation of the spandex or silicone cover as the haptic signal a finger perceives; if that smooth cover deformation does not translate into the contact forces and skin strains a real fingertip experiences, the reported continuity gains may not be felt.

Editorial extensions

If this is right

  • A one-dimensional CRS with five pixels and a 30 mm pitch can hold a 5 mm ball at arbitrary positions between pixels, which pixel-only devices cannot do.
  • For one-dimensional sine-wave displays, both position distortion and shape distortion are lower than for pixel-only and straight-line (origami-like) connections, with position distortion about an order of magnitude lower.
  • For two-dimensional square and hexagonal lattices, the CRS roughly halves shape and position distortion relative to the same lattice without the skeleton.
  • In a VR writing task, adding the CRS raises digit recognition accuracy from 50.3% to 67.8% compared with pixel-only haptics.
  • The design rule $\Delta = 16\pi^4 E I / (27 \beta d^4) > 1$ separates no-collapse from collapsed regimes and is preserved under proportional scaling, giving a practical guide for beam thickness, pixel spacing, and skin stiffness.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A direct next experiment would vary the displayed peak's speed and acceleration relative to the reported 75 ms device latency and 160 ms system latency, mapping the range of stroking speeds over which the interpolation remains perceptually continuous; the paper reports the latencies but does not test motion perception.
  • The distortion framework could be extended to sharp-edged virtual objects: since the CRS surface is a smooth buckled beam, a blade-like contact will be rounded to a radius set by beam stiffness and pixel spacing, and the useful quantity would be the minimum displayable edge radius as a function of $d/l$.
  • The scale invariance of the no-collapse condition suggests the same skeleton could be built at millimeter scales with MEMS or shape-memory actuators, where the pixel-pitch-versus-travel trade-off is hardest; the paper's prototypes all use centimeter-scale servos.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper introduces a Continuity Reinforcement Skeleton (CRS) for pixel-based haptic displays: thin steel beams are attached to discrete actuating pixels and compressed at the boundaries, so that buckled beam shapes provide a smooth, continuous off-plane displacement between pixels. The authors define position and shape distortion metrics (PD, SD), derive a no-collapse condition for a beam on a Winkler elastic foundation (Eq. 4), and experimentally characterize 1D, 2D, and curved CRS devices using digital image correlation (DIC) on silicone and spandex surfaces. They also integrate a 2D CRS with a VR system and report a digit-identification experiment in which accuracy improves from 50.3% (pixel-only) to 67.8% (with CRS). The central claim is that the CRS physically interpolates between actuators, enabling continuous moving contact without increasing pixel density.

Significance. If the claims hold, the CRS offers a mechanically simple, scalable solution to a long-standing limitation of pixel-based shape displays: the loss of haptic information between pixels. The work combines a derived, parameter-free design condition (no-collapse) with independent experimental validation of the phase boundary, and it demonstrates working 1D, 2D, and curved prototypes. The DIC-based quantification of surface continuity is a useful contribution, and the paper is careful to report the mechanical model with material parameters measured independently rather than fitted to the distortion results. However, the central claim is about haptic information, and the evidence for perceptual benefit is much weaker than the geometric evidence: the only user study is a single recognition experiment reported without statistical detail, and the surface used for DIC measurement (spandex/silicone) is not validated as a proxy for fingertip contact.

major comments (4)
  1. [Mechanical model of CRS, Eq. (4)] The no-collapse condition is derived by modelling the skin surrogate (silicone) as a Winkler elastic foundation with a single coefficient β. A real fingertip is not a Winkler foundation: it is nonlinear, viscoelastic, has a finite contact area, and imposes local normal and tangential tractions. Since the continuity enhancement depends on the beam not collapsing under finger pressure, the design condition's validity for real skin is load-bearing. Please either validate the model against a more realistic skin/contact model or human-tissue indentation, or clearly state the range of foundation stiffness in which the no-collapse condition remains valid and discuss the sensitivity of Eq. (4) to β.
  2. [2D CDS device, Figs. 4f and 4g] The experimental distortion values for the CRS in 2D are reported as single points without error bars or repeated trials. The statement that 'the CRS can reduce the shape and position distortions by half' is therefore not statistically supported. At minimum, the authors should report multiple target positions or repeated measurements with error bars and a formal comparison (e.g., paired test) against the pixel-only condition.
  3. [Visual-haptic integrated virtual reality with CRS, Fig. 5b and Supplementary Discussion 9] The digit identification improvement from 50.3% to 67.8% is the only perceptual evidence, but the main text reports no sample size, error bars, or significance test. Moreover, the digits are smaller than the pixel pitch (average height and width are 0.81 and 0.49 pixel pitch), so this experiment tests recognition of sub-pixel-size shapes rather than the perceived continuity of a moving contact between pixels. The central claim that CRS 'displays haptic information between pixel gaps' is therefore not yet validated perceptually. Please add a statistically rigorous user study targeting perceived continuity, or revise the claim to refer to geometric continuity.
  4. [Results, 1D CRS device and Eq. (2)] The DIC-based PD and SD values in Figs. 2d and 4f/4g are measured on a spandex fabric cover or silicone elastomer, with the fabric sewn to the pixels by fishing line. A pressing finger will deform the cover and skin differently, and the fishing-line attachments may create local discontinuities that do not appear in the unloaded DIC measurement. The paper should either demonstrate that the measured surface deformation corresponds to the stimulus delivered to a fingertip (e.g., by measuring contact pressure or using a more skin-like surrogate), or explicitly restrict the continuity claim to the surface geometry rather than the user-perceived haptic experience.
minor comments (6)
  1. [Section heading] The heading '2D CDS device' (Section 2, page 10) appears to be a typo for '2D CRS device'; please correct it.
  2. [Abstract] The phrase 'physical driven interpolation' should read 'physically driven interpolation'.
  3. [Eq. (3) and surrounding text] The trigonometric series expression in Eq. (3) is garbled in the provided text (missing symbols, unclear terms). Please ensure the equation is rendered correctly and define all quantities (e.g., the meaning of the series index n and the form of the buckling mode).
  4. [Eq. (4)] The dimensionless parameter Δ is used in Eq. (4) and in the following paragraph but is not explicitly defined before its first use; define Δ clearly (e.g., as the ratio of the left side to the right side of the inequality).
  5. [Fig. 3d caption] The caption states that triangles and circles mark the experimental results, but it does not specify which marker corresponds to collapse and which to no-collapse; please add that information to the caption.
  6. [Visual-haptic integrated virtual reality with CRS] The statement about the full system latency of 160 ms (Methods) should include a short description of the measurement method in the main text or at least a cross-reference to Supplementary Discussion 11, since latency is an important usability metric.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the CRS buckling/interpolation claim is supported by independent mechanics inputs and empirical DIC measurements, not by a fitted or self-referential derivation.

full rationale

The central derivation is the no-collapse condition, Eq. (4), obtained from the trigonometric-series solution for a beam on a Winkler foundation (Hetenyi 1946) by setting the denominator in Eq. (3) to zero and requiring N_cr^(3) > N_cr^(1). The input parameters E, I, d, and beta are measured independently: SUS301 steel modulus, beam geometry, and uniaxial compression tests of Ecoflex silicone. The predicted collapse/no-collapse boundary is then checked against the experimental phase diagram, so the condition is not fitted to the continuity outcome. The PD/SD continuity claim is an empirical comparison: CRS distortion is measured by DIC and placed against analytic/empirical baselines for pixel-only and linear-connection displays. No CRS-specific parameter is tuned to force the measured crosses below those baseline curves. The baseline PD and SD formulas concern the comparators, not the CRS claim, and are derived separately as sampling/interpolation properties of pixel-only and straight-line displays. The self-citations (refs. 23 and 41) appear only in background enumerations of prior interactive-object and deformation-driven devices; they are not used to justify the buckling-interpolation mechanism, the no-collapse condition, or the distortion measurements. The acknowledged limitations—that the haptic stimulus is inferred from DIC displacement fields on spandex/silicone, and that digit recognition rises only from 50.3% to 67.8%—are external-validity and effect-size concerns about the skin-device transfer, not definitional or statistical circularity. No equation in the paper is defined in terms of the quantity it is claimed to predict, and no load-bearing result reduces to a self-citation chain.

Assumptions & free parameters 4 free parameters · 5 assumptions · 1 invented entities

The central design rests on classical beam mechanics plus a measured Winkler foundation coefficient, so it is not heavily parameterized. The main free parameters are empirical baseline distortion coefficients used for comparison, not for the CRS mechanism itself. The key unstated assumptions are the equivalence of measured surface deformation to perceived haptic stimulus and the adequacy of the Winkler model for skin.

free parameters (4)
  • c_pixel_SD_1D = 0.994
    Empirical coefficient in the pixel-only shape distortion formula SD = 0.994(d/l), used as a baseline in Fig. 2d. It is fitted to data, not derived from first principles.
  • c_linear_SD_1D = 1.545
    Empirical coefficient in the linear-connection shape distortion formula SD = 1.545(d/l)^2, used as baseline in Fig. 2d.
  • c_square_SD_2D = 1.412
    Empirical coefficient in the square-pixel 2D shape distortion formula SD = 1.412(d/l), baseline in Fig. 4f.
  • c_hex_SD_2D = 1.318
    Empirical coefficient in the hexagon-pixel 2D shape distortion formula SD = 1.318(d/l), baseline in Fig. 4g.
assumptions (5)
  • domain assumption Euler-Bernoulli beam theory with a Winkler foundation accurately models the CRS beam interacting with skin-like elastomer.
    Used to derive critical buckling loads and the no-collapse condition Eq. (4), assuming small elastic deflections and a linear foundation.
  • domain assumption The skin or elastomer can be represented as a Winkler foundation with a constant subgrade modulus beta.
    Section 'Mechanical model of CRS' states the elastomer is simplified to a Winkler foundation; real skin is inhomogeneous, nonlinear, and curved.
  • domain assumption Sinusoidal target shapes and squared-error distortion metrics capture haptic display quality.
    The Discussion justifies sine waves as common contacts and Fourier basis, but no perceptual validation is provided beyond one digit-recognition test.
  • domain assumption The DIC-measured displacement of spandex fabric or silicone equals the stimulus delivered to the finger.
    Methods and Fig. 4 use a spandex cover for DIC; if the fabric decouples from skin contact, the continuity improvement may not transfer.
  • domain assumption Beam ends have zero rotation and moveable ends, and the peak is located at the midpoint between pixels.
    Stated before Eq. (3) in the mechanical model; this idealization simplifies the trigonometric series solution.
invented entities (1)
  • Continuity reinforcement skeleton (CRS) independent evidence
    purpose: Thin steel beams tied to haptic pixels that buckle to interpolate off-plane displacement between pixels.
    CRS is a fabricated physical device demonstrated in 1D, 2D, and curved prototypes with DIC measurements and VR integration, so it has direct observable evidence, not merely a postulated entity.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Continuity Reinforcement Skeleton for Pixel-based Haptic Display." pith.science (2026). https://pith.science/paper/LCDH7U62

@misc{pith2026241115445,
  author       = {Pith},
  title        = {Pith review of: Continuity Reinforcement Skeleton for Pixel-based Haptic Display},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LCDH7U62}},
  note         = {Machine review of arXiv:2411.15445}
}
read the original abstract

Haptic displays are crucial for facilitating an immersive experience within virtual reality. However, when displaying continuous movements of contact, such as stroking and exploration, pixel-based haptic devices suffer from losing haptic information between pixels, leading to discontinuity. The trade-off between the travel distance of haptic elements and their pixel size in thin wearable devices hinders solutions that solely rely on increasing pixel density. Here we introduce a continuity reinforcement skeleton (CRS), which employs physically driven interpolation to enhance haptic information. The CRS enables the off-plane displacement to move conformally and display haptic information between pixel gaps. Efforts are made to quantify haptic display quality using geometric, mechanical, and psychological criteria. The development and integration of one-dimensional (1D), two-dimensional (2D), and curved CRS devices with virtual reality systems highlight the impact of CRS on haptic display, showcasing its potential for improving haptic experience.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

54 extracted references · 54 canonical work pages

  1. [1]

    Wang, G. et al. Development of metaverse for intelligent healthcare. Nat. Mach. Intell. 4, 922–929 (2022)

    work page 2022

  2. [2]

    R., Rogers, J

    Pyun, K. R., Rogers, J. A. & Ko, S. H. Materials and devices for immersive virtual reality. Nat. Rev. Mater. 7, 841–843 (2022)

    work page 2022

  3. [3]

    Su, H. et al. Physical human –robot interaction for clinical care in infectious environments. Nat. Mach. Intell. 3, 184–186 (2021)

    work page 2021

  4. [4]

    Ernst, M. O. & Banks, M. S. Humans integrate visual and haptic information in a statistically optimal fashion. Nature 415, 429–433 (2002)

    work page 2002

  5. [5]

    Yu, X. et al. Skin-integrated wireless haptic interfaces for virtual and augmented reality. Nature 575, 473–479 (2019)

    work page 2019

  6. [6]

    Yang, T. et al. Recent Advances and Opportunities of Active Materials for Haptic Technologies in Virtual and Augmented Reality. Adv. Funct. Mater. 31, 2008831 (2021)

    work page 2021

  7. [7]

    J., Jax, S

    Kapur, P., Jensen, M., Buxbaum, L. J., Jax, S. A. & Kuchenbecker, K. J. Spatially distributed tactile feedback for kinesthetic motion guidance. in 2010 IEEE Haptics Symposium 519–526 (IEEE, Waltham, MA, USA, 2010)

    work page 2010

  8. [8]

    Wang, M. et al. Fusing stretchable sensing technology with machine learning for human–machine interfaces. Adv. Funct. Mater. 31, 2008807 (2021)

    work page 2021

Show all 54 references
  1. [9]

    Social touch technology: a survey of haptic technology for social touch

    Huisman, G. Social touch technology: a survey of haptic technology for social touch. IEEE Trans. Haptics 10, 391–408 (2017)

    2017

  2. [10]

    Sundaram, S. et al. Learning the signatures of the human grasp using a scalable tactile glove. Nature 569, 698–702 (2019)

    2019

  3. [11]

    & Steinicke, F

    V ogel, D., Lubos, P. & Steinicke, F. AnimationVR - interactive controller-based animating in virtual reality

  4. [12]

    M., Nocera, C

    Ackerman, J. M., Nocera, C. C. & Bargh, J. A. Incidental haptic sensations influence social judgments and decisions. Science 328, 1712–1715 (2010)

    2010

  5. [13]

    & Visell, Y

    Biswas, S. & Visell, Y . Emerging material technologies for haptics. Adv. Mater. Technol. 4, 1900042 (2019)

    2019

  6. [14]

    C., Gonzalez-Franco, M., Ofek, E

    Berger, C. C., Gonzalez-Franco, M., Ofek, E. & Hinckley, K. The uncanny valley of haptics. Sci. Robot. 3, eaar7010 (2018)

    2018

  7. [15]

    Chang, E., Kim, H. T. & Yoo, B. Virtual reality sickness: a review of causes and measurements. Int. J. Human–Computer Interact. 36, 1658–1682 (2020)

    2020

  8. [16]

    Zhang, Z. et al. Active mechanical haptics with high -fidelity perceptions for immersive virtual reality. Nat. Mach. Intell. 5, 643–655 (2023)

    2023

  9. [17]

    & Paik, J

    Mintchev, S., Salerno, M., Cherpillod, A., Scaduto, S. & Paik, J. A portable three- degrees-of-freedom force feedback origami robot for human –robot interactions. Nat. Mach. Intell. 1, 584–593 (2019)

    2019

  10. [18]

    Choi, C. et al. Surface haptic rendering of virtual shapes through change in surface temperature. Sci. Robot. 7, eabl4543 (2022)

    2022

  11. [19]

    Johnson, B. K. et al. A multifunctional soft robotic shape display with high-speed 21 actuation, sensing, and control. Nat. Commun. 14, 4516 (2023)

    2023

  12. [20]

    -L., Zhakypov, Z., Sonar, H

    Huang, J. -L., Zhakypov, Z., Sonar, H. & Paik, J. A reconfigurable interactive interface for controlling robotic origami in virtual environments. Int. J. Robot. Res. 37, 629–647 (2018)

    2018

  13. [21]

    Tahouni, Y ., Qamar, I. P. S. & Mueller, S. NURBSforms: a modular shape - changing interface for prototyping curved surfaces. in Proceedings of the Fourteenth International Conference on Tangible, Embedded, and Embodied Interaction 403–409 (ACM, Sydney NSW Australia, 2020)

    2020

  14. [22]

    F., Gonzalez, E

    Siu, A. F., Gonzalez, E. J., Yuan, S., Ginsberg, J. B. & Follmer, S. ShapeShift: 2D spatial manipulation and self-actuation of tabletop shape displays for tangible and haptic interaction. in Proceedings of the 2018 CHI Conference on Human Factors in Computing Systems 1–13 (ACM...

    2018

  15. [23]

    & Chen, C

    Wang, X., Meng, Z. & Chen, C. Q. Robotic materials transformable between elasticity and plasticity. Adv. Sci. 10, 2206637 (2023)

    2023

  16. [24]

    Zhu, M. et al. Haptic-feedback smart glove as a creative human-machine interface (HMI) for virtual/augmented reality applications. Sci. Adv. 6, eaaz8693 (2020)

    2020

  17. [25]

    Qi, J., Gao, F., Sun, G., Yeo, J. C. & Lim, C. T. HaptGlove—untethered pneumatic glove for multimode haptic feedback in reality–virtuality continuum. Adv. Sci. 10, 2301044 (2023)

    2023

  18. [26]

    & Lee, C

    Sun, Z., Zhu, M., Shan, X. & Lee, C. Augmented tactile -perception and haptic - feedback rings as human -machine interfaces aiming for immersive interactions. Nat. Commun. 13, 5224 (2022)

    2022

  19. [27]

    Novich, S. D. & Eagleman, D. M. Using space and time to encode vibrotactile information: toward an estimate of the skin’s achievable throughput. Exp. Brain Res. 233, 2777–2788 (2015)

    2015

  20. [28]

    Oh, S. et al. Easy‐to‐wear auxetic SMA knot‐architecture for spatiotemporal and multimodal haptic feedbacks. Adv. Mater. 35, 2304442 (2023)

    2023

  21. [29]

    Hinchet, R. J. & Shea, H. Glove‐ and sleeve‐format variable‐friction electrostatic clutches for kinesthetic haptics. Adv. Intell. Syst. 4, 2200174 (2022)

    2022

  22. [30]

    Wang, Y ., Li, L., Hofmann, D., Andrade, J. E. & Daraio, C. Structured fabrics with tunable mechanical properties. Nature 596, 238–243 (2021)

    2021

  23. [31]

    & Shea, H

    Leroy, E., Hinchet, R. & Shea, H. Multimode hydraulically amplified electrostatic actuators for wearable haptics. Adv. Mater. 32, 2002564 (2020)

    2020

  24. [32]

    & Alexander, J

    Sturdee, M. & Alexander, J. Analysis and classification of shape -changing interfaces for design and application -based research. ACM Comput. Surv. 51, 1– 32 (2019)

    2019

  25. [33]

    & Troiano, G

    Boem, A. & Troiano, G. M. Non -Rigid HCI: a review of deformable interfaces and input. in Proceedings of the 2019 on Designing Interactive Systems Conference 885–906 (ACM, San Diego CA USA, 2019)

    2019

  26. [34]

    & Alexander, J

    Everitt, A. & Alexander, J. 3D printed deformable surfaces for shape -changing displays. Front. Robot. AI 6, 80 (2019)

    2019

  27. [35]

    Zhu, L. et al. TapeTouch: a handheld shape-changing device for haptic display of 22 soft objects. IEEE Trans. Vis. Comput. Graph. 28, 3928–3938 (2022)

    2022

  28. [36]

    & Shinoda, H

    Hoshi, T., Takahashi, M., Iwamoto, T. & Shinoda, H. Noncontact tactile display based on radiation pressure of airborne ultrasound. IEEE Trans. Haptics 3, 155– 165 (2010)

    2010

  29. [37]

    & Visell, Y

    Reardon, G., Dandu, B., Shao, Y . & Visell, Y . Shear shock waves mediate haptic holography via focused ultrasound. Sci. Adv. 9, eadf2037 (2023)

    2023

  30. [38]

    Berkelman, P. J. & Hollis, R. L. Lorentz magnetic levitation for haptic interaction: device design, performance, and integration with physical simulations. Int. J. Robot. Res. 19, 644–667 (2000)

    2000

  31. [39]

    Lin, W. et al. Super-resolution wearable electrotactile rendering system. Sci. Adv. 8, eabp8738 (2022)

    2022

  32. [40]

    & Ishii, H

    Follmer, S., Leithinger, D., Olwal, A., Hogge, A. & Ishii, H. inFORM: dynamic physical affordances and constraints through shape and object actuation. in Proceedings of the 26th annual ACM symposium on User interface software and technology 417–426 (ACM, St. Andrews Scotland, ...

    2013

  33. [41]

    Meng, Z. et al. Encoding and storage of information in mechanical metamaterials. Adv. Sci. 10, 2301581 (2023)

    2023

  34. [42]

    & Ishii, H

    Leithinger, D. & Ishii, H. Relief: a scalable actuated shape display. in Proceedings of the fourth international conference on Tangible, embedded, and embodied interaction 221–222 (ACM, Cambridge Massachusetts USA, 2010)

    2010

  35. [43]

    & Wang, Y

    Cai, Y ., Wang, J., Zhao, L., Liu, Y . & Wang, Y . A novel shape-changing haptic table-top display. in 2017 International Conference on Optical Instruments and Technology: Optoelectronic Imaging/Spectroscopy and Signal Processing Technology (eds. Situ, G., Dong, L., Cao, X. & ...

    2017

  36. [44]

    Yu, M. et al. A self-sensing soft pneumatic actuator with closed -Loop control for haptic feedback wearable devices. Mater. Des. 223, 111149 (2022)

    2022

  37. [45]

    Messerschmidt, M. A. et al. ANISMA: a prototyping toolkit to explore haptic skin deformation applications using shape-memory alloys. ACM Trans. Comput.-Hum. Interact. 29, 1–34 (2022)

    2022

  38. [46]

    Besse, N., Rosset, S., Zarate, J. J. & Shea, H. Flexible active skin: large reconfigurable arrays of individually addressed shape memory polymer actuators. Adv. Mater. Technol. 2, 1700102 (2017)

    2017

  39. [47]

    K., Ji, S., Wang, D

    Han, A. K., Ji, S., Wang, D. & Cutkosky, M. R. Haptic surface display based on miniature dielectric fluid transducers. IEEE Robot. Autom. Lett. 5, 4021 –4027 (2020)

    2020

  40. [48]

    Alexander, J. et al. Grand challenges in shape -changing interface research. in Proceedings of the 2018 CHI Conference on Human Factors in Computing Systems 1–14 (ACM, Montreal QC Canada, 2018)

    2018

  41. [49]

    Hawkes, E. et al. Programmable matter by folding. Proc. Natl. Acad. Sci. 107, 12441–12445 (2010)

    2010

  42. [50]

    E., Rasmussen, M

    Grønbæk, J. E., Rasmussen, M. K., Halskov, K. & Petersen, M. G. KirigamiTable: 23 designing for proxemic transitions with a shape-changing tabletop. in Proceedings of the 2020 CHI Conference on Human Factors in Computing Systems 1–15 (ACM, Honolulu HI USA, 2020)

    2020

  43. [51]

    & Alexander, J

    Everitt, A. & Alexander, J. PolySurface: a design approach for rapid prototyping of shape-changingdisplays using semi-solid surfaces. in Proceedings of the 2017 Conference on Designing Interactive Systems 1283–1294 (ACM, Edinburgh United Kingdom, 2017)

    2017

  44. [52]

    & Gonzalez -Franco, M

    Steed, A., Ofek, E., Sinclair, M. & Gonzalez -Franco, M. A mechatronic shape display based on auxetic materials. Nat. Commun. 12, 4758 (2021)

    2021

  45. [53]

    Kuo, C. -H. & Smith, S. Mechanical feedback analysis of a ferrofluid -based module with 2D dynamic traveling waves for tactile display application. Displays 61, 101926 (2020)

    2020

  46. [54]

    Beams on Elastic Foundation : Theory with Applications in the Fields of Civil and Mechanical Engineering

    Hetenyi, M. Beams on Elastic Foundation : Theory with Applications in the Fields of Civil and Mechanical Engineering. (The University of Michigan Press, 1946). 24 List of Figures Fig. 1 Continuity reinforcement in haptic display. a Examples of continuous contact in VR. b Conce...

    1946

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.