Research ArticleMATERIALS SCIENCE

Role of indentation depth and contact area on human perception of softness for haptic interfaces

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Science Advances  30 Aug 2019:
Vol. 5, no. 8, eaaw8845
DOI: 10.1126/sciadv.aaw8845
  • Fig. 1 Overview of experimental approach and fabrication scheme.

    (A) Hertzian contact model of a finger of radius, R, presses with a force, F, into a deformable slab with Young’s modulus, E, and a controlled thickness, h. This pressing action displaced the interface between both objects by an indentation depth, δ. The finger and the slab shared an interface with a contact area of πa2. (B) The creation of pits in the surface of the slab by micropatterning reduced the contact area between the finger and the slab. (C) The thickness of the slab, h, was controlled by cutting a pocket into an acrylic substrate to a depth equal to h. (D) The acrylic substrate served as a mold for a liquid PDMS prepolymer. Before curing, a micropatterned (or planar) wafer (E) was placed on top of the uncured PDMS (F). The micropatterned pillars had a radius, r, and were spaced by a distance, s. The Young’s modulus, E, was controlled by the prepolymer/cross-linker ratio of the prepolymer. (G) The slab was exposed to ultraviolet (UV)/ozone to minimize surface viscoelasticity.

  • Fig. 2 Computed indentation depth and contact area of thin PDMS slabs.

    (A) The contact area (πa2) and indentation depth (δ) as a function of slab thickness (h) and Young’s modulus (Es) for an applied force of 1 N. (B) Contact area and indentation depth as a function of force for a slab with a Young’s modulus of 0.8 MPa. Results are obtained from Eqs. 2 to 4. (C) Differences in the ratio of indentation depth to contact radius between two slabs that differ in thickness by 0.1 mm as a function of force. The thicker of the two slabs has a slab thickness of hf. Negative values indicate that thinner films have larger ratios of δ/a.

  • Fig. 3 Properties of PDMS slabs.

    (A) Optical images of the microstructured slabs. Patterned microstructures reduce the effective contact area to either 30 or 50% of the original area. Scale bars, 100 μm. (B) Electrical impedance tomography (EIT) of a finger and acrylic indenter to visualize the contact area with different applied masses. The color is proportional to the displacement. (C) Measurements of indentation depth of an acrylic indenter on slabs that vary in the Young’s moduli or slab thickness.

  • Fig. 4 Results of the two-alternative forced-choice test.

    (A) Aggregate percentage of times a slab was judged as the softer slab compared to the other slabs. The line is to guide the eye. (B) This plot is a sample-by-sample, head-to-head comparison, in which the slabs are arranged in the rows and columns by increasing aggregate percentage. The color of each square quantifies whether a sample on the x axis was judged as softer than a sample on the y axis. (C) Aggregate percentage of times a slab was judged as the softer slab as a function of intrinsic slab parameters: thickness, effective surface area, and Young’s modulus. (D) Same as (C) but as a function of extrinsic parameters (i.e., those produced as a result of contact with an indenter): indentation depth and contact area. Indentation depth and contact area are calculated for F = 1 N, a representative force used for the purpose of plotting. Marker shape represents extent of micropatterning (effective surface areas: triangles, 30%; stars, 50%; circles, 100%), color represents Young’s modulus, and shade represents relative thickness (darkest is the thickest, within each color group). Error bars are excluded because the aggregated data ignore sample-by-sample trends. Data represent a total of 540 individual comparisons between five participants (n = 5).

  • Fig. 5 Comparison of models that best relate human perception of softness to the indentation depth and contact area in a two-alternative forced-choice test.

    The predictive power, based on the AIC (lower values are better predictors), is shown at different applied forces. Two Hertzian models are shown (dashed and solid lines) where the finger is treated as a “deformable finger” (EF = 0.1 MPa) and a “rigid finger” (EF = ∞). Five different combinations of indentation depth, δ, and/or contact radius, a, are shown. The scale bar denotes a 100-fold increased probability of a model fitting the data from an incremental change in AIC. The scale bar can be translated along the y axis, but a linear increase in the distance represents an exponential increase that a scenario is more probable.

  • Fig. 6 Results of the magnitude estimation test.

    (A) Participants (n = 5) ranked slabs on a numerical scale of perceived softness, where the distance between slabs indicated relative levels of perceived softness. A “1” indicated the hardest sample and a “10” represented the “softest” sample. Hollow symbols at the bottom represent average values; solid markers represent participant responses. Slabs were judged on a scale of 1 to 10 with 33 discrete locations. (B) Participant response on the number line test as compared to a two-alternative forced-choice test. (C) Predictive power of different Hertzian models and combinations of indentation depth and contact area. The scale bar denotes a 100-fold increased probability of a model fitting the data from an incremental change in AIC. A linear increase in the differences in AIC between two models represents an exponential increase in probability. (D) Individual, head-to-head comparisons from the magnitude estimation test. (E) Curve representing the ratio between the Young’s modulus of two slabs so that slab 2 feels twice as soft as slab 1. Slab 1 is shown for different Young’s moduli (Eq. 8) and at applied forces similar to human touch.

  • Table 1 Slab parameters.

    SlabYoung’s
    modulus
    E (MPa)
    Thickness
    h (mm)
    Effective
    surface area
    (% of original
    surface area)
    Marker
    Dark red(dkR)3.04.2030Embedded Image
    Red(R)3.01.4030Embedded Image
    Light red(ltR)3.00.6050Embedded Image
    Dark blue(dkB)0.80.58100Embedded Image
    Blue(B)0.80.50100Embedded Image
    Light blue(ltB)0.80.30100Embedded Image
    Dark green(dkG)0.10.4030Embedded Image
    Green(G)0.10.2050Embedded Image
    Light green(ltG)0.10.13100Embedded Image

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/8/eaaw8845/DC1

    Comparing the elastic energy of a single feature supported on a substrate

    Hertzian contact model of a deformable finger

    Model parameters

    Two-alternative forced-choice test counterexample

    Analyzing participant responses

    AIC for all modeling scenarios

    Finite element model of strain fields

    Testing generalization accuracy using leave-one-out cross-validation

    Validation of findings on a second set of slabs

    Power analysis

    Fig. S1. Schematic of indentation depth and contact area.

    Fig. S2. Flowchart for analyzing participant responses.

    Fig. S3. AIC of all scenarios for both psychophysical tests.

    Fig. S4. Finite element modeling of stress between micropatterned surface and finger.

    Fig. S5. Leave-one-out cross-validation of participant responses of the two-alternative forced-choice test.

    Fig. S6. Leave-one-out cross-validation of participant responses of the magnitude estimation test.

    Fig. S7. Validating results with psychophysical testing on a second set of slabs.

    Table S1. Model parameters for the finger and substrate.

    Table S2. Slab parameters.

  • Supplementary Materials

    This PDF file includes:

    • Comparing the elastic energy of a single feature supported on a substrate
    • Hertzian contact model of a deformable finger
    • Model parameters
    • Two-alternative forced-choice test counterexample
    • Analyzing participant responses
    • AIC for all modeling scenarios
    • Finite element model of strain fields
    • Testing generalization accuracy using leave-one-out cross-validation
    • Validation of findings on a second set of slabs
    • Power analysis
    • Fig. S1. Schematic of indentation depth and contact area.
    • Fig. S2. Flowchart for analyzing participant responses.
    • Fig. S3. AIC of all scenarios for both psychophysical tests.
    • Fig. S4. Finite element modeling of stress between micropatterned surface and finger.
    • Fig. S5. Leave-one-out cross-validation of participant responses of the two-alternative forced-choice test.
    • Fig. S6. Leave-one-out cross-validation of participant responses of the magnitude estimation test.
    • Fig. S7. Validating results with psychophysical testing on a second set of slabs.
    • Table S1. Model parameters for the finger and substrate.
    • Table S2. Slab parameters.

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