Scale Dependence of Force Patterns During the
Scanning of a Surface by a Bare Finger
Marco Janko, Richard Primerano, and Yon Visell
Drexel University, ECE Department, Philadelphia, USA{marco.a.janko,richard.a.primerano,yon.visell}@drexel.edu

Abstract. This study investigated how the geometry of a touched surface influences forces felt during the scanning of an object with the finger.
Although prior research, and basic mechanical considerations, have shedlight on force production during haptic interaction with a touched object,surprisingly little is known about how to relate surface detail at different
scales to the specific patterns of force that are observed. To address this,we designed an apparatus that could accurately measure normal and tangential forces between a finger and a surface. We fabricated sinusoidal
surfaces with precisely controlled geometry, and measured spatial variations in resultant forces generated while subjects repeatedly scanned thesurfaces at specified speed and pressure. Subsequent analysis revealed
that the resulting force patterns varied in an organized way with spatial
scale, and that fluctuations, in the form of aperiodic signal componentsthat proved difficult to model, played an increasingly important role as
the spatial scale of the surface geometry decreased. The results may help
to explain differences in how surface detail is recovered by the haptic
perceptual system at different length scales.
Keywords: Haptics, texture, vibration, finger, system identification

1

Introduction

There are many variables that affect the mechanical stimuli that underlie thesense of touch. A finger moving over an object experiences normal and tangential
forces, and even torques, that depend on the structure, geometry and material
properties of the touched object. These signals manifest themselves at a varietyof length and time scales. Reproducing the full range of force and displacement
stimuli felt by the hand during palpation is a long term goal of haptic engineering,but, to date, we have, at best, a limited understanding of what these stimuli are.
It has been observed that the production of forces by a sliding finger canbe more readily interpreted in the spatial domain [1]. Basic contact mechanics
can be sufficient to predict average forces as the finger slides across featuresthat are large compared to its width [2], but the prediction of such forces when
the geometric scale is smaller than the size of the finger remains daunting, andeven at larger scales, fluctuations are difficult to account for. Prior research has
shed some light on the interaction between tribological factors associated with

2

Marco Janko, Richard Primerano, Yon Visellscanning a surface with a synthetic fingertip [3], but the characterization andprediction of interaction forces involving a real finger have received limited attention. Several approaches to rendering force or acceleration information fromsurface measurements have been developed [4], Such measurement-based rendering algorithms are capable of realizing plausibly realistic interactions withdiverse textured objects. However, there is little published work on predicting
texture-induced forces felt by the bare finger [5]. In addition, measurement-based
rendering algorithms are of limited utility in predicting forces that would be produced by a previously unexplored surface. Physically-motivated approaches torendering forces produced during the scanning of virtual surface geometries canyield highly evocative experiences [6], but fall short of perceptual realism andphysical accuracy.
Within the field of tribology, force production during frictional sliding andthe identification of friction models have been extensively explored [7], but thiswork has been primarily concerned with the interaction between solid, machined
surfaces. The complex morphology, and highly viscoelastic nature of the fingertip precludes the use of such models for analyzing or predicting finger-generated
forces, although the system identification methods we investigated here are inspired by those used in the aforementioned studies.
The study presented here is motivated by the question of whether the spatial
pattern of forces produced during the sliding of a finger on a structured surface
can be predicted from knowledge of the geometry of the surface itself. We assumed that such a prediction should necessarily depend on a number of factors,
most notably: the dynamics of the finger, and the interfacial contact mechanics
between the finger and the surface, on surface properties, and on interaction
parameters including normal force and scanning speed. A long term aim of thisresearch would be to further explain how a model for force production from asliding finger may be structurally interpreted in terms of the former three factors,
and may be inferred to vary with the latter two.
As a first step in this direction, we engineered a sensing instrument thatallowed us to accurately measure contact forces and kinematics of a finger sliding on a structured surface with high dynamic range and temporal sensitivity.
We fabricated surfaces of precisely known sinusoidal geometry, and recorded
the interactions performed by several participants at specified normal force andscanning speed. We analyzed the resulting force patterns in the spatial domain,
and related these spatial force patterns, and their variations between trials, tothe surface geometry itself. In a further step, we estimated deterministic but
nonlinear contact force models that could predict, to varying levels of accuracy,
the mean force pattern that resulted from a given surface geometry. The results
indicate that it is possible to predict mean interaction force patterns from geometry when the spatial scale of the surface geometry is sufficiently long, but thatat smaller scales other physical processes that proved difficult to model dominated force production. The results have implications for the haptic simulationof surfaces and for the perceptual recovery of surface geometry via palpation.

Scale dependence of forces during the scanning of a surface by a bare finger

2

3

Methods

We developed an apparatus and instrument for measuring mechanical interactions and kinematics of a fingertip sliding on a surface, fabricated surfaces withknown geometry, consisting of sinusoidal gratings with different wavelengths, andmeasured force and kinematic data as individuals scanned the grating surfaces
with their fingers. In order to extract invariant properties of these interactions,
we analyzed these data in the spatial domain, and used system identification
analyses to build predictive models for the generation of motion-dependent forces
during surface exploration.
2.1

Measurement Apparatus

The apparatus (Fig. 1) consists of a multi-axis load cell designed to capture
forces applied by a finger to its surface independent of the position at which
they were applied, by measuring strain in the normal (vertical) direction at
two locations, and tangential strain in the horizontal direction. The load cell
was fabricated from type 6010 aluminum alloy using precise electrical dischargemachining. The three force components were measured with three full-bridgestrain gauges, bonded at the locations shown. The output of each strain gauge
was amplified by an AD8429 low-noise instrumentation amplifier. The gain ofeach amplifier was 1000, and the measurement frequency bandwidth was 100
kHz. Structural resonances limit the usable bandwidth to a few hundred Hz,
which, after digital correction of the frequency response in the band of interest(compensating effects of a resonance at 130 Hz), was sufficient for this study. The
signal from each instrumentation amplifier was digitized (0.1 ms sample period,
16 bits) via a data acquisition device (USB-6009, National Instruments
Inc., Austin, TX). Finger kinematic trajectories were captured using an opticalmotion capture system (Natural Point, Corvallis, OR) with a sampling
period of 8.3 ms and an approximate spatial resolution of 0.2 mm.
Force calibration At each time instant, the apparatus measures force and position corresponding to an effective point load F = (FN , FT ), where FN and FT
are normal and tangential force components, applied at a position x. In order totranslate measured voltage to force, we calibrated the device by applying standardized normal and tangential loads at an array of points on the measurement
surface, and recording output voltage. The force-voltage relations proved highlylinear, so that a minimum least squares linear fit could be used to compute force
from voltage. The sum of outputs from strain sensors for normal (resp. tangential) directions proved sufficiently constant that we were able to accurately
estimate force independent of the location at which a load was applied.
Surface profile stimuli We fabricated relief surfaces with known geometry,specified as height functions h(x) that varied in a single dimension, in order tostudy the variation of forces with geometry during scanning of the surface with

4

Marco Janko, Richard Primerano, Yon VisellA
surfacepsample

straingauges

B

z

v
x

40pmm

5V

y

C

x
topNi-DAQ
350 Ω

AD842925pmm

120pmmFig. 1. A, B The measurement apparatus used in the experiment. Isometric view ofthe masurement apparatus. C. Simplified schematic of the strain gauge amplification
circuit.

a finger. These surfaces were sinusoidal gratings with height profiles given byh(x) = A sin(2πx/λ), where amplitude A and spatial wavelength λ varied foreach sample. Four such surfaces were used in our measurements, with λ = 1
mm, 2.5 mm, 3 mm and 4 mm (Fig. 2). Amplitude was equal to a fixed fractionof the wavelength for all samples, A = 0.1λ, ensuring that the maximum slope
was constant for all samples – only the scale varied. The gratings were modeled
parametrically and fabricated using a photopolymer resin 3D printer (maximum
resolution 100 µm) yielding an artifact-free finish at the scales of interest (Objet
30, Stratasys Inc., Boston, USA). No further processing was used to modify
the surface finish. The samples were firmly affixed to the force measurement
apparatus with two-sided adhesive tape during the experiments.
4 mm
0
0

10 mm

λ = 1mm010 mm

λ = 2.5mm

0

10 mm

λ = 3mm

010 mm

λ = 4mm

4 mm
0Fig. 2. Sinusoidal gratings used in the measurements differed only in spatial scale, λ.

2.2Measurement procedure

During the measurements, the apparatus described above was used to capturenormal forces, tangential forces, and finger position during scanning of the sam-

Scale dependence of forces during the scanning of a surface by a bare finger

5

ples with the index finger. Three subjects (two male, one female, ages 20 to 33
years, all right hand dominant) volunteered to participate in the experiment.
None evidenced any abnormality of biomechanics or function of the finger. Subjects were seated in front of the apparatus with the elbow supported and forearm
held at a comfortable angle.
During each of five sets of trials, every subject scanned a surface 10 times inalternating directions with his or her index finger, yielding 50 scans per subject
for each surface. Subjects were provided training and real-time feedback via a
computer and graphical user interface that assisted them in maintaining constantnormal force, and via an audio metronome that assisted them in maintaining a
specified mean sliding speed (v = 240 mm/s), although we expected the realized
velocity profiles to vary. The surfaces were cleaned after each set of trials withisopropyl alcohol.
2.3

Analysis of surface-dependent tangential force patterns

In our analysis, we focused on the tangential, frictional, force between the surface and finger. Following digitization, force and position data were resampled
to a common rate of 10 kHz. Force data was band pass filtered to a range from10 to 500 Hz using zero-phase filtering in order to remove variations due to
low-frequency motor behavior and high-frequency artifacts from structural resonances. The synchronous force and position data were used to infer a spatial
force pattern F (x) for each scan across the surface sample. We further limited
our measurement range to the central 80 mm of the grating to eliminate edge
effects.

Force (mN)

λ = 1mm50

2.5 mm3 mm% Var= 445% Var= 258

0

0

4 mm
% Var= 229% Var= 163

0-50-40 -2020

40 -40 -20

20 40 -40 -20 0
Finger Position (mm)2040 -40 -20

020

Fig. 3. The ensemble of patterns of tangential force components representing all trials
from a single subject repeatedly scanning each sample. The black line displays themean force pattern. The results clearly reflect the geometry of the underlying surface.
The relative variation (%var) shown is the ratio of the standard deviation to the rms
signal average. Its growth with decreasing λ decreases, evidence the relative increasein magnitude of fluctuations as scale decreases.

The force patterns for each participant, sample (wavelength), and scanning
direction (left, right) were grouped for comparison (Fig. 3). For each grouping,the mean force pattern and variance were computed for further analysis. In order
to compare with prior research on force production by sinusoidal surfaces, weanalyzed spatial frequency content by computing a magnitude spectrum for each40

6Marco Janko, Richard Primerano, Yon VisellFig. 4. Spatial spectrum (mean shown in black) for the tangential force of 75 trials for
3 subjects (25 trials per subject going right to left) scanning the 4 sinusodal gratings.

scan, using a Fourier transform in the spatial domain (Fig. 4). The results at
all four scales evidence three main effects: a strong fundamental spatial period,
corresponding to the surface wavelength λ, integer harmonic components, suggestive of a nonlinearity in the relation between surface height and tangential,
and a 1/f trend of decreasing magnitude with frequency, consistent with priorliterature on the spatial spectrum of forces during bare-finger contact [1].
2.4

Predictability of force production from surface geometry

Motivated by the extent to which force patterns F (x) seemed to reflect theunderlying geometry h(x), albeit in a possibly dynamical or nonlinear manner,
we investigated the extent to which it is possible to predict these patterns given
prior knowledge of h(x). Since our goal was to determine whether prediction
is possible, we deferred developing a specific model of mechanical interactions
between the surface and a sliding finger, and instead used utilized powerful blackbox nonlinear system identification techniques to estimate optimal predictivemodels [8].
The models we estimated are generic nonlinear autoregressive processes expressed in the spatial domain with height h(x) = u(x) as input and force
FT (x) = y(x) as output. They are parametrized by linear autoregressive weightvectors A, B of order N, M and a nonlinearity G, in the form of a wavelet basis
network with Nw kernels and Nr regressors; see Fig. 5, left panel. We adopted
this model structure after extensive experimentation with alternatives. We optimized the models by performing a simultaneous grid search over the integermodel order parameters N, M, Nw and Nr , and by maximizing the goodnessof-fit (GOF), between the measured data (y) and the estimated data from ourmodel (ŷ), for a given model order, where
GOF = 100% × ||y − ŷ||/||y − mean(ŷ)||A total of 1600 candidate models were estimated at each wavelength λ, with
6400 models considered across all conditions. The optimal values of N and M lie
between 2 and 10, and the optimal nonlinearity order Nw was between 8 and 18.
There was no discernable pattern relating their values to λ. We used a training
data set to estimate the models, and evaluated fit quality (Fig. 5) using separate
testing data.

Scale dependence of forces during the scanning of a surface by a bare finger

7h(x) = u(x)u = {u(x),u(x-dx),...,u(x-N dx)}y = {y(x-dx),y(x-2dx),...,y(x-M dx)}
u,y

y(x)

y(x) = A u + B y + G(u, y)F(x) = y(x)Fig. 5. Left: We investigated the use of geometry h(x) to predict average tangential
force patterns FT (x) by estimating nonlinear autoregressive system models in the spatial domain, with sample interval dx. Right: Optimal fit quality (%) at each scale λover all models considered for previously unseen data, with sample model predictions(black line) and measurements (gray line). For large λ, accurate prediction is possible,
but at short scales, force fluctuations are difficult to capture.

The results are summarized in Fig. 5. At the longest wavelength, the qualitative and quantitative correspondence is good, indicating that force data was well
predicted by geometry. At shorter scales, no consistently predictive model could
be determined, and many of the models in the search space failed to converge
during estimation. At a scale of λ = 1 mm and at the exploration speed imposed
here, the force patterns appear to be fundamentally difficult to predict, due tothe presence of of aperiodic signal components that are, as noted above, large in
relative magnitude and difficult to capture.

3

Conclusion

The forces that result from the scanning of a textured surface by a bare finger
vary in a complex fashion as a function of surface geometry, even when other interaction parameters, such as normal force and scanning speed, are held constant.
Nonetheless, this study revealed regularities in the correspondence between force
and surface geometry that depend systematically on surface geometry h(x). We
demonstrated this by fabricating surfaces with known geometry h(x) and bymeasuring force and position with high temporal and spatial resolution. The
resulting forces exhibit quasi-regular fluctuations that we were partly successful
in modeling as effects of the geometry of the surfaces. At spatial wavelengths
greater than about 1 mm, we were successful in using nonlinear system identification techniques to predict observed forces from surface geometry. At short

8

Marco Janko, Richard Primerano, Yon Visell

wavelengths, quasi-random force fluctuations became more important, with large
variances that were readily observed in our measurements.
Despite the promising nature of this study, several open questions remain.
Based on our experiment, it was not possible to definitively identify the originof fluctuations that are observed at small wavelengths, but they could be due
to a number of factors, including coupling to finger dynamics, finger ridges, themany surface contact patches involved, or to the presence of unstable stick-slip
motion, or other unstable or chaotic modes of oscillation.
The nonlinear autoregressive models we employed are well suited to investigating the question of predictability of forces from geometry, which was ourgoal, but are of limited utility in supplying or suggesting mechanical interpretations for how these forces arise. In future work, we intend to further investigate
the mechanical origin of finger-surface sliding forces, by relating a system modelof force production to mechanical and geometric parameters. We also intend to
relate finger surface forces to texture perception, in order to determine the extent to which different spatial signal components, including regular and irregularforce components, contribute to surface perception. Finally, this study investigated force generation for a limited range of surfaces, and for a single material
type, interaction speed, and normal force magnitude. In future work, we hope
to explore the generalizability of these results to broader settings.

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