ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

Serina et al. [8] who presented experimental curves for force-displacement and forcecontact
area of the fingertip pulp of the index finger pressing against a flat, rigid surface
obtained in a previous work [14]. The experimental data of this work, corresponding to
displacements from 0 mm to 2.5 mm were fitted to approximated curves following
equations (7) and (8):
F a x
A c x
= ⋅
b
(7)
n = ⋅
d
(8)
where x is the displacement of the finger with respect to the flat surface, F is the contact
force, An is the contact area normalised by the square of the fingertip width and a, b, c
and d are parameters. The following values were obtained for the parameters:
a = 0.052 b= 5.0 c = 0.11 d = 1.0
3.3. Adjustment of parameters for the mEFM
The parameters of the mEFM were obtained using an optimization procedure to
minimize the differences between force-displacement and force-contact area curves
obtained with the model and that obtained from curves fitted to experimental data (Eqs.
7 and 8). This process was performed in Matlab© using the fmincon built-in function.
The parameters f, m, and δref were iterated and the error function to be minimized was
defined as indicated by Eq. 9, were index i corresponds to each of the n different points
of the force-displacement and force-contact area curves (points taken for constant
increments of displacement), F stands for the contact force, A stands for the contact
area, the subscript mod refers to the model result and exp to experimental data. The
error in Eq.9 is a measure of the mean relative error between the experimental data and
the model results. A value of n = 5 was used for the optimisation.
2 2
mod_ i − exp_ i mod_ i − ⎞ exp_ i
n 1 ⎛F F ⎞ ⎛ A A
error = ∑ ⎜ +
2n
⎜
⎟
i= 1 F ⎟
⎜
⎝ exp_ i ⎠ ⎝ Aexp_
i
The contact model requires the definition of the geometry of the contacting bodies and
its relative position and orientation. Also the surface of one of the bodies must be
divided in discrete elements, defining the discrete spring positions in the interference
volume. In this work the geometry of the flat surface was modelled as a flat disc with 15
mm radius, and the geometry of the fingertip was approximated by a toroidal surface
with principal radii 30.6 and 8.7 mm respectively, characteristic values for a male
subject index fingertip. The flat disc was divided using polar coordinates to define a
grid with the same number of divisions in radial than in circumferential direction. The
effect of the grid spacing on the results was tested changing the intrinsic coordinates
increment (Δu=Δv) from 0.01 to 0.2, equivalent to a radial distance between discrete
springs from 0.15 mm to 3 mm.
The Young modulus and Poisson ratio used in Eq. 6 for the fingertip were respectively
0.050 MPa and 0.38. These values were taken as mean values of those obtained by
Shimawaki et al. [10] as optimal to predict experimental deformation of the fingertip
with a finite element model. A Young modulus of 207000 MPa and a Poisson ratio of
⎟
⎠
(9)