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

0.3 were used for the flat surface (typical values of steel). A value of 5 mm was used for
h in the Eq. 6.
4. RESULTS AND DISCUSSION
The optimised parameters of the mEFM obtained from the minimisation procedure for
different values of grid spacing (Δu=Δv) are shown in the Table 1, together with the
approximate CPU time for a contact position calculation in a computer with processor
AMD Turion 64 X2, 1.79 GHz and the mean error obtained with Eq. 9. The results
indicate, as expected, a reduction of the error with finer grids, although mean error is
small even for coarse grids. A grid spacing of Δu=Δv=0.05 or even 0.1 are a good
choice for intensive computations with the model, providing quite good results with
computation times far below one second.
Table 1. Optimised parameters for the mEFM
Δu=Δv f m δref (mm) CPU time (s) error (Eq. 9)
0.01 1.471 3.803 0.276 30 0.10%
0.02 1.471 3.803 0.276 4.0 0.12%
0.05 1.474 3.802 0.275 0.6 0.25%
0.1 1.540 3.837 0.313 0.17 0.81%
0.2 1.512 3.900 0.252 0.05 1.42%
Figure 2 shows two plots comparing the experimental data and the results of the model
with Δu=Δv =0.02 represented for constant increments of displacement of 0.1 mm.
Figure 2a shows the contact force versus displacement and figure 2b the contact area
against the contact force. The agreement is quite good.
Force, F (N)
5.00
4.50
4.00
3.50
3.00
2.50
2.00
1.50
1.00
0.50
0.00
0 1 2 3
Displacement, x (mm)
Fexp(N)
Fmod(N)
Area, A (mm^2)
90
80
70
60
50
40
30
20
10
0
0.00 1.00 2.00 3.00 4.00 5.00
Force, F (N)
Aexp(mm2)
Amod(mm2)
(a) (b)
Fig. 2. Comparison of experimental data and model results (Δu=Δv =0.02)
The method proposed in the present work allows a fast computation, interesting when
using a contact model for dynamic grasping simulation with the whole hand, where
finite element simulation would require excessive computation time. The mEFM could
predict accurately contact force and area, with the final accuracy of the model
depending on the quality of the available experimental data. The inclusion of friction or
viscous effects in this model is straightforward. Viscous damping could be modeled by
adding a discrete damper in parallel to each discrete spring in the model. On the other
hand, the Coulomb friction could be modeled with a friction force at each grid node as