Page 132 - Human Inspired Dexterity in Robotic Manipulation

130 Human Inspired Dexterity in Robotic Manipulation

Object (tofu) Fluid fingertip
Object Fingertip
f fingertip®object k 1

k 2 f object®fingertip

x 2 x 1
Fig. 7.19 Model of Interaction between the fluid fingertip and soft object (tofu) [3].

viscosity was neglected because of the low speed used in the test. Let k 1
and k 2 be the stiffness of the fluid fingertip and the object, respectively;
x 1 and x 2 denote the displacements of the fingertip and the object, respec-
tively; f object!fingertip be the force applied to the fingertip by the object,
and f fingertip!object be the force applied to the object by the fingertip. Then,
we have

ð
f object!fingertip ¼ k 1 x 1 x 2 Þ (7.3)
f fingertip!object ¼ k 2 x 2 (7.4)
Here, f object!fingertip ¼ f fingertip!object , and then,

k 2
x 1 ¼ 1+ x 2 (7.5)
k 1
It should be noted that k 1 and k 2 change with the change in displace-
ments x 1 and x 2 . Here, it is supposed that initially, the stiffness of the fluid
fingertip is greater than that of the object (when there is no contact). In this
case, k 1 ≫ k 2 . Then, Eq. (7.5) becomes

k 2
x 1 ¼ 1+ x 2 ffi x 2 : (7.6)
k 1
Eq. (7.6) indicates that the fingertip displacement, x 1 , corresponds to the
deformation of the tofu, x 2 , for example, there is no deformation in the fin-
gertip and it behaves like a rigid object Fig. 7.20. This state is denoted by
Phase 1. In observing the captured image in Phase 1, it was found that there
was no deformation of the fingertip at that phase (note that only visible parts
were examined). Therefore, at Phase 1, fluid pressure does not correspond to
the contact pressure of the object, and it cannot be used for observing the