# Structure and Sensing Theory

>> BACK

1. STRUCTURE

The structure of the sensor element which acquires the contact force and the cotnact area is very simple as shown Fig.1.
There are soft and hard layers of urethane foam, and three pieces of conductive fabric.
The area of the conductive piece (3 cm × 3 cm) is the sensing area of the sensor element.
We measure the capacitances between the conductive pieces (C1 and C2).
 Fig.1 Cross-section of sensor element. The soft and hard layers are 2 mm in thickness, and the side length of the conductive piece is 3 cm. We measure the capacitances C1 and C2.

2. SENSING THEORY

We show that the structure enables us to obtain the contact force and the contact area by simulation.
 Fig.2 Supposed surface stress distribution. We suppose a constant surface stress distribution σ loaded to the surface of the sensor element verticallyin a contact field S. Parameters that we want to obtain are F and S.

 Fig.3 Nonlinear elasticity. Urethane foam has its displacement limit because it is very soft (Young's modulus and Poisson's ratio are small). We assume that the nonlinear elasticity of urethane foam is the entropy elasticity* expressed as . The soft layer (λ1) is easily compressed to its displacement limit.

 Fig.4 Result of simulation (Capacitance variations). Owing to the nonlinear elasticity and the hardness difference, (ΔC1, ΔC2)s draw trajectories which vary with D. And the larger F becomes, the larger the distance between the origin point and (ΔC1, ΔC2) is. By mapping from (ΔC1, ΔC2) to (F, S) in advance, we can obtain F and S simultaneously. (D means the diameter of the circular area S.)

* Entropy elasticity:
The description derived from the elasticity of rubber.
REFERENCE: G. R. Strobl: The Physics of Polymers: Concepts for Understanding Their Structures and Behavior, Chap. 7, Springer, 1997.

Release: 1 Apr. 2005
Update: 22 Sep. 2005
Takayuki Hoshi: star(at)alab.t.u-tokyo.ac.jp