handbook of modern sensors

324 9 Force, Strain, and Tactile Sensors
Table 9.1. Mechanical Units
System of Units Force Mass Acceleration
SI Newton (N) kilogram (kg) m/s 2
British Pound (lb) Slug ft/s 2
Note: Boldface indicates base units.
In the British and U.S. Customary systems of units, however, force (lb), length
(ft), and time (s) are selected as the base units. The mass unit is defined as the mass
which is accelerated at 1 ft/s 2 when it is subjected to force of 1 lb. The British unit of
mass is slug. The mechanical units are as shown in Table 9.1.
Newton’s third law establishes the principle of a mutual interaction between two
bodies: To every action there is always opposed an equal reaction; or, the mutual
actions of two bodies upon each other are always equal, and directed to contrary
parts.
In engineering measurements, it is often necessary to know the density of a
medium, which is amount of matter per unit volume. Density is defined through
mass m and volume V as
ρ = m V . (9.2)
The unit of density is kg/m 3 or lb/ft 3 (British system). Densities of some materials
are given in Table A.12 of the Appendix.
The SI unit of force is one of the fundamental quantities of physics. The measurement
of force is required in mechanical and civil engineering, for weighing objects,
designing prosthesis, and so forth. Whenever pressure is measured, it requires the
measurement of force. It could be said that force is measured when dealing with
solids, whereas pressure is measured when dealing with fluids (i.e., liquids or gases);
that is, force is considered when action is applied to a spot, and pressure is measured
when force is distributed over a relatively large area.
Force sensors can be divided into two classes: quantitative and qualitative. A
quantitive sensor actually measures the force and represents its value in terms of
an electrical signal. Examples of these sensors are strain gauges and load cells. The
qualitative sensors are the threshold devices which are not concerned with a good
fidelity of representation of the force value. Their function is merely to indicate
whether a sufficiently strong force is applied; that is, the output signal indicates when
the force’s magnitude exceeds a predetermined threshold level. An example of these
detectors is a computer keyboard, on which a key makes a contact only when it is
pressed sufficiently hard. The qualitative force sensors are frequently used for the
detection of motion and position, as described in Chapter 7. A pressure-sensitive
floor mat and a piezoelectric cable are examples of the qualitative pressure sensors.
The various methods of sensing force can be categorized as follows [2]:
1. By balancing the unknown force against the gravitational force of a standard
mass
2. By measuring the acceleration of a known mass to which the force is applied