Page 64 - The Mechatronics Handbook

humans come into contact with water, but on a human scale the associated forces are typically insignif-
icant. The world in which humans live is governed by the same forces as the world in which these insects
live, but the forces are present in very different proportions. This is due in general to the fact that inertial
forces typically act in proportion to volume, and surface forces typically in proportion to surface area.
Since volume varies with the third power of length and area with the second, geometrically similar but
smaller objects have proportionally more area than larger objects.
Exact scaling relations for various types of forces can be obtained by incorporating dimensional analysis
3
techniques [1–5]. Inertial forces, for example, can be dimensionally represented as F i = rL x ˙˙ , where F i
is a generalized inertia force, ρ is the density of an object, L is a generalized length, and x is a displacement.
This relationship forms a single dimensionless group, given by

∏ = ----------
F i
3
pL x ˙˙
Scaling with geometric and kinematic similarity can be expressed as

L s x s t s
----- = ---- = N, --- = 1
L o x o t o
where L represents the length scale, x the kinematic scale, t the time scale, the subscript o the original
system, and the s represents the scaled system. Since physical similarity requires that the dimensionless
4
group (P) remain invariant between scales, the force relationship is given by F s /F o = N , assuming that
4
the intensive property (density) remains invariant (i.e., ρ s = ρ o ). An inertial force thus scales as N , where
N is the geometric scaling factor. Alternately stated, for an inertial system that is geometrically smaller
4
by a factor of N, the force required to produce an equivalent acceleration is smaller by a factor of N . A
2
x ˙
similar analysis shows that viscous forces, dimensionally represented by F v = µL , scale as N , assuming
2
the viscosity µ remains invariant, and elastic forces, dimensionally represented by F e = ELx, scale as N ,
assuming the elastic modulus E remains invariant. Thus, for a geometrically similar but smaller system,
inertial forces will become considerably less significant with respect to viscous and elastic forces.
General Mechanisms of Electromechanical Transduction
The fundamental mechanism for both sensing and actuation is energy transduction. The primary forms
of physical electromechanical transduction can be grouped into two categories. The first is multicomponent
transduction, which utilizes “action at a distance” behavior between multiple bodies, and the second is
deformation-based or solid-state transduction, which utilizes mechanics-of-material phenomena such as
crystalline phase changes or molecular dipole alignment. The former category includes electromagnetic
transduction, which is typically based upon the Lorentz equation and Faraday’s law, and electrostatic
interaction, which is typically based upon Coulomb’s law. The latter category includes piezoelectric effects,
shape memory alloys, and magnetostrictive, electrostrictive, and photostrictive materials. Although mate-
rials exhibiting these properties are beginning to be seen in a limited number of research applications,
the development of micro-scale systems is currently dominated by the exploitation of electrostatic and
electromagnetic interactions. Due to their importance, electrostatic and electromagnetic transduction is
treated separately in the sections that follow.

Sensor and Actuator Transduction Characteristics

Characteristics of concern for both microactuator and microsensor technology are repeatability, the
ability to fabricate at a small scale, immunity to extraneous influences, sufficient bandwidth, and if
possible, linearity. Characteristics typically of concern specifically for microactuators are achievable force,
displacement, power, bandwidth (or speed of response), and efficiency. Characteristics typically of con-
cern specifically for microsensors are high resolution and the absence of drift and hysteresis.

©2002 CRC Press LLC