Page 67 - The Mechatronics Handbook

Examples of harmonic-drive motors are those by Mehragany et al. [17,18], Price et al. [19], Trimmer
and Jebens [20,21], and Furuhata et al. [22]. Electrostatic microactuators remain a subject of research
interest and development, and as such are not yet available on the general commercial market.
Electromagnetic Actuation

Electromagnetic actuation is not as omnipresent at the micro-scale as at the conventional-scale. This
probably is due in part to early skepticism regarding the scaling of magnetic forces, and in part to the
fabrication difficulty in replicating conventional-scale designs. Most electromagnetic transduction is
based upon a current carrying conductor in a magnetic field, which is described by the Lorentz equation:

dF = Idl B
x
where F is the force on the conductor, I is the current in the conductor, l is the length of the conductor,
and B is the magnetic flux density. In this relation, the magnetic flux density is an intensive variable and
thus (for a given material) does not change with scale. Scaling of current, however, is not as simple. The
resistance of wire is given by
pl
R = ----
A
where ρ is the resistivity of the wire (an intensive variable), l is the length, and A the cross-sectional area.
If a wire is geometrically decreased in size by a factor of N, its resistance will increase by a factor of N.
2
Since the power dissipated in the wire is I R, assuming the current remains constant implies that the
power dissipated in the geometrically smaller wire will increase by a factor of N. Assuming the maximum
power dissipation for a given wire is determined by the surface area of the wire, a wire that is smaller by
2
a factor of N will be able to dissipate a factor of N less power. Constant current is therefore a poor
assumption. A better assumption is that maximum current is limited by maximum power dissipation,
which is assumed to depend upon surface area of the wire. Since a wire smaller by a factor of N can
2
dissipate a factor of N less power, the current in the smaller conductor would have to be reduced by a
3/2
factor of N . Incorporating this into the scaling of the Lorentz equation, an electromagnetic actuator
5/2
that is geometrically smaller by a factor of N would exert a force that is smaller by a factor of N .
Trimmer and Jebens have conducted a similar analysis, and demonstrated that electromagnetic forces
2 5/2
scale as N when assuming constant temperature rise in the wire, N when assuming constant heat
3
(power) flow (as previously described), and N when assuming constant current density [23,24]. In any
of these cases, the scaling of electromagnetic forces is not nearly as favorable as the scaling of electrostatic
forces. Despite this, electromagnetic actuation still offers utility in microactuation, and most likely scales
more favorably than does inertial or gravitational forces.
Lorentz-type approaches to microactuation utilize surface micromachined micro-coils, such as the one
illustrated in Fig. 5.5. One configuration of this approach is represented by the actuator of Inoue et al. [25],

FIGURE 5.5 Schematic of surface micromachined
microcoil for electromagnetic actuation.

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