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FIGURE 5.6  Microcoil array for planar positioning of a permanent micromagnet, as described by Inoue et al. [25].
                                 Each coil produces a field, which can either attract or repel the permanent magnet, as determined by the direction
                                 of current. The magnet does not levitate, but rather slides on the insulated surface.


















                                 FIGURE 5.7  Cantilevered microcoil flap as described by Liu et al. [26]. The interaction between the energized coil
                                 and the stationary electromagnet deflects the flap upward or downward, depending on the direction of current
                                 through the microcoil.

                                 which utilizes current control in an array of microcoils to position a permanent micro-magnet in a plane,
                                 as illustrated in Fig. 5.6. Another Lorentz-type approach is illustrated by the actuator of Liu et al. [26],
                                 which utilizes current control of a cantilevered microcoil flap in a fixed external magnetic field to effect
                                 deflection of the flap, as shown in Fig. 5.7. Liu reported deflections up to 500 µm and a bandwidth of
                                 approximately 1000 Hz [26]. Other examples of Lorentz-type nonrotary actuators are those by Shinozawa
                                 et al. [27], Wagner and Benecke [28], and Yanagisawa et al. [29]. A purely magnetic approach (i.e., not
                                 fundamentally electromagnetic) is the work of Judy et al. [30], which in essence manipulates a flexure-
                                 suspended permanent micromagnet by controlling an external magnetic field.
                                   Ahn et al. [31] and Guckel et al. [32] have both demonstrated planar rotary variable-reluctance type
                                 electromagnetic micromotors. A variable reluctance approach is advantageous because the rotor does not
                                 require commutation and need not be magnetic. The motor of Ahn et al. incorporates a 12-pole stator and
                                 10-pole rotor, while the motor of Guckel et al. utilizes a 6-pole stator and 4-pole rotor. Both incorporate
                                 rotors of approximately 500 µm diameter. Guckel reports (no load) rotor speeds above 30,000 rev/min, and
                                 Ahn estimates maximum stall torque at 1.2 µN m. As with electrostatic microactuators, microfabricated
                                 electromagnetic actuators likewise remain a subject of research interest and development and as such are
                                 not yet available on the general commercial market.

                                 5.3 Microsensors

                                 Since microsensors do not transmit power, the scaling of force is not typically significant.  As with
                                 conventional-scale sensing, the qualities of interest are high resolution, absence of drift and hysteresis,
                                 achieving a sufficient bandwidth, and immunity to extraneous effects not being measured.
                                   Microsensors are typically based on either measurement of mechanical strain, measurement of
                                 mechanical displacement, or on frequency measurement of a structural resonance. The former two types

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