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another component If a wrong decision is made during the sequence, the pin gets stuck in the wheel This device is equipped with an antireverse spring so that an incorrect sequence cannot be corrected by trial and error A modi ed design with a translating groove cam is discussed next 1564 Micromechanical Lock II Translating Groove Cam The mechanical lock shown in Fig 1510a is more sophisticated than the one just discussed It has a slider in which there is a groove cam The slider also has rack teeth so that it can be actuated A pin runs in the groove and is actuated with an electrostatic comb drive The slider is engaged with an antireverse pinion to prevent backtracking The independent actuations of the slider and the pin are coordinated to permit the slider to move its entire course and to release another component A detailed view of the groove cam is shown in Fig 1510b 1565 Countermeshing Gear Discriminator Device Another MEMS device that acts like a mechanical lock is the gear discriminator shown in Fig 1511a It has three levels of gears with some teeth missing on each of them and the remaining teeth selectively placed These gears countermesh in the sense that the meshing gear teeth approach each other from opposite directions, unlike conventional gears where the approach for both teeth is in the same direction Consequently, they need

In calculus, the set S (called the domain of the function) and the set T (called the range of the function) will usually be sets of numbers; in fact they will often consist of one or more intervals in R The rule f will usually be given by one or more formulas Many times the domain and range will not be given explicitly These ideas will be illustrated in the examples below

FIGURE 1510 (b) Close-up view of the translating groove cam (courtesy, Sandia National Labs MEMS, S&T Department, wwwmemssandiagov)

or in mathematical symbolism,

Let S = R, T = R, and let f ( x) = x 2 This is mathematical shorthand for the rule ``assign to each x S its square'' Determine whether f : R R is a function

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FIGURE 1511 (b) Close-up view of teeth in the discriminating gears (courtesy, Sandia National Labs MEMS, S&T Department, wwwmemssandiagov)

to be rotated independently in a speci c sequence to prevent interference between teeth located at the same level Only when the gears are rotated according to a speci c code will this device unlock and activate another component This device also contains an antireverse mechanism to prevent backward rotation so that a code cannot be corrected and tried again if it is entered incorrectly Thus, this gear discriminator device interprets a digital code as angular rotations of the countermeshing gears in a fail-safe manner 1566 Microvibromotor with an Inverse Cam Researchers at the Berkeley Sensor and Actuator Center have applied the concept of a vibromotor to the microscale One version of a microvibromotor is shown schematically in Fig 1512a A scanning electron microscopic image of a fabricated prototype is shown in Fig 1512b Although it resembles the traditional cam-follower arrangement, its operating principle is different Here, the follower and the cam are not in continuous contact; the follower drives the cam (ie, the rotor) by impacting it The follower is given an upward as well as sideward motion with the help of two translating inputs at either end of a clamped-clamped beam When the two inputs are given appropriately, point A, where the follower is attached to the beam, experiences both transverse displacement and rotation This motor has also shown to be operational in both clockwise and counterclockwise rotations of the rotor with slight modi cations and additions of more followers in other directions The two translating inputs for this device shown in Fig 1512a and b come from

We see that f is a function since it assigns to each element of S a unique element of T ---namely its square

(b) FIGURE 1512 (a) Schematic of the angular microvibromotor (b) Scanning electron microscope picture of a prototype (courtesy of Abraham P Lee, National Institute of Standards and Technology)

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