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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

17:

SOLUTION The y value corresponding to x = 3 is y = f (3) = 11/2 Therefore the point (3, 11/2) lies on the graph of f Similarly, f (4) = 6 so that (4, 6) lies on the graph However, f is unde ned at x = 1, so there is no point on the graph with x coordinate 1 The sketch in Fig 138 was obtained by plotting several points Math Note: Notice that for each x in the domain of the function there is one and only one point on the graph namely the unique point with y value equal to f (x) If x is not in the domain of f , then there is no point on the graph that corresponds to x EXAMPLE 129

Show(); }

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(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)

public int Sum() { return x+y; } public bool IsBetween(int i) { if((x < i) && (i < y)) return true; else return false; } public void Set(int a, int b) { ConsoleWrite("Inside Set(int, int) "); x = a; y = b; Show(); } // Overload Set public void Set(double a, double b) { ConsoleWrite("Inside Set(double, double) "); x = (int) a; y = (int) b; Show(); } public void Show() { ConsoleWriteLine("Values are x: {0}, y: {1}", x, y); } } class AnotherClass { string msg; public AnotherClass(string str) { msg = str; } public void Show() { ConsoleWriteLine(msg); } } class Demo { static void Main() { ConsoleWriteLine("This is a placeholder"); } }

This file contains MyClass, which we have been using in the previous examples It also adds a second class called AnotherClass and a third class called Demo Thus, the assembly

As seen in the previous examples, both linear and rotary microactuators are available to drive microcams and other micromechanical elements Although a very large number of actuators using a variety of transduction principles are available, only electrostatic linear

SOLUTION Observe that, corresponding to x = 3, for instance, there are two y values on the curve Therefore the curve cannot be the graph of a function You Try It: Graph the function y = x + |x| EXAMPLE 130

Part I:

produced by this program will contain three classes Next, compile this file so the file MyClassesexe is produced This is the assembly that will be interrogated The program that will discover information about MyClassesexe is shown here Enter it at this time

and rotary actuators are described here It is interesting to note that it is often not practical to take power out of rotary motors to transmit to other components The problem lies in attaching the other components Recently this problem has been overcome by some indirect means Such a design, called a microengine, is also described in this section 1571 Electrostatic Micromotors Although elastically deformable micron-scale mechanical structures existed even in the 1960s, interest in MEMS began with the development of electrostatic micromotors because they enabled rigid-body motion at the microscale The key development was a surface micromachining batch process used to make an assembled rotor and post without explicit part-by-part assembly This was made possible by a layered construction with structural and sacri cial materials wherein each layer was photolithographically patterned Removal of the sacri cial layer at the end of processing creates the necessary clearance and gaps for the assembled structure This is illustrated in Fig 1513a Using such a freely movable rotor around a xed post, several variations of electrostatic motors were developed Side-

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