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1342 Symbols ai, bi = Cosine and sine term coef cients, respectively, to be determined in the cam pro le function y, Eq (1326) A1, A2, A3 = User-de ned coef cients in Eq (1322) for performance index P Bi = Coef cients of the sine series terms in the desired follower lift function X, Eq (1311) Ci, Di = Cosine and sine term coef cients, respectively, to be determined in the cam pro le function y, Eq (1316) F2 = w2q0/(pw) normalized inverse operating speed F2h, F2l = The high and low speed operating limits, respectively, of F2 for the system being analyzed H = Required follower lift at the end of the cam segment P = Performance index to be minimized to nd the optimum cam lift function y over a range of frequencies, Eq (1325) P = Performance index which when minimized indicates an optimum cam lift function y at one frequency, Eq (1322) r = The follower displacement relative to its static equilibrium position R = The residual vibration the magnitude of r induced by one cycle of the cam pro le as de ned by Eq (135) Rs = The steady state follower vibration induced by the cam pro le t = Time T = pwt/q0, normalized time Ti = Normalized time corresponding to X(Ti) and Xi V1 = Required follower velocity at start of cam segment V2 = Required follower velocity at end of cam segment X(Ti) = Follower displacement at time Ti Xi = Desired follower displacement X at time Ti y = (w 2/w 2)y, normalized cam displacement 1 2 yk = Desired normalized cam displacement y at time Tk, Eq (1323) () = d()/dT x1 = Damping ratio for the cam input x2 = Damping ratio for the follower motion q0 = Angle of cam rotation over which the cam pro le segment being analyzed occurs w = Angular rate of cam rotation w1 = Square root of the coef cient of y determining the follower input, Eq (132) w2 = No-damping follower natural frequency 1343 Tuned Cam Design In many applications a cam operates at a constant or nearly constant speed It is then theoretically possible to completely control the follower motion by using dynamically compensated (ie, tuned) cam designs To do this, the desired motion is speci ed and the required cam pro le determined through the equations of motion We here consider the problem of designing a cam pro le segment to move the follower exactly from one state of position and velocity to another To begin, we start with the usual single-degree-of-freedom linear system of the form.

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Once an interface has been defined, one or more classes can implement that interface To implement an interface, the name of the interface is specified after the class name in just the same way that a base class is specified The general form of a class that implements an interface is shown here: class class-name : interface-name { // class-body } The name of the interface being implemented is specified in interface-name When a class implements an interface, the class must implement the entire interface It cannot pick and choose which parts to implement, for example A class can implement more than one interface When a class implements more than one interface, specify each interface in a comma-separated list A class can inherit a base class and also implement one or more interfaces In this case, the name of the base class must come first in the comma-separated list

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NET . Let's face it—most Microsoft Visual Basic applications have some sort of data access. If your application uses ActiveX Data Objects ( ADO ), you probably.

21/4 4

12:

(132)

The methods that implement an interface must be declared public The reason for this is that methods are implicitly public within an interface, so their implementation must also be public Also, the return type and signature of the implementing method must match exactly the return type and signature specified in the interface definition Here is an example that implements the ISeries interface shown earlier It creates a class called ByTwos, which generates a series of numbers, each two greater than the previous one

// Implement ISeries class ByTwos : ISeries { int start; int val; public ByTwos() { start = 0; val = 0; } public int GetNext() { val += 2; return val; } public void Reset() { val = start; } public void SetStart(int x) { start = x; val = start; } }

( 1) 2 3 3 5

Before we can proceed further, we need to mathematically de ne a vibration criterion The quality of the dynamic behavior of any system is re ected by its displacement relative to its static equilibrium position We de ne the relative vibration as r= In terms of r, Eq (132) becomes

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As you can see, ByTwos implements all three methods defined by ISeries As explained, this is necessary since a class cannot create a partial implementation of an interface Here is a class that demonstrates ByTwos:

// Demonstrate the ByTwos interface using System; class SeriesDemo { static void Main() { ByTwos ob = new ByTwos(); for(int i=0; i < 5; i++) ConsoleWriteLine("Next value is " + obGetNext()); ConsoleWriteLine("\nResetting"); obReset(); for(int i=0; i < 5; i++) ConsoleWriteLine("Next value is " + obGetNext());

(133)

Part I:

ConsoleWriteLine("\nStarting at 100"); obSetStart(100); for(int i=0; i < 5; i++) ConsoleWriteLine("Next value is " + obGetNext()); } }

2x 5 Area = [ x + 2] [x 2] dx = 4x 5 21/4 = 4 21/4 = 32 21/4 5

(134)

To compile SeriesDemo, you must include the files that contain ISeries, ByTwos, and SeriesDemo in the compilation The compiler will automatically compile all three files to create the final executable For example, if you called these files ISeriescs, ByTwoscs, and SeriesDemocs, then the following command line will compile the program:

If you are using the Visual C++ IDE, simply add all three files to your C# project One other point: It is perfectly valid to put all three of these classes in the same file, too The output from this program is shown here:

2 4 6 8 10

Our primary goal is to minimize the vibration levels in the steady state operation of the cam-follower system This level, Rs, is dependent on the magnitude R of r induced by one cycle of y and the amount of damping present The residual vibration (R) is de ned as r 2 (t ) R = r 2 ( t ) + F22

1 3

Starting at 100 Next value is 102 Next value is 104 Next value is 106 Next value is 108 Next value is 110