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public override bool Equals(object v) public bool Equals(float v) public override int GetHashCode( ) public TypeCode GetTypeCode( ) public static bool IsInfinity(float v) public static bool IsNaN(float v)

Part I:

The resulting curve (3) in Fig 46 is the displacement y = 490q 5 - 2968q 6 + 7820q 7 - 11235q 8 + 9170q 9 - 4004q 10 + 728q 11 which has a peak acceleration of 84 As noted in this section, the polynomial techniques can be employed to satisfy any motion requirement The designer has great exibility in the nal choice Matthew (1979) has demonstrated the use of seventh-degree polynomials to minimize cam pressure angles, stresses, and torque for the ultimate nal design choice A trade-off is always necessary between the various criteria and speci cations Also, in high-speed action, the higher-order polynomials bring with them possible resonances with the follower system This will be considered in the dynamic analysis of the later chapters

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SOLUTION The point X is 1 unit to the right of the y-axis and 3 units below the x-axis Therefore its coordinates are (1, 3) The point Y is 2 units to the left of the y-axis and 1 unit above the x-axis Therefore its coordinates are ( 2, 1)

The general form of a class declaration that inherits a base class is shown here: class derived-class-name : base-class-name { // body of class } You can specify only one base class for any derived class that you create C# does not support the inheritance of multiple base classes into a single derived class (This differs from C++, in which you can inherit multiple base classes Be aware of this when converting C++ code to C#) You can, however, create a hierarchy of inheritance in which a derived class becomes a base class of another derived class (Of course, no class can be a base class of itself, either directly or indirectly) In all cases, a derived class inherits all of the members of its base class This includes instance variables, methods, properties, and indexers A major advantage of inheritance is that once you have created a base class that defines the attributes common to a set of objects, it can be used to create any number of more specific derived classes Each derived class can precisely tailor its own classification For example, here is another class derived from TwoDShape that encapsulates rectangles:

// A derived class of TwoDShape for rectangles class Rectangle : TwoDShape { // Return true if the rectangle is square public bool IsSquare() { if(Width == Height) return true; return false; } // Return area of the rectangle public double Area() { return Width * Height; } }

Curve shape adjustment can be accomplished by changing the exponents of the polynomial This procedure at best is one of trial and error with some degree of predictability For example, the fth-order polynomial can have the powers 3-4-5, 3-5-7, 3-6-9, etc The seventh-order polynomial can have powers of 4-5-6-7, 4-6-8-10, 4-8-12-16, 4-7-10-13, and so forth Figures 47 and 48 show the progressive changes of the polynomials Note that the higher the powers, the greater is the maximum acceleration that shifts toward the start of the displacement curve Polynomial curves having exponents as high as 50 have been used experimentally for automotive cams (see Thoren et al, 1952) Figure 49 shows some high-order DRRD polynomial curves The rise boundary conditions are when q = 0, y = 0, y = 0, y = 0, y = 0, d4y =0 dq 4 (49)

The Rectangle class includes TwoDShape and adds the methods IsSquare( ), which determines if the rectangle is square, and Area( ), which computes the area of a rectangle

The point Z is 5 units to the right of the y-axis and 4 units above the x-axis Therefore its coordinates are (5, 4) The point W is 6 units to the left of the y-axis and 5 units below the x-axis Therefore its coordinates are ( 6, 5) You Try It: Sketch the points (3, 5), (2, 4), ( , /3) on a set of axes Sketch the set {(x, y): x = 3} on another set of axes EXAMPLE 16

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