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Al-Daccak, M, and Angeles, J, The Calculation of the Volumetric Properties of Sweep-Generated Solids Via Line Integration, ASME, J of Mechanical Design, 115 (1): 110 118, 1993 Angeles, J, Chaoming, Z, Duarte, R, and Ning, H, The Evaluation of Moments of 3-D Solids of Revolution Using Spline Approximations of the Boundary, ASME, J of Mechanical Design, 112: 108 110, 1990 Angeles, J, and Lopez-Caj n, CS, Optimization of Cam Mechanisms, Kluwer Academic Publishers, Dordrecht, 1991 Brand, L, Advanced Calculus, John Wiley, New York, 1965 Chan, YW, and Kok, SS, Optimum Cam Design, Int J Comput Appl Technol, 9 (1): 34 47, 1996 Dierckx, P, Curve and Surface Fitting with Splines, Oxford University Press, New York, 1993 Golub, GH, and Van Loan, CF, Matrix Computations, Johns Hopkins University Press, Baltimore, 1983 Gonz lez-Palacios, MA, and Angeles, J, The Design of a Novel Mechanical Transmission for Speed Reduction, ASME, Journal of Mechanical Design, 121 (4): 538 551, 1999 Kahaner, D, Moler, C, and Nash, S, Numerical Methods and Software, Prentice Hall, Englewood Cliffs, NJ, 1989 Koloc, Z, and V clac k, M, Cam Mechanisms, Elsevier, New York, 1993 Lee, MK, Design for Manufacturability of Speed-Reduction Cam Mechanisms, M Eng Thesis, Department of Mechanical Engineering, McGill University, Montreal, 2001 Marsden, JE, and Tromba, AJ, Vector Calculus, WH Freeman and Company, New York, 1988 Navarro-Mart nez, OR, The Synthesis of Speed-Rectifying Mechanisms for Mechatronic Applications, MEng Thesis, Department of Mechanical Engineering, McGill University, Montreal, 1999 Rogers, DF, An Introduction to NURBS: With Historical Perspective, Academic Press, San Francisco, Calif, 2001 Srinivasan, LN, and Ge, QJ, Fine Tuning of Rational B-Spline Motions, Proc ASME Design Engineering Technical Conferences, September, Sacramento, Calif, 1997

A(xj )

It receives an object of type Triangle, and it passes that object (through base) to this TwoDShape constructor:

public TwoDShape(TwoDShape ob) { Width = obWidth; Height = obHeight; }

INTRODUCTION 218 WORKING LOADS 218 IMPACT FORCES 219 INERTIA FORCES 219 VIBRATORY FORCES 220 FRICTIONAL FORCES 220 SPRING FORCES 222 COMPARISON OF CAM CURVES FOR SPRING DESIGN 223 89 OPERATING FORCES 224 810 CAM SURFACE LOADS 225 811 TORQUE 228 8111 Translating Roller-Follower Torque 228

Part I:

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The key point is that TwoDShape( ) is expecting a TwoDShape object However, Triangle( ) passes it a Triangle object As explained, the reason this works is because a base class reference can refer to a derived class object Thus, it is perfectly acceptable to pass TwoDShape( ) a reference to an object of a class derived from TwoDShape Because the TwoDShape( ) constructor is initializing only those portions of the derived class object that are members of TwoDShape, it doesn t matter that the object might also contain other members added by derived classes

SOLUTION Examine Fig 85 We have laid the cone on its side, so that it extends from x = 0 to x = 6 The upper edge of the gure is the line y = 3 x/2 At position x,

81 82 83 84 85 86 87 88

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A virtual method is a method that is declared as virtual in a base class The defining characteristic of a virtual method is that it can be redefined in one or more derived classes Thus, each derived class can have its own version of a virtual method Virtual methods are interesting because of what happens when one is called through a base class reference In this situation, C# determines which version of the method to call based upon the type of the object referred to by the reference and this determination is made at runtime Thus, when different objects are referred to, different versions of the virtual method are executed In other words, it is the type of the object being referred to (not the type of the reference) that determines which version of the virtual method will be executed Therefore, if a base class contains a virtual method and classes are derived from that base class, then when different types of objects are referred to through a base class reference, different versions of the virtual method are executed You declare a method as virtual inside a base class by preceding its declaration with the keyword virtual When a virtual method is redefined by a derived class, the override modifier is used Thus, the process of redefining a virtual method inside a derived class is called method overriding When overriding a method, the name, return type, and signature of the overriding method must be the same as the virtual method that is being overridden Also, a virtual method cannot be specified as static or abstract (discussed later in this chapter) Method overriding forms the basis for one of C# s most powerful concepts: dynamic method dispatch Dynamic method dispatch is the mechanism by which a call to an overridden method is resolved at runtime, rather than compile time Dynamic method dispatch is important because this is how C# implements runtime polymorphism Here is an example that illustrates virtual methods and overriding:.

8113 Torque-Controlled Cams 232 8114 Torque-Controlled Wrapping Cams 235 812 ROTATABLE INVERSE CAM MECHANISM 236 8121 Kinematic Principles 237 8122 Cam Output Motion 238 8123 Design Procedure 244 8124 Force Closure 245 8125 Quasikinetostatic Analysis 245

// Demonstrate a virtual method using System; class Base { // Create virtual method in the base class public virtual void Who() { ConsoleWriteLine("Who() in Base"); } } class Derived1 : Base { // Override Who() in a derived class public override void Who() { ConsoleWriteLine("Who() in Derived1"); } }

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