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The stress parameter, sce, is that fraction of the Hertzian cam contact stress resulting from the effective follower-spring force Ffe, ie, the preload effect has been eliminated as was the case in the minimization of the follower-spring force The quadratic formulation in Ffe is used to ensure that a negative value for force Ffe is undesirable

Part I:

x 2/3 1/3 + = x 1 x+2 (x 1)(x + 2)

By default, enumerations are based on type int, but you can create an enumeration of any integral type, except for type char To specify a type other than int, put the desired type after the enumeration name, separated by a colon For example, this statement makes Apple an enumeration based on byte:

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1356 Formulation of Optimization Problem At this stage it is possible to de ne the problem of the optimization of a high-speed cam-follower system using Eqs (1335) and (1340), with weight factors Wi (i = 1, 2, 3) as follows: Minimize

enum Apple : byte { Jonathan, GoldenDel, RedDel, Winesap, Cortland, McIntosh };

At first glance you might think that enumerations are an interesting but relatively unimportant part of C#, yet this is not the case Enumerations are very useful when your program requires one or more specialized symbols For example, imagine that you are writing a program that controls a conveyor belt in a factory You might create a method called Conveyor( ) that accepts the following commands as parameters: start, stop, forward, and reverse Instead of passing Conveyor( ) integers, such as 1 for start, 2 for stop, and so on, which is error-prone, you can create an enumeration that assigns words to these values Here is an example of this approach:

2 4 0 2+ 1 0 6

(1342)

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// Simulate a conveyor belt using System; class ConveyorControl { // Enumerate the conveyor commands public enum Action { Start, Stop, Forward, Reverse }; public void Conveyor(Action com) { switch(com) { case ActionStart: ConsoleWriteLine("Starting conveyor"); break; case ActionStop: ConsoleWriteLine("Stopping conveyor"); break;

12:

subject to the system Eq (1330) and boundary conditions Eq (1332) To design for desirable output characteristics, weight factor W3 may be set to zero To design for favorable cam characteristics, weight factor W3 is chosen as large as necessary relative to weight factors W1 and W2, with W2 nonzero Weight factor W2 must be nonzero to provide suf cient boundary conditions to ensure continuity of the cam acceleration function When weight factor W3 does not vanish, the problem cannot be solved by linear methods due to the nonlinearity of parameter NF It can, however, be solved using optimal control theory

case ActionForward: ConsoleWriteLine("Moving forward"); break; case ActionReverse: ConsoleWriteLine("Moving backward"); break; } } } class ConveyorDemo { static void Main() { ConveyorControl c = new ConveyorControl(); cConveyor(ConveyorControlActionStart); cConveyor(ConveyorControlActionForward); cConveyor(ConveyorControlActionReverse); cConveyor(ConveyorControlActionStop); } }

The output from the program is shown here:

1357 Introduction to System Optimization Having formulated an optimization criterion, we are now faced with its evaluation Various linear techniques have been used in the design optimization of high-speed cam-follower systems Linear methods are certainly preferable when applicable However, for the synthesis of cam-follower systems with nonlinearities such as contact stresses, pressure angles, cam curvature, and follower guide friction, more general methods are needed In this section the nonlinearities are handled by means of optimal-control theory Although this method is powerful, it requires a well-de ned problem In certain instances an optimal solution does not exist The solution of an optimization problem using optimal control theory always results in a two-point boundary-value problem Such problems can be tedious and time consuming Except for simple linear problems, the vast majority require a numerical solution Such a procedure will be described

Because Conveyor( ) takes an argument of type Action, only the values defined by Action can be passed to the method For example, here an attempt is made to pass the value 22 to Conveyor( ):

cConveyor(22); // Error!

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