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In the foregoing example we have assigned one or more of the displacement derivatives to be zero at the boundary In the dwell-rise-return-dwell cam, other modes of control may be required to optimize the cam curve We can impose the following three modes of control: 1 no control 2 interior control 3 assignment of nite quantities to terminal point displacement derivations The last category, the assignment of nite quantities to terminal point displacement derivations, will not be discussed here For more see Stoddart (1953) and Chen (1982) In no control, at the ends of a symmetrical DRRD cam (Fig 45), the displacement, the velocity, and the acceleration are to be zero However, at the midstation, displacement, of course, is 1, velocity is zero, and acceleration is left loose (no control) In addition, there is zero jerk at the midpoint Thus the boundary conditions for the rise portion of the motion are when q = 0, y = 0, y = 0; y = 0 when q = 1 ( midpoint ), y = 1, y = 0, y = no control, and y = 0 A polynomial y = C0 + C1q + C2q 2 + C3q 3 + C4q 4 + C5q 5 is assumed which reduces to y = C3q 3 + C4q 4 + C5q 5

The first use of extern indicates that a method is provided by unmanaged code that is not part of the program In other words, that method is supplied by external code To declare a method as external, simply precede its declaration with the extern modifier The declaration must not include any body Thus, the general form of an extern declaration is as shown here: extern ret-type meth-name(arg-list); Notice that no braces are used In this use, extern is often used with the DllImport attribute, which specifies the DLL that contains the method DllImport is in the SystemRuntimeInteropServices namespace It supports several options, but for most uses, it is sufficient to simply specify the name of the DLL that contains the extern method In general, extern methods should be coded in C (If you use C++, then the name of the method within the DLL might be altered with the addition of type decorations) To best understand how to use extern methods, it is helpful to work through an example The example consists of two files The first is the C file shown here, which defines a method called AbsMax( ) Call this file ExtMethc

integer Ceil(number input_parameter)

#include <stdlibh> int __declspec(dllexport) AbsMax(int a, int b) { return abs(a) < abs(b) abs(b) : abs(a); }

y=1 y, y''

The AbsMax( ) method compares the absolute values of its two parameters and returns the maximum Notice the use of __declspec(dllexport) This is a Microsoft-specific extension to the C language that tells the compiler to export the AbsMax( ) method within the DLL that contains it You must use this command line to compile ExtMethc

number Cos(number input_parameter)

This creates a DLL file called ExtMethdll Next is a program that uses AbsMax( ):

Substituting the end conditions yields C3 + C4 + C5 = 1 3C3 + 4C4 + 5C5 = 0 6C3 + 24C4 + 60C5 = 0 Solving gives y= 20 3 25 4 8 5 q - q + q 3 3 3 100 3 40 4 q + q 3 3 160 3 q 3 (47)

using System; using SystemRuntimeInteropServices; class ExternMeth { // Here an extern method is declared [DllImport("ExtMethdll")] public extern static int AbsMax(int a, int b); static void Main() { // Use the extern method int max = AbsMax(-10, -20); ConsoleWriteLine(max); } }

Part III:

20:

U n s a f e C o d e , P o i n t e r s , N u l l a b l e Ty p e s , D y n a m i c Ty p e s , a n d M i s c e l l a n e o u s To p i c s

y = 20q 2 -