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1351 Introduction Any cam design requires trade-offs between characteristics at the cam (such as contact stresses, lateral forces, etc) and at the output (such as vibrations, forces, etc) Any procedure that optimizes only one of these characteristics penalizes the others One method that provides an approach to optimizing several of these characteristics simultaneously is based on optimal control theory (Chew et al, Parts 1 and 2, 1983) Here, we de ne suitable optimality criteria and show how to use them to design systems to optimize several parameters simultaneously 1352 Symbols

public ThreeD() { x = y = z = 0; } public ThreeD(int i, int j, int k) { x = i; y = j; z = k; }

// Overload binary + for ThreeD + ThreeD public static ThreeD operator +(ThreeD op1, ThreeD op2) { ThreeD result = new ThreeD(); /* This adds together the coordinates of the two points and returns the result */ resultx = op1x + op2x; resulty = op1y + op2y; resultz = op1z + op2z; return result; } // Overload binary + for ThreeD + int public static ThreeD operator +(ThreeD op1, int op2) { ThreeD result = new ThreeD(); resultx = op1x + op2; resulty = op1y + op2; resultz = op1z + op2; return result; } // Overload binary + for int + ThreeD public static ThreeD operator +(int op1, ThreeD op2) { ThreeD result = new ThreeD(); resultx = op2x + op1; resulty = op2y + op1; resultz = op2z + op1; return result; } // Show X, Y, Z coordinates public void Show() { ConsoleWriteLine(x + ", " + y + ", " + z); } } class ThreeDDemo { static void Main() { ThreeD a = new ThreeD(1, 2, 3); ThreeD b = new ThreeD(10, 10, 10); ThreeD c = new ThreeD();

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Part I:

ff = compressive force exerted by follower spring on output mass ffe = effective follower spring force = ff - sp hc, h = cam rise and corresponding (total) output rise ks, kf = stiffness of return and follower spring m0, mf = mass of output and of follower p(t) = costate vector sp = preload force of closing spring t0 = natural period of vibration of system t1, t2 = rise, return time t = time x(t) = state variable vector y, yc = displacement of follower output and cam, respectively h = distance between axis of rotation of cam and center of roller, measured in direction of follower motion sc = Hertzian contact stress at cam-follower interface sce = effective cam contact stress q1, q2 = cam rotation during rise, return w = angular frequency of cam rotation w 0 = angular frequency of vibration = 2p/t0 ( ) = derivative with respect to time, t

ConsoleWrite("Here is a: "); aShow(); ConsoleWriteLine(); ConsoleWrite("Here is b: "); bShow(); ConsoleWriteLine(); c = a + b; // ThreeD + ThreeD ConsoleWrite("Result of a + b: "); cShow(); ConsoleWriteLine(); c = b + 10; // ThreeD + int ConsoleWrite("Result of b + 10: "); cShow(); ConsoleWriteLine(); c = 15 + b; // int + ThreeD ConsoleWrite("Result of 15 + b: "); cShow(); } }

Percent Contribution 30%

The output from this program is shown here: