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on the interval ( /2, /2) At the endpoints of the interval, and only there, the function Sin x takes the values 1 and +1 Therefore Sin x is increasing on its entire domain So it is one-to-one Furthermore the Sine function assumes every value in the interval [ 1, 1] Thus Sin : [ /2, /2] [ 1, 1] is one-to-one and onto; therefore f (x) = Sin x is an invertible function We can obtain the graph of Sin 1 x by the principle of re ection in the line y = x (Fig 616) The function Sin 1 : [ 1, 1] [ /2, /2] is increasing, one-to-one, and onto

64 CAM RADIUS OF CURVATURE 169 641 Radius of Curvature 169 642 Undercutting of Cam Roller Follower 170 643 Undercutting of Cam Flat-Faced Follower 173 644 Hub Design 173 65 SUMMARY 174

The output is shown here:

23:

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A = follower overhang, in B = follower bearing length, in dh = hub diameter, in ds = shaft diameter, in F = force normal to cam pro le, lb l = distance from force Fn to follower axis, in Lo = external load on follower N1N2 = forces normal to follower stem, lb QoQb = reactions at pivot point Q, in r = radius to cutter center in rb = base circle radius, in Rg = cutter or grinder radius, in Rr = roller follower radius, in s = follower rise, in (other chapters usually shown as y) T = total torque on system, lb/in W = radius of follower stem, in a = pressure angle, deg am = maximum pressure angle, deg c = angle for radius r, rad k = distance from normal force Fn to pivot point Q, in m = coef cient of friction mc = coef cient of friction between cam and at-faced follower r = radius of curvature, in rc = radius of curvature of cam pro le, in rk = radius of curvature of pivot curve, in q = cam angle for rise, s, rad

Decrement Thread is waiting for the mutex In Increment Thread, SharedResCount is 1 In Increment Thread, SharedResCount is 2 In Increment Thread, SharedResCount is 3 In Increment Thread, SharedResCount is 4 In Increment Thread, SharedResCount is 5 Increment Thread releases the mutex Decrement Thread acquires the mutex In Decrement Thread, SharedResCount is 4 In Decrement Thread, SharedResCount is 3 In Decrement Thread, SharedResCount is 2 In Decrement Thread, SharedResCount is 1 In Decrement Thread, SharedResCount is 0 Decrement Thread releases the mutex

_ F/2

As the output shows, access to SharedResCount is synchronized, with only one thread at a time being able to change its value To prove that the Mtx mutex was needed to produce the preceding output, try commenting out the calls to WaitOne( ) and ReleaseMutex( ) in the preceding program When you run the program, you will see the following sequence (the actual output you see may vary):

This chapter introduces the physical factors and forces involved with the development of the proper cam pro le shape This chapter is complemented by Chap 7, which contains algorithms for the establishment of the cam pro le including manufacturing information The three basic factors for this kinematic study are: cam pro le cam pressure angle cam curvature In the past the cam pro le was developed by observing the cam shape from the graphical construction method explained below

In In In In In In In In In Increment Decrement Increment Decrement Increment Decrement Increment Decrement Increment Thread, Thread, Thread, Thread, Thread, Thread, Thread, Thread, Thread, SharedResCount SharedResCount SharedResCount SharedResCount SharedResCount SharedResCount SharedResCount SharedResCount SharedResCount is is is is is is is is is 1 0 1 0 1 0 1 0 1

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