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driven by a motor or other power unit, the torque rating of the prime mover would have to be larger than the value of the maximum torque Figure 89 shows the roller follower comparisons for the simple harmonic, cycloidal, and modi ed sine curves These were obtained by substituting values in Eq (87) for the dwell-rise-dwell cam Figure 89a shows the torque with a constant external load, L and the inertia load m = 0 for a slow-speed cam Figure 89b shows the high-speed system with inertia load m and zero external load, L = 0 It can be seen that the modi ed sine curve is most advantageous when inertia loads dominate, giving the lowest maximum value of torque 8112 Translating Flat-Faced Follower Torque A cam with a reciprocating at-faced follower is shown in Fig 810a Let rb = base circle radius, in Vs = sliding component of velocity, ips m = coef cient of friction between the follower and the cam By the principle of virtual work Tw = Fn y + m Fn Vs or

1 3

C# provides a set of bitwise operators that expand the types of problems to which C# can be applied The bitwise operators act directly upon the bits of their operands They are defined only for integer operands They cannot be used on bool, float, or double They are called the bitwise operators because they are used to test, set, or shift the bits that comprise an integer value Among other uses, bitwise operations are important to a wide variety of systems-level programming tasks, such as analyzing status information from a device Table 4-1 lists the bitwise operators

The bitwise operators AND, OR, XOR, and NOT are &, |, ^, and ~ They perform the same operations as their Boolean logic equivalents described earlier The difference is that the bitwise operators work on a bit-by-bit basis The following table shows the outcome of each operation using 1s and 0s:

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Cycloidal curve Torque,T Modified sine curve Simple harmonic curve Dwell 0 Dwell b/4 Cam angle q (b) Inertia load only (external load L = 0)

In terms of its most common usage, you can think of the bitwise AND as a way to turn bits off That is, any bit that is 0 in either operand will cause the corresponding bit in the outcome to be set to 0 For example 1101 0011 & 1010 1010 -------------------1000 0010

A useful way and one that we encounter frequently in everyday life for generating solids is by revolving a planar region about an axis For example, we can think of a ball (the interior of a sphere) as the solid obtained by rotating a disk about an axis (Fig 812) We can think of a cylinder as the solid obtained by rotating a rectangle about an adjacent axis (Fig 813) We can think of a tubular solid as obtained by rotating a rectangle around a non-adjacent axis (Fig 814)

Result Bitwise AND Bitwise OR Bitwise exclusive OR (XOR) Shift right Shift left One s complement (unary NOT)

FIGURE 89 Torque comparison of cam curves (DRD cam)

Part I:

The following program demonstrates the & by using it to convert odd numbers into even numbers It does this by turning off bit zero For example, the low-order byte of the number 9 in binary is 0000 1001 When bit zero is turned off, this number becomes 8, or 0000 1000 in binary

(88)

// Use bitwise AND to make a number even using System; class MakeEven { static void Main() { ushort num; ushort i; for(i = 1; i <= 10; i++) { num = i; ConsoleWriteLine("num: " + num); num = (ushort) (num & 0xFFFE); ConsoleWriteLine("num after turning off bit zero: " + num + "\n"); } } }

There are two main methods for calculating volumes of solids of revolution: the method of washers and the method of cylinders The rst of these is really an instance of volume by slicing, just as we saw in the last section The second uses a different geometry; instead of slices one uses cylindrical shells We shall develop both technologies by way of some examples

The output from this program is shown here:

From the velocity diagram, Fig 810b, it is seen that the sliding component velocity Vs = w ( y + rb ) Substituting Eq (89) into Eq (88) gives y T = Fn + m ( y + rb ) w (810) (89)

num: 1 num after turning off bit zero: 0 num: 2 num after turning off bit zero: 2 num: 3 num after turning off bit zero: 2 num: 4 num after turning off bit zero: 4 num: 5 num after turning off bit zero: 4 num: 6 num after turning off bit zero: 6 num: 7 num after turning off bit zero: 6 num: 8 num after turning off bit zero: 8 num: 9 num after turning off bit zero: 8

4:

A solid is formed by rotating the triangle with vertices (0, 0), (2, 0), and (1, 1) about the x-axis See Fig 815 What is the resulting volume

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