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The function Csc x is de ned to be the restriction of Csc x to the set [ /2, 0) (0, /2] The graph is exhibited in Fig 625 Then Csc x is one-to-one For these values of the x variable, the sine function takes on all values in the interval [ 1, 1] except for 0 Therefore Csc takes on all values greater than or equal to 1 and all values less than or equal to 1; Csc 1 therefore has domain ( , 1] [1, ) and takes values in [ 1, 0) (0, 1] (Fig 626)

The manual cam layout method described in this section is used primarily for information In general, designers use CAD digitized packages to generate the cam pro le on the drawing Cam-follower designs begin with crude sketches using cartesian coordinates, as in Fig 122 In this gure we see that the cam-follower action may be considered equivalent to a wedge action of in nite length The wedge is shown moving at a constant speed from right to left to raise the follower a maximum distance, h The rst cycle of the follower movement is the curve ABCA continued to B C A B C A B , and so forth A radial cam may be considered a wedge rolled in the plane of the paper having a length of one cycle (wedge cam ABCA ) equal to the

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// Demonstrate ArrayList using System; using SystemCollections; class ArrayListDemo { static void Main() { // Create an array list ArrayList al = new ArrayList(); ConsoleWriteLine("Initial number of elements: " + alCount); ConsoleWriteLine(); ConsoleWriteLine("Adding 6 elements"); // Add elements to the array list alAdd('C');

24:

circumference of a circle A cylindrical cam is one in which the wedge ABCA is twisted in a plane perpendicular to the paper with the length of the wedge cam ABCA equal to the circumference of the cylinder The contour AB, which is the rise portion of the cam, should not be too steep since this will produce jamming of the translating follower on the sides This curve slope can be reduced by using a longer cam length for the same rise of the follower, h A larger cam results Also the speed of the wedge is pertinent to later investigation of the dynamics of the cam-follower action Let s construct a simple radial cam with a roller follower having a given rise in a given time The means for nding the cam shape is one of inversion, that is, the pro le is developed by xing the cam and moving the follower around the cam at its respective relative positions If we used an in nite number of points, the envelope of the cam contour would be formed Also, the layout of a roller follower requires plotting the center of the roller and then drawing the curve tangent to the rollers For clarity, only a few points will be shown

ConsoleWriteLine(y + " "); } ConsoleWriteLine(); x = 1; ConsoleWriteLine("Series generated using y = x + ++x;"); for(i = 0; i < 10; i++) { y = x + ++x; // prefix ++ ConsoleWriteLine(y + " "); } ConsoleWriteLine(); } }

_ F/2

The output is shown here:

Series generated using y = x + x++; 2 4 6 8 10 12 14 16 18 20 Series generated using y = x + ++x; 3 5 7 9 11 13 15 17 19 21

follows: 1 rise of 5/8 in in 90 degrees of rotation 2 fall of 5/8 in in 90 degrees of cam rotation 3 dwell for the last 180 degrees of the cam cycle The procedure (Fig 123), which consists of xing the cam and moving the follower around it, is: 1 Draw two perpendicular axes locating the cam center at A 2 Assume the location of the lowest point of the roller-follower center at point 0, on one of the radial lines 3 The maximum rise, point 1, should be shown 5/8 in above point 0 4 With the cam center A and radius A1, swing an arc until it intersects line A1 , which is 90 degrees opposite the direction of cam rotation 5 Draw a smooth curve through points 0 and 1 , providing the rise portion of the cam 6 Draw roller diameters and then a tangent curve to the rollers This is the cam surface 7 Check the steepness of the curve If at any point it is excessive, redesign with larger radii A0 and A1, which means a larger cam 8 Repeat the process for the 90-degree fall portion 1 2 The last 180 degrees of cam action 2 0 is a dwell, a constant radial distance

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