through; the hole is 21" diameter, and the key is "

square.

72. The proportions of the several parts are as follow:

73. THE change of rotary or circular motion into reciprocating rectilinear motion by means of the Crank, the Eccentric, and Cams.

The Crank. In this chapter we shall consider the change of motion as stated above, taking for the first example the crank and connecting-rod, which is the most common arrangement used. The crank consists of an arm AC, fig. 133, Plate XVIII., which turns about a fixed centre C; the end A therefore describes a circle at each revolution of the arm. Attached to A is one end A of a connecting-rod Aa, while its other end a moves in the straight line baCD. In this example we shall consider the crank to be the driver, because then the change is from circular to rectilinear motion; and we shall suppose it to be turning in the direction indicated by the arrow. For every revolution of the crank-arm AC, the end a of the connecting-rod moves through the space bd +db; or, in other words, if the crank starts from the initial position CD and moves in the direction DAB, and

a starts from d moving in the direction db, at the same instant that A arrives at B, a will arrive at b; for the other half revolution B3D of AC, a will move from b to d. The distance bd (BD) is termed the stroke of the crank, and is equal to 2AC. A being the centre of the crank-pin, the circle DAB is called the path of the crankpin; the length of the path of the crank-pin is nearly 3.1416 times the length of the stroke.

74. Owing to the obliquity of the crank AC, which varies for every new position on each side of BD, except the positions BC, DC, the end a of the connecting-rod aA does not pass through equal spaces for equal arcs described by the crank. A common problem is to find the position of a for any given position of A, and vice versa. By taking a number of positions for A we can find corresponding positions for a, and thus show the varying motion of a resulting from the regular motion of A.

Divide the circumference of the semicircle B3D, fig. 133, into any convenient number of equal parts, say six; and from 1, 2, 3, &c., as centres with a radius equal to the length of the connecting-rod Aa, describe arcs of circles cutting bd in 1, 2, 3, &c. ; then the distances between b—1, 1—2, 2—3, 3—4, 4—5, 5-d, represent the spaces moved through by the end a of the connecting-rod for the equal arcs B-1, 1-2, 2—3, 3—4, 4—5, 5—D, described by the crank. The motion of a when it is in the position b is 0; in passing from 6 to 3 it increases from 0 to its maximum; and from 3 to d it decreases to 0; the point c marks the middle position of the path of the sliding end a. This variable motion of a, especially its decreasing at each end of the path, is of great advantage in some kinds of machinery.

75. In the steam-engine the reverse of the motion just described takes place; the sliding piece a, connected to the piston-rod of the engine, becomes the driver; the change is therefore from rectilinear to rotary motion.

76. In figs. 134, 135, Plate XVIII., is shown in plan and elevation one form of wrought-iron crank and crank

shaft, the whole being welded together. AC is the crankarm, A the centre of the crank-pin B, C the centre of the crank-shaft, and D, D, are its bearings. The following are the dimensions:-AC (the stroke) is 7"; the diameter of the crank-shaft is 4", the bearings are 6" long and 31" diameter; the crank-arms are 4" wide at e, and 21′′ thick at ƒ; the distance g between the arms is 41′′.

77. The drawing of these figures requires no special notice except for the curves ab, fig. 134, which we will now explain. Figs. 136, 137, represent a portion of the former figures, containing the curve ab drawn full size, and the mode of obtaining the plan of the curves. If the crank-arms, which are of a rectangular cross-section, were connected to the shaft, leaving angles at E, as AEB, fig. 137, the curved line ab would be a straight one eb; but for the purpose of strengthening such connections, angles are always avoided when circumstances permit; the angles AEB are filled-up leaving the outline, as seen at A, 1, 2, &c., to B, a quadrant of a circle, which is a projection of A'B', fig. 136. This circular filling-up is continued on each side of A'B', as shown at A'a', B'o'. If we take sections as kl, a'p', which do not pass through the centre of the shaft C, the plans of mn, a'b' will not be circular as AB. The general problem will be to find the form of the curve made by such cutting planes. In the present case the cutting plane is represented by the surface a'b'p', the cut portion of the circular filling-up being a'b', of which we are required to show the plan. Divide AB into any number of parts, 1, 2, 3, &c., not necessarily equal parts; and through these points draw lines parallel to AA' cutting A'B' in 1, 2, 3, &c.; from C as a centre with radii C1, C2, C3, &c., describe arcs of circles cutting a'b' in 1', 2', 3', &c. From these points draw lines parallel to AA' cutting lines drawn parallel to Aa from 1, 2, 3, &c., fig. 137; and number the intersections of these lines I, II, III, &c. Through I, II, III, &c., draw the line ab, which is the required projection of a'b'.

78. We have employed the construction just described