is called a uniformly accelerated motion cam. The distances which the follower passes through during equal periods of time increase uniformly, so that, if, for instance, the follower moves a distance equal to 1 length unit during the first second, and 3 during the second, it will move 5 length units during the third second, 7 during the fourth, and so forth. When the motion is retarded, it will move 7, 5, 3 and 1 length units during successive seconds, until its motion becomes zero at the reversal of the direction of motion of the follower.

In Fig. 145 is shown a uniformly accelerated motion plate cam. Only one-half of the cam has been shown complete, the other half being an exact duplicate of the half shown, and constructed in the same manner. The motion of the follower is back and forth from A to G, the rise of the cam being 180 degrees, or one-half of a complete revolution. To construct this cam, divide the half-circle, AKL, in six equal angles, and draw radii HB1, HC1, etc. Then divide AG first in two equal parts AD and DG, and then each of these parts in three divisions, the length of which are to each other as 1:3:5, as shown. Then with H as a center draw circular arcs from B, C, D, etc., to B1, C1, D1, etc. The points of intersection between the circles and the radii are points on the cam surface.

If the half-circle AKL had been divided into 8 equal parts, instead of 6, then the line AG would have been divided into 8 parts, in the proportions 1:3:5:7:7:5:3:1, each division being the same amount in excess of the previous division while the motion is accelerated, and the same amount

less than the previous division while the motion is being retarded. With a cam constructed on this principle the follower starts at A from a velocity of zero; it reaches its maximum velocity at D; and at G the velocity is again zero, just at the moment when the motion is reversed.

A graphical illustration of the shape of the uniformly accelerated motion curve is given in Fig.

146. To the right is shown the development of the curve as scribed on the surface of a cylindrical cam. This development is necessary for finding the projection on the cylindrical surface, as shown at the left. To construct the curve, divide first the base circle of the cylinder in a number of equal

parts, say 12; set off these parts along line AL, as shown; only one division more than one-half of the development has been shown, as the other half is the same as the first half, except that the curve to be constructed here is falling instead of rising. Now divide line AK in the same number of divisions as the half-circle, the divisions being in the proportion 1:3:5:5:3:1. Draw horizontal lines from the divisions on AK and vertical lines from B, C, D, etc. The intersections between the two sets of lines are points on the developed cam curve. These points are transferred to the cylindrical surface at the left simply by being projected in the usual

manner.

In order to show the difference between the uniform motion cam curve, and that illustrating the uniformly accelerated motion, a uniform motion cylinder cam has been laid out in Fig. 147. The base circle is here divided in the same number of equal parts as the base circle in Fig. 146. The divisions are set off on line AL in the same way. The line AK, however, is divided into a number of equal parts, the number of its divisions being the same as the number of divisions in the half-circle. By drawing horizontal lines through the division points on AK, and vertical lines through points B, C, D, etc., points on the uniform motion cam curve are found. It will be seen that this curve is merely a straight line AM. The curve is transferred to its projection on the cylinder surface at the left, as shown.

It is evident from the developments of the two curves in Figs. 146 and 147, that the uniform motion

curve, Fig. 147, causes the follower to start very abruptly, and to reverse from full speed in one direction to full speed in the opposite direction. The uniformly accelerated motion curve, Fig. 146, permits the follower to start and reverse very smoothly, as is clearly shown by the graphical

illustration of the curve. The abrupt starting and reversal of the follower in the uniform motion curve is the cause why this form of cam, while the simplest of all cams to lay out and cut, cannot be used where the speed is considerable, without a perceptible shock at both the beginning and the end of the stroke.