Principles of cam drawings
Introduction
A rotary cam, Fig. 18-1, is a part on a machine which mechanically changes cylindrical motion to straight-line motion.
fig. 18-1. Cams
The cam, which is mounted on a shaft, is usually driven by a motor either applied directly to the cam shaft or connected by pulleys or gears. The purpose of a cam is to transmit various kinds of motion to other parts of a machine. T
he cams on a machine for stitching shoes, for example, change the rotation of the motor spindle to the irregular or up and down action which is required for stitching leather. Cams are considered the best means of producing a wide variety of different motions.
Practically every cam must be designed and manufactured to fit special requirements. Cams are seldom purchased as a catalog item. In general, cams are custom made. Thus, it is almost certain that a machine draftsman will be called upon to make the working drawings of a cam.
Cams are used on linotype machines, gasoline engines, printing presses, textile machines, metal shapers, shoe machinery, stamping machines, feed mechanisms for production machines, and, in fact, on practically all kinds of automatic machinery.
How cams work
Though each example in Fig. 18-2 appears to be quite different, all the cams work in a similar way.
fig. 18-2. Examples of commonly used cams
In each case, as the cam is rotated or turned, another part in contact with the cam, called a follower, is moved either left and right, up and down, or in and out. The follower is usually connected to other parts on the machine (not shown in Fig. 18-2) to accomplish the desired action.
The direction the follower moves depends upon the position of the framework which attaches the cam and follower to the machine. In Fig. 18-2 A through D, the cam consists of an irregularly shaped metal plate.
Note the different kinds of
followers illustrated. In these examples, as the cam rotates, the follower moves
up and down. It is held in contact with the cam edge either by its own weight or
by a spring. If the follower loses contact with the cam, it will fail to work.
In Fig. 18-2 E and F, cams with grooves are shown. The follower cannot lose contact with cams of this type, since the follower works in the groove and is held in place by the groove.
A follower which is in contact with a cylindrical end cam is shown in Fig. 18-2G. As the cam rotates, the follower is caused to move left and right.
The faster the cam turns, the more rapid is the motion of the follower. The motion of the follower caused by rotating the cam is exactly the same for each complete turn of the cam. The same principle is involved for all cams.
Designing cams
In most companies, engineers or designers prepare the design layouts for cams. Design layouts may include specifications for velocity and acceleration, appropriate cam materials, machining requirements, and heat treatment. In addition, the design for the required follower for the cam system is worked out.
Basically, there are two steps involved in designing and drawing a cam.
step 1
Working out the displacement diagram, establishing the desired motion, and designing the cam and follower. The design engineer is usually responsible for this step for complicated motions.
step 2
Preparing the detail drawings of the cam and cam follower. The machine draftsman is responsible for this step.
The displacement diagram
Various kinds of motion or action may be transferred to the follower, depending upon the shape and type of the cam. The shape of the cam is determined by the displacement diagram which is usually made before any of the views of the cam are drawn.
A displacement diagram is a kind of graph which shows the timing and rate of speed of the follower during one complete cam rotation.
The term displacement diagram is used because it shows the amount the follower is displaced or moved from one position to another. The displacement diagram also shows the position or path of the follower at any given position as the cam rotates.
Figure 18-3 shows a displacement diagram. The length can be drawn to any convenient size, but it should represent one complete 360° rotation of the cam. The length is spaced off in degrees and represents the time for one revolution of the cam.
The height is spaced off in inches and is drawn full size to an accurate scale. The height represents the maximum or total rise (displacement) of the follower. We shall discuss the various spacings of the height in subsequent paragraphs. The rise is the total distance the follower is moved (or displaced) from the starting position through one complete turn of the cam.
From Fig. 18-3 we can determine the position of the follower at any interval or period of the cam rotation.
fig. 18-3. A displacement diagram
The follower starts at 0° and rises 1 inch in 90°, or one fourth of the cam rotation; at 180°, or one half of the cam rotation, its rise is at a maximum of 2 inches; at 270°, or three fourths of the cam rotation, it falls to 1 inch; and it finally returns to its original starting point at 0°.
From this graphic illustration we can determine the motion of the follower at any period through one complete turn of the cam (360°).
Cam motions
There are three standard types of cam motions in common use. A working knowledge of each is important. The design engineer decides upon the type of motion he will use after studying the requirements of the machine using the cam.
The displacement diagram for this type of motion is then made and the cam shape and size are worked out.
Uniform motion
Figure .18-4A shows half a displacement diagram for uniform motion.
fig. 18-4. Uniform and modified uniform motion
This motion is used when the mechanism can be designed to be sturdy and rigid enough to withstand the shock which is transmitted to the follower at the starting position. Here, the rate of speed is the same from the start to the stop positions. The action of the cam is rough and abrupt.
Engineers avoid using this type of motion whenever possible, preferring the curve shown in Fig. 18-4B. Here, the shocks at the start and the stop positions have been made less abrupt by using a transition curve.
A cam with this type of curve is said to have modified uniform motion. The cam is usually operated at relatively low speeds. Some machine operations require cams such as this which deliver motion to moving parts at a constant speed.
Simple harmonic motion
This motion, shown in Fig. 18-5, is used when uniformity of motion is not especially essential and when a smooth start and stop are desired, as in feed mechanisms. It is also used where high speeds are necessary.
One revolution of the cam produces maximum velocity at 90°, zero velocity at 180°, maximum velocity at 270°, and zero velocity at 360° (0°). Simple harmonic motion produces a smooth and easy follower action.
fig. 18-5. Harmonic motion
Constantly accelerated and decelerated motion
The motion shown in Fig. 18-6 results in a gradual increase and decrease in speed. The half of the curve from 0° to 90° is exactly the reverse of the half from 90° to 180°. At no time is the speed uniform. It is considered the smoothest of all three motions.
fig. 18-6. Constantly accelerated and decelerated motion
The basis for the motion is the same as for a free-falling body:
An object dropped from a high point would fall to the earth with a constant acceleration. In the same way as a free-falling body, the speed of the cam follower increases by equal amounts in equal intervals of time and decreases by equal amounts in equal intervals of time.
The follower speed is the greatest at 90° and the least at the top of the curve, 180°. The speed increases inversely on the fall and reaches a maximum at 270°.
Combination of motions
Any one of the three motions thus described may be used on a particular cam. The motions may also be combined to produce a variety of motions.
Subsequent examples show how a combination of motions may be used for any one cam design. One cam can combine uniform motion, simple harmonic motion and constantly accelerated and decelerated motion.
Cam models
As an aid in understanding how cams work, a cam model may be made. It is suggested that firm cardboard be used. The model may be made by placing a cam drawing such as Figs. 18-10, 18-13, or 18-16 over the cardboard.
Important points, such as the camshaft center and intersecting points formed by the radial lines and the cam edge working surface, may be transferred to the cardboard surface by pricking through the drawing with a sharp point.
The cam curve is made by connecting the points thus located on the cardboard and cutting around the curve. Next, a small piece of cardboard should be cut, resembling the type of follower desired.
Assemble the pieces as shown in Fig. 18-7 by fastening the cam cutout and follower to a drawing board. The cam cutout may now be rotated in contact with the follower.
fig. 18-7. A working model of a cam
The model will be suitable for examining what actually happens when a cam is rotated in contact with a follower. Study carefully the action of the follower as the cam is rotated.
Examples of cam motions
The following examples illustrate the procedure for drawing the displacement diagram and the required views of various cam forms and followers.
Example 1. modified uniform motion
This is the method a machine draftsman uses to draw a radial plate cam with modified uniform motion.
Requirements
Assume a knife-edge follower is to rise 1-1/2 inches with modified uniform motion in 180° and fall 1-1/2 inches with the same motion in 180°. The rotation of the cam is counterclockwise.
Procedure
PART I:
Draw the displacement diagram as shown in Fig. 18-8, and as described in steps 1 through 6.
fig. 18-8. Displacement diagram : cam with modified uniform motion
1. Lay off the rise 0-A equal to the maximum rise of the follower (1-1/2 inches).
2. Lay off the base line 0-12 equal to any convenient distance.
3. Mark the midpoint 6 on line 0-12 and divide both 0-6 and 6-12 into 6 equal divisions. Each division will be equal to 30° of cam rotation. Draw vertical lines through these points.
4. Divide the rise 0-A into the same number of divisions as 0-6 (in this case, 6 divisions). Draw horizontal lines through these points.
5. With a radius equal to 1/3 OA, draw the arcs as shown. While there are other methods used to draw the arcs for the transition curve, R = 1/3 OA is considered accurate enough for most purposes. (For graph work, even though a straight line is used, it is called a curve.)
6. Draw straight lines tangent to the arcs, which will complete the displacement diagram with the required modified uniform motion curve.
PART II:
Draw the views of a radial plate cam, as shown in Figs. 18-9 and 18-10, and as described in steps 1 through 4 and 5 and 6.
fig. 18-9. Layout of a radial plate cam
fig. 18-10. Assembly drawing of a radial plate cam
1. Draw the main center lines to intersect at point C. The designer will specify the sizes of the camshaft diameter, the key, the hub diameter, and the location of point 0.
The base-circle radius will always be equal to distance CO. Point 0 on the base circle represents the starting point of the knife-edge follower on the cam edge. This is its closest position to the camshaft. The diameter of the base circle and the maximum rise of the follower govern the size of the cam.
2. Draw radial lines spaced equally every 30°, labeled 1, 2, 3, and so on, clockwise. The number of spacings around the circle should correspond to the number of divisions 0-12 on the displacement diagram (in the case of every 30°, 12 divisions). The angle between the radial lines is called the angle of action.
3. From point 0, lay off the rise 0-A, or 1-1/2 inches, on the vertical center line. The spacings on line 0-A are equal to the spacings 0-A transferred from the displacement diagram.
4. With the compass set at point C and with radii equal to distances C-1, C-2, C-3, and so on, draw light circles.
The arc swung through point 1 will now intersect radial line 1; the arc swung through point 2 will intersect radial line 2; and so on. Since both lobes (halves) of the cam in this example are identical, points in the small circles on radial lines 1 and 11,2 and 10, and so on, are directly across from each other.
At this point it would be well to discuss a fundamental principle which is involved each time a cam is drawn. In actual use, the cam rotates and the follower moves. In this example, the follower will rise and fall 1-1/2 inches for each complete turn of the cam.
On the drawing, however, the cam cannot rotate, but must remain in place. Therefore, we must imagine that the follower is being rotated about the cam on the drawing. The small circles on the radial lines illustrate the different positions of the knife-edge follower as it rotates about the cam.
5. Through the intersections of the arcs thus drawn and the corresponding radial lines (marked with small circles) draw a smooth curve. We now have the cam curve, or edge working surface, as shown in Fig. 18-10.
6. Complete the right-side view. Dimensions for the knife-edge follower and cam plate would normally be supplied to the draftsman by the designer.
The accuracy of the cam curve may be increased by dividing distance 0-12 on the displacement diagram into, for example, twice as many parts. Instead of constructing 12 radial lines (spaced every 30°), we would construct 24 radial lines (spaced every 15°).
The main advantage in having 24 follower positions is in obtaining a more accurate cam curve. In special cases, the draftsman may space the radial lines every 5° or even as close as 1° apart.
Figure 18-10 shows the final cam drawing with the required knife-edge follower.
Example 2. simple harmonic motion