Rotating plate cams, like those thus far considered, are most commonly met with in practice. A straight-line, reciprocating motion of a plate, however, may be made to produce similar follower movements, in which case the cam is known as a translation cam. A straight-line movement is equivalent to movement along an arc with infinite radius. With this understanding, the same principles may be made to apply to translation cams as to rotating cams.

## Development Of Translation Cam

Suppose it is required to produce the same movement of the follower as in Fig. 90, by means of moving a plate in a straight line instead of rotating it. This case is shown in Fig. 91.

### 1. Follower Positions

The same follower motion being required as in Fig. 90, the path is laid out exactly in the same way, the follower positions for the rise along path D8 fulfilling the requirement of harmonic motion, and for the fall along path IF5, fulfilling the requirements of uniformly accelerated and retarded motion. This is shown in the figure, and it is observed that no change from the method of Fig. 90 is employed.

The base circle does not exist in this case as a circle, but has become a straight line, and may be chosen of any length, say Dx. The cam radii, being always perpendicular to the cam arc (in this case the straight line Dx), become parallel lines, perpendicular to Dx. The cam arc of rise in Fig. 90 is now represented in Fig. 91 by the distance D8, which should fulfill the relation:

Fig. 91. Diagram Showing Development of (Translation Cam.

Dk/Dx=120/360; in order to make the same relative movement of cam during rise as in Fig. 90, Dk should likewise be divided into 8 equal parts.

The arc of rest in Fig. 90, being ½ the arc of rise, the distance kl in Fig. 91 is made ½ the distance Dk. The arc of fall in Fig. 90 being 1¼ the arc of rise, the distance lv in Fig. 91 is made 1¼ the distance Dk. The final arc of rest in Fig. 90 being ½ the first arc of rest, the distance v x in Fig. 91 is made ½ the distance kl. This completes the cycle; and the parallel lines aa', bb', cc', etc., drawn through the several points of division as noted, represent the several positions of the cam radii.

### 3. Follower Rotation

Since the lines of follower rotation are all perpendicular to the cam radii - which in this case are all parallel - the rotation, or translation, of the follower is accomplished by drawing parallel lines through the determined points of the path, producing the intersections R1, R2, R3, R4, etc. Between points R8 and F8, the follower rests; and for the period of fall, the intersections F8,F7, F6, F5, etc., are determined as for the rise, by producing the parallel lines through the points in the path of fall. From point v to x the follower again rests. These intersections represent the centers of the follower in its translated positions.

Now, with a radius equal to the radius of the follower roll, arcs are struck to represent the outline of the follower in each of its translated positions.

### 4. Tangent Line

A smooth curve is now drawn tangent to the several translated positions of the follower roll. In this cam a new feature is introduced by drawing these tangent lines on both sides of the roll, thus making a groove which holds the follower firmly in position at all times. This gives an absolutely positive fall to the follower roll. The same grooved construction might have been made on any of the cams heretofore studied, instead of allowing the follower to come down by gravity or by the force of a spring.

### 5. Testing

The cam may be tested by the tracing-cloth method as before, the procedure in this case, however, being one of translation instead of rotation. The original radius, with the follower in its several positions being traced upon the cloth, is set upon each of its translated positions, and, by careful inspection, it is noted whether the roll, in this position, just touches the faces of the cam groove as drawn.

### 6. Pressure Line

The pressure lines are drawn precisely as in all cases thus far considered, and may be translated back to the path of the follower in order to study their direction as the follower moves along its path.

Although the same cycle of follower movement has been accomplished in this case as in the rotating cam, Fig. 90, the translation cam is not in position to begin a repetition of the cycle by further movement. If we reversed the motion of the cam, the cycle also would be reversed; and in the cam under discussion we should have a rest, then a uniformly accelerated and retarded rise, then a rest, then a harmonic fall, the periods of time being reversed as well as the motion. We could, of course, by choosing the motion for rise and fall exactly the same, secure the same motion for the reversed as for the forward movement of the cam.