line, the speed of the first driving member of the train, the countershaft, being 300, the required speed of the last member, the lathe spindle, being represented by x, and having the belt on the largest step of the countershaft cone so as to obtain the highest speed with back-gears, gives an arrangement of the case as below. The sizes of the backgears are the same as those on the lathe spindle, the gear C being 6 inches in pitch diameter, and the gear D 4 inches in pitch diameter.

From this it is seen that with the sizes of the gears as above, the highest speed with back-gears would be the same as the lowest speed without the back-gears. This, of course, would be useless duplication of speeds.

For another trial we will make the sizes of the gears B and D each 34 inches in pitch diameter. The calculation then becomes:

х

6 Gear A on lathe

x Speed of spindle

= 144x

153, nearly.

A speed of 153 revolutions per minute for the fastest back-gear speed follows quite regularly the series of speeds which the direct drive gives.

Instead of using the pitch diameters of the gears in making the calculations the number of teeth which the gears would have, the pitch being first decided on, might be used. In this manner it is possible to make slight changes in the diameters of the gears without bringing troublesome fractions into the calculations.

Many lathes and other machine tools have trains of mechanism much more complicated than any here shown, but the method of procedure here outlined can be applied to all of them.

CHAPTER XX

QUICK RETURN MOTIONS

IN a large class of machinery the work is done during the forward motion of a reciprocating part; the return of the part to its starting point is then a question of time. The quicker the part can be returned to its starting point, the more efficient becomes the machine. When the stroke is long, as in the case of the bed of an iron planer for large work, this rapid return motion is usually obtained by means of shifting the driving belt onto a return pulley so arranged that a higher ratio of speed is procured; but in other cases, where the reciprocating motion is shorter, and the stroke is actuated by means of a crank, the actuating mechanism is made such that the crank gives a slow forward and a quick return motion to the reciprocating part. Iron planers for small work, shapers, and the like, and some classes of engines and pumps, use such quick return motions. Below are described the principal devices used for such purposes.

Fig. 213 shows a method of securing a quick return by having the axis of the crank outside of the path of the reciprocating end of the connectingrod. Let A be a crank, the crank-pin of which, a, acting upon the connecting-rod B represented by the heavy line, causes the block b to move back and

forth in the path CD. When the crank is in the position shown the block is at the extreme left of its stroke, the connecting-rod and crank being in the same straight line, the center line of the connecting-rod coinciding with the axis of the crank. As the crank swings downward, the block b is driven to the right; but an examination of the illustration will show that the crank must make

more than a half revolution before it again forms a straight line with the connecting-rod, which it will do when the block has reached its extreme position to the right. As, therefore, the block makes its movement to the right while the crank is swinging through the lower angle included between these two positions, and as it makes its return stroke while the crank is swinging through the upper angle included between these same two positions, the time of the forward stroke of the block will be to the time of its return stroke as the lower angle is to the upper angle.

The upper angle being the smaller of the two, the block has a quick return motion. To secure ease of motion to the block as it starts on its stroke to the right, the angle abC, the angle which the connecting-rod makes with the path of the block, should not be more than about 45 degrees.

To design a quick return motion of this type, lay out a horizontal line ab, Fig. 214, and on it mark off cb equal to the required length of stroke. From c draw the line cd of indefinite length at such an

e

α

с

FIG. 214.-Lay-out of Quick Return Motion in Fig. 213.

b

obliquity that the angle acd shall not be more than 45 degrees. From b draw the line be at the angle required to give the desired quick return. The intersection of these two lines at ƒ will be the axis of the crank. The length bf will be seen by referring back to Fig. 213 to be equal to the length of the crank plus the length of the connecting-rod. The length of cf will be seen to be equal to the length of the connecting-rod minus the length of the crank. If in a given case the length cb is made 12 inches, and ef is found to be 10 and bf 21 inches, which they would be if the angles were as