This section is from the book "A Course In Wood Turning", by Archie S. Milton, Otto K. Milton . Also available from Amazon: A Course in Wood Turning.
The sizes of turning lathes are given as 10", 12", etc. These figures denote the diameter, or size, of the largest piece of work that can be turned on them. The measurement is taken from the center point of the live center to the bed of the lathe (usually 5" or 6") and is one-half the diameter of the entire circle. The length of a lathe is determined by the length of a piece of work that can be turned. This measurement is taken from the points of the live and dead centers when the tail stock is drawn back the full extent of the lathe bed. Fig. 1 shows a turning lathe with sixteen principal parts named. The student should learn the names of these parts and familiarize himself with the particular function of each.
The lathe should be oiled every day before starting. At the end of the period the lathe should be brushed clean of all chips and shavings, after which it should be rubbed off with a piece of waste or cloth to remove all surplus oil. All tools should be wiped clean and put in their proper places. If a student finds that his lathe is not running as it should, he should first call the attention of the instructor to that fact before attempting to adjust it; and then only such adjustments should be made as the instructor directs.
The speed of the lathe should range from 2400 to 3000 revolutions per minute when the belt is on the smallest step of the cone pulley. At this speed stock up to 3" in diameter can be turned with safety. Stock from 3" to 6" in diameter should be turned on the second or third step, and all stock over 6" on the last step. The speed at which a lathe should run depends entirely upon the nature of the work to be done and the kind of material used. Pieces that cannot be centered accurately and all glued-up work with rough corners should be run slowly until all corners are taken off and the stock runs true. At high speed the centrificial force on such pieces is very great, causing the lathe to vibrate, and there is a possibility of the piece being thrown from the lathe thus endangering the worker as well as those around him. After the stock is running true the speed may be increased.

Fig. 1. - Wood Turning Lathe
Suppose a motor runs 1500 R.P.M. and is fitted with a 4" pulley. Suppose also, a main shaft should run 300 R.P.M.
Then, 1500 : 300 :: x : 4;
Or, 300x = 6000,
x = 20, or the diameter of the large pulley on the main shaft.
Suppose again that a line shaft runs 300 R.P.M., and a counter shaft 600 R.P.M. The counter shaft has a pulley 4" in diameter. The pulley on the line shaft must then have a diameter of 8".
300 : 600 :: 4 : x;
Or, 300x = 2400,
x = 8"
Suppose the cone pulley on the counter shaft runs 600 R.P.M.; a lathe spindle runs 2200 R.P.M., when connected with the small cone pulley which has a diameter of 3". The large cone pulley has then a diameter of 11".
600 : 2200 :: 3 : x
Or, 600x = 6600;
x = 11"
1. To find the diameter of the driving pulley:
Multiply the diameter of the driven by the number of revolutions it should make and divide the product by the number of revolutions of the driver. (20 x 300 = 6000; 6000 ÷ 1500 = 4"--diameter of motor pulley.)
2. To find the diameter of the driven pulley:
Multiply the diameter of the driver by its number of revolutions and divide the product by the number of revolutions of the driven. (4 x 1500 = 6000; 6000 ÷ 300 = 20"--diameter of the driven pulley.)
3. To find the number of revolutions of the driven pulley:
Multiply the diameter of the driver by its number of revolutions and divide by the diameter of the driven. (4 x 1500 = 6000; 6000 ÷ 20 = 300--revolutions of driven pulley.)
The counter shaft should be about 7' above the lathe. A distance of 6' from the center of the shaft to the center of the spindle is sufficient. In setting a lathe or hanging a counter shaft it is necessary that both be level. The counter shaft must be parallel to the line shaft. When the counter shaft is in position a plumb bob should be hung from the counter shaft cone to the spindle cone; the lathe should be adjusted so that the belt will track between the two cone pulleys. The axis of the lathe must be parallel to that of the counter shaft. The lathe, however, need not be directly beneath the counter shaft as the belt will run on an angle as well as perpendicular.
 
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