If you pull the lever handle around one turn, its outerend has described a circle. The circumference of thiscircle is equal to 2x. (Remember that n equals 3.14, or22/7).That is the distance you must apply the effort of thelever arm.At the same time, the screw has made onerevolution, raising its height to equal its pitch (y).Youmight say that one full thread has come up out of thebase. At any rate, the load has risen a distance p.Remember that the theoretical mechanical advan-tage (T.M.A.) is equal to the distance through which youapply the effort or pull, divided by the distance andresistance the load is moved. Assuming a 2-foot, or24-inch, length for the lever arm and a 1/4-inch pitch forthe thread, you can find the theoretical mechanicaladvantage by the formula27trT.M.A. = —Pin thatr = length of handle = 24 inchesp = pitch, or distance between correspondingpoints on successive threads = 1/4 inch.Substituting,A 50-pound pull on the handle would result in atheoretical lift of 50 x 602 or about 30,000 pounds—15tons for 50 pounds.However, jacks have considerable friction loss. Thethreads are cut so that the force used to overcomefriction is greater than the force used to do useful work.If the threads were not cut this way and no friction werepresent, the weight of the load would cause the jack tospin right back down to the bottom as soon as youreleased the handle.THE MICROMETERIn using the jack you exerted your effort through adistance of 2nr, or 150 inches, to raise the screw 1/4inch. It takes a lot of circular motion to get a smallamount of straight line motion from the head of the jack.You will use this point to your advantage in themicrometer; it’s a useful device for making accuratesmall measurements—measurements of a fewthousandths of an inch.In figure 5-3, you see a cutaway view of amicrometer. The thimble turns freely on the sleeve,Figure 5-3.-A micrometer.Figure 5-4.—Taking turns.rigidly attached to the micrometer frame. The spindleattaches to the thimble and is fitted with screw threadsthat move the spindle and thimble to the right or left inthe sleeve when you rotate the thimble. These screwthreads are cut 40 threads to the inch. Hence, one turnof the thimble moves the spindle and thimble 1/40 ofinch. This represents one of the smallest divisions on themicrometer. Four of these small divisions make 4/40 ofan inch, or 1/10 inch. Thus, the distance from 0 to 1 or1 to 2 on the sleeve represents 1/10, or 0.1, inch.To allow even finer measurements, the thimble isdivided into 25 equal parts. It is laid out by graduationmarks around its rim, as shown in figure 5-4. If you turnthe thimble through 25 of these equal parts, you havemade one complete revolution of the screw. Thisrepresents a lengthwise movement of 1/40 of an inch. Ifyou turn the thimble one of these units on its scale, youhave moved the spindle a distance of 1/25 of 1/40 inch,or 1/1000 of an inch—0.001 inch.The micrometer in figure 5-4 reads 0.503 inch, thatis the true diameter of the half-inch drill-bit shankmeasured. This tells you that the diameter of this bit is0.003 inch greater than its nominal diameter of 1/2inch—0.5000 inch.5-2

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