Text-Book of Mechanics Volume . 4

Text-Book of Mechanics Volume . 4

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1913 edition. Excerpt: ...motions and if the efficiency for reversed motion is zero? Exercise 172. Show that the efficiency of a complex machine equals the product of the efficiencies of its individual parts. Exercise 173. From the result of Ex. 172 show that the efficiency of a machine must decrease with an increase in the number of its parts. Section XLX SCREWS The discussion of screws used for transmitting force or energy involves sliding friction. Square-threaded Screws.--In Fig. 90 assume the p couple, formed by the forces--at a distance / from the 2 axis of the screw, to be on the point of overcoming the useful resistance Q acting along the axis of the screw. Then the only other forces acting upon the screw are the reactions of the nut upon it. These reactions will be distributed over the left-hand helicoidal surfaces of the threads. The forces acting along any element of these surfaces (from a radius ti to a radius r2) may, without serious error, be assumed concentrated on this element at a mean radius r = r 1 T2, so that all reactions may 2 be assumed to act along a helix lying upon a cylinder of radius r. The sum of the projections of these reactions, 2J?', upon a plane normal to the axis must then balance the p moment due to the two driving forces--, so that r2, R' = PI 2 or 2R' =-r Moreover, as Fig. 90 shows, the normal to the helicoidal surface is everywhere inclined to the axis of the screw at an angle a, the pitch angle of the threads, and thus the reaction between nut and threads must be inclined at an angle of a + fa to the axis. Thus the sum of the reactions themselves, Si?, will be zjg= gg PI sin (a + fa) r sin (a + fa) and as the sum of the axial components of the reactions R must equal Q, the only other axial force, we have (222) cos (a + fa) =...show more

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  • Paperback
  • 189 x 246 x 3mm | 118g
  • Rarebooksclub.com
  • United States
  • English
  • black & white illustrations
  • 1236821270
  • 9781236821270