Question 9.2.3: A single-stage gear train is shown in Figure 1. The input fo...
ANALYSIS OF A FRICTIONLESS GEAR TRAIN²
A single-stage gear train is shown in Figure 1. The input force F_{in} causes Shaft 1 to rotate counterclockwise. Gear 1 meshes with Gear 2 and causes Shaft 2 to rotate clockwise and exert the output forceF_{out} on an output device (not shown). Each gear is mounted on a shaft of 5-mm radius supported by journal bearings, as shown. The gear train is rotating at a constant rate. The gear diameters are r_{1} = 25 mm and r_{2} = 35 mm.
(a) Determine the ratio of output M_{out} to input M_{in} moments in terms of the diameters of various gears and shafts when the journal bearings are frictionless. This ratio is the mechanical advantage of this gear train. Also find the ratio for the particular case when r_{1}= 25 mm and r_{2} = 35 mm.
(b) Find the forces acting on the four journal bearings in terms of F_{in}.
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