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Question 3.13: For the two gears. A and B. in Figure 3-19, compute the rela...

For the two gears. A and B. in Figure 3-19, compute the relative deflection between them in the plane of the paper that is due to the forces shown in Part (c). These separating forces, or normal forces, are discussed in Chapters 9 and 10. It is customary to consider the loads at the gears and the reactions at the bearings to be concentrated. The shafts carrying the gears are steel and have uniform diameters as listed in the figure.

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Objective          Compute the relative deflection between gears A and B in Figure 3-19.
Given                The layout and loading pattern are shown in Figure 3-19. The separating force between gears A and B is 240 lb. Gear A pushes downward on gear B. and the reaction force of gear B pushes upward on gear A, Shaft 1 has a diameter of 0.75 in and a moment of inertia of
0.0155 in^4. Shaft 2 has a diameter of 1.00 in and a moment of inertia of 0.0491 in^4. Both
shafts are steel. Use E = 30 × 10^6 psi.

Analysis       Use the deflection formulas from Appendix 14 to compute the upward deflection of shaft 1 at gear A and the downward deflection of shaft 2 at gear B. The sum of the two deflections is the total deflection of gear A with respect to gear B.

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