Answer to Question #200274 in Mechanical Engineering for Muhammad Idrees

Question

A reverted epicyclic gear train for a hoist block is shown in Fig. 13.39. The arm E is keyed to the same shaft as the load drum and the wheel A is keyed to a second shaft which carries a chain wheel, the chain being operated by hand. The two shafts have common axis but can rotate independently.

The wheels B and C are compound and rotate together on a pin carried at the end of arm E. The wheel D has internal teeth and is fixed to the outer casing of the block so that it does not rotate.

The wheels A and B have 16 and 36 teeth respectively with a module of 3 mm. The wheels C and D have a module of 4mm. Find : 1. the number of teeth on wheels C and D when the speed of A is ten times the speed of arm E, both rotating in the same sense, and 2. the speed of wheel D when the wheel A is fixed and the arm E rotates at 450 r.p.m. anticlockwise.

Answer 1

from,

$\omega_A×t_A× m_A= ω_B×t_B× m_B = ω_C×t_C× m_C$

$16\ teeth× 3× 4500= 36\ teeth× 3× x$

$ω_C = 2000\ rev/s$