Given Find the torque T2 required to keep the gear system in

Given Find the torque (T_2) required to keep the gear system in Equilibrium.

Solution

a) The intermediate pulleys or gears can be regarded as idler gears/pulleys and have no effect if friction is absent.

So the outermost pulley of dia 30 inch merely transmits the working of the force driven inner pulley of dia 9 inch

At the circumeference this means a reverse force of , resulting in a net torque of 23640 lbin

Another idler pulley occurs inbetween, the final ratio is 6/12 so the output torque becomes 1/2* 23640

or 11820 lbin. To stop the rotations a reverse torque of this amount must be applied.

If no reverse torque of 300 il in (?) were applied, the system of pulleys can be regarded as a drive chain with intermediate driver pulleys, with a ratio 9/6 meaning the input torque is reduced by 2/3 or output torque is 2000*9 *2/3 =12000 . The inner torque of 360 gets reduced by 6/12 or 180 . You can check that 180+11820 =12000