Question

The sun gear is the input and is driven clockwise at 100 rpm. The ring gear is held stationary by being fastened to the frame. Find the angular velocity and direction of rotation of arm 3.

A. Calculate the angular velocity of arm 3 due to sun gear rotation.
B. Analyze the gear system for angular speed and direction.
C. Determine the rotational motion of arm 3 in the gear mechanism.
D. Find the resultant torque exerted by the sun gear on arm 3.

Answer 1

The angular velocity of gear B increases in magnitude with more force applied to gear A, resulting in a clockwise or counterclockwise rotation of arm 3 depending on the gear arrangement.

Step-by-step explanation:

The question relates to the angular velocity and direction of rotation of an arm in a gear mechanism where the sun gear is the input and the ring gear is held stationary. When more force is applied to the driving gear (Gear A), it results in an increased torque being transmitted to Gear B. Consequently, the angular velocity of Gear B would increase in magnitude provided the gears do not slip and the system handles the increased force without failure. The direction of arm 3's rotation will depend on the gear arrangement. The system adheres to the principle that torque and angular acceleration are proportionally related, following the equation a = net T/I, where 'a' is the angular acceleration, 'T' is the net torque, and 'I' is the moment of inertia.