(6 pts] The e system shown in Figure P6 below is used to move a 20o lb load from

Question

(6 pts] The e system shown in Figure P6 below is used to move a 20o lb load from e a 200 lb lo s e point to another. The motor runs at 800 rpm and is connected to a reducer. Assume the gears are massless, the damping losses are negigible e shafts are rigid (no springs.) 4:1 speed reducer 200 lb payload leadscrew motorafere carriage Figure P6: Motor-driven Load f the payload is translating -100 iches per minute,determine the equivalent rotary inertia of the payload (Jload)reflected reflected onto the motor shaft.

Explanation / Answer

Given:

Mass of payload is 200 lb

The linear velocity is 100 inch per minute.

The motor is running at 800 rpm and gear is reducing at 4:1 ratio,

implies the lead screw is running at 800/4 or 200 rpm.

we know, linear velocity is product of angular velocity and radius.
thus, 100 inch/min = r x 200 rpm
so, r = 0.5 inch

rotary inertia is product of mass and square of distance between object and axis.
J = 200 x 0.52 = 50 lb-inch2

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