Simple Pulley Hoist Mechanical Advantage

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The illustration below shows a simple pulley system with equations for various design attributes.

Load being raised and accelerating

Torque T= Tf + Ib + mR(a + g)

Where b = a/R

Pulley System

Load rising and coming to rest, no drive

Tf - lb =mR(d -g)

Deceleration d = [mgR + Tf ] / [ mR + (I/R) ]

Load being lowered and accelerating, no drive

Tf + lb = mR(g -a)

Accelaration b = [mgR - Tf ] / [ mR + (I/R)]

Load falling and being brought to rest

T=Ib- Tf +mR(g +d)

Where:

Symbols used:
m = mass of load
I = moment of inertia of drum, etc.
R = drum radius
T = torque to drive drum
Tf = friction torque
a = acceleration of load
d = deceleration of load
b = angular acceleration/deceleration
g = gravity

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