Establishing equations for a worm screw mechanism

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clurt
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Hey guys :)

So I'm looking to form equations that I can apply a Laplace transformation to. The mechanism specifically is a trailer jack - it converts rotational motion to linear motion. And its high torque provides a mechanical advantage to lifting heaving loads.

Can anyone help me form differential equations that I can apply a Laplace function to?

Thanks
 
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What is the actual arrangement of components you want to analyse ? Picture or good drawing please .
 
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Why do you think the motion of a jack needs to be described with a differential equation?
The motion can be described with a simple linear equation; x rotational motion equals y change in height.