Need help in modelling a Scroll compressor

I am trying to model a scroll compressor, please suggest me some material for doing it. I am trying to model scrolls based on the following equations.

x=a*(cos(t)+t*sin(t))
y=a*(sin(t)-t*cos(t)). Is my approach correct or is there any other way to model them directly.?

Coming to the assembly part, how do I assemble the Conjugate spirals profile.

Also suggest me how to write a User Defined Function to animate it according to its working.

Thanks in advance

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if you want the simplest spiral (the spiral of Archimedes)

The radius r(t) and the angle "t" are proportional.
Therefore the equation is:

Polar equation: r(t) = a*t [a is constant].

or Parametric form:
x(t) = a t cos(t),

y(t) = a t sin(t),
In solidworks you haveat least two path. Draw a simple circle an then (see figures attached 0 and 1) Use specific funtion spiral a = pitch.
Or use a drive equation driven curve ( see figures 2 and 3).

But if you want a more technical information (non-mathematical) In this video, https://www.youtube.com/watch?v=dsabYhhOko0 you have an excellent explanation of how a scroll compressor works and you can see details of how it is constructed.

 
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