Geometric algebra and mechanical assembly

[etm...@gmail.com]

Dear all,

I am designing 3d parts using the freecad system, for educational purposes. 

There are approximately 1000 assemblies used in electrification that have a pole and associated parts like belt, saddle, crosshead, top pin, insulator. 

In the figure below we see an assembly where the pieces were drawn separately with the same Cartesian reference 0,0,0. 

Later the pieces were grouped using a python script, and then manually moved to their correct locations. (assembly module).

There is a table that defines the movement (angles and displacements) for a part with reference to 0,0,0 so that it fits in another piece. 

So the saddle must be moved to fit the strap, the crosshead must be moved to fit into the saddle, the top pin must be moved to fit the crosshead. etc. 

I am initiating studies in geometric algebra and need a help to: 

(a) Calculate the movement (angles and displacement) of a piece # 4 when it is moved to fit a piece # 3, and # 3 is moved to fit # 2 and # 2 is moved to fit # 1. and so on. This information is to be used in python script. 

(b) Is geometric algebra a good way to calculate this?

Thank you.