Hey guys,

I am half way into my own simpson build and I was wondering, isn't there a simpler, analytic way to express the GUS simpson's kinematics, to avoid iterative numerical solving? I wonder this because it would be really great to write the kinematic solutions into the arduino firmware, as opposed to doing it with a python post-processing script.

Anyway, tell me if the below makes sense:

If you consider the bot as a sort of tetrahedron, with the top point being the extruder head and the movement of the geared arms being like extending or retracting the length of the tetrahedron's edges, several key assumptions (which I think are true for this design) simplify the kinematic problem and we should be able to write an equation for it.

Assumption 1: The geared arms are like linear actuators. (I think this has been proven)

Assumption 2: the angle of the joints always forms a straight line between the point represented by the print head and the corner of the base of the tetrahedron, if you look straight down on the printer from above.

Assumption 3: un-actuated joints always stay in the same plane, parallel to the tetrahedron's base.

Here is a picture:

Thus, at any X,Y,Z position, we can calculate what the angles of all the un-actuated joints should be, and in so doing find exactly what the length of the edges (and thus arm extensions and motor positions) should have to be.

I have not written the full equation yet but I imagine it will not be too difficult to do so.

Is there anything I am missing?