Nice!
I've used magnet ball joints on a hexapod with great results.

Kinematics are found using trig and the law of cosines. Find an old high school text regarding solving triangles angles and side lengths.

Calibration and error mapping is very important to accuracy on mechanisms like these because link lengths are never perfect. Renishaw has a tripod/delta for dental milling and they get 10 micron accuracy through a painful calibration process.
http://www.renishaw.com/en/incise-sc...oftware--10249

To get motion accurately in X,Y,Z directions is more difficult than in a cartesian machine (even after you've applied the kinematic transforms) because tiny length differences in the fixed-length struts cause 'dishing' in the motion and divergence from linearity. To correct for this we do 3D volumetric error mapping, i.e. we use the machine to probe the locations of a large array of accurately mapped balls (previously measured on a CMM). Depending on the accuracy you are looking for, you may not have to do this. Our machine is tiny (roughly spherical working envelope about 90mm diameter) and without error mapping can be out by 0.3mm or more. With error mapping it is accurate to sub 10 microns.
SO either take special care in "perfect" mechanical geometry, or you will need to calibrate and error map for accuracy.

I haven't used error mapping yet on the deltas I make... I will soon.


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