2 different ALPHA Modules in action.

Video showing 2 different ALPHA (Automated Lego Pipette Head Assembly) Modules in action

The same code and mathematical computation can be used on 2 different pipette head assembles with different physical dimensions and geometric designs.
In the first pipette head, the 3 motors are at 120 degrees apart. In the second design, the 3 motors are at 0, 90 and 180 degree posiiton. The length of the control arm and the linkage arm is also different for both pipette head assemblies.

The difference in the code between the 2 pipette head assemblies are 4 physical constants (TO, BO, TR, BR - see below) and 1 rotational matrix.

DETAILS OF MATH MODEL
This robot is made up of 3 sets of double jointed arms, which we called the control arm and the linkage arm. The control arm moves in a circle of fixed radius, TR (Top Radius). The loci of the linkage arm is the surface of a sphere of fixed radius BR (Bottom Radius). TR and BR are at horizontal offsets TO and BO respectively from the vertical axis through the center of the robot, The 3 arms are at a fixed angle, PHI from each other, eg. 120 degrees, or even 90 degrees. The problem is to compute the 3 angles that the 3 control arms made with the vertical axis (ie THETA1, THETA2 and THETA3) for any point, with cartesian coordinates X, Y and Z in 3 dimenstional space, in terms of the constants TR, TO, BR, BO and the PHI.

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