Initialization - Zero reference

During homing the robot has to set his zero position. Zero position is choosen as the point where all three arms of the robot are in horizontal position.

The mechanical dimensions are given by L = 0.0175m, B = 0.015m, s = 0.006m. The upper limit can be calculated as follows:

(1) tan(β) = sin(β) / cos(β) = (B - y) / L
(2) cos(β) = s / y

Substitute (2) into (1) to get:

(3) L * sin(β) - B * cos(β) = -s

Using following trigonometric formulas in (3):

(4) t = tan(β / 2)
(5) sin(β) = 2 * t / (1 + t^2)
(6) sin(β) = (1 - t^2 / (1 + t^2)

Leads to:

(7) (s + B) * t^2 + 2 * L * t + (s - B) = 0

Solutions are:

t1 = 0.2264 -> β = 0.445
t2 = -2.1157 (neg. solution)

Hence, the maximum angle the axis can turn is π/2 + β ≅ 2.016.

For the lower limit of the Axis Motor the angle γ is measured to be about 5°.