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.
Mechanical Limits of the Axis Motors - Upper limit
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)
(7) (s + B) * t^2 + 2 * L * t + (s - B) = 0
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.