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--- motors_init [2019/08/06 11:07] – created visentin
+++ motors_init [2021/06/11 16:19] (current) – [Mechanical Limits of the Axis Motors - Upper limit] ursgraf
@@ Line 1: / Line 1: @@
 ====== Initialization - Zero reference ======
-The ''Calibration Sequence'' can be started by triggering the safety event ''doCalibrating''. This can be done by pressing the red button until this lights up. Press and hold the red button for 2 seconds, this will trigger the Safety Event ''doCalibrating''. When finished with calibrating, press the red button once again. Press the green button to get back in normal operation mode.
+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.
@@ Line 6: / Line 6: @@
-|{{:delta:zero_ref_ntb.jpg?350|}}|{{:delta:zero_ref_ntb_2.jpg?250|Upper limit calculation detail}}|
+|{{:delta:software:zero_ref_ntb.jpg?350|}}|{{:delta:software:zero_ref_ntb_2.jpg?250|Upper limit calculation detail}}|
 |Upper limit calculation shown below| Upper limit calculation detail |
-L = 17.5 \\
+The mechanical dimensions are given by L = 0.0175m, B = 0.015m, s = 0.006m. The upper limit can be calculated as follows:
-B = 15   \\
-s = 4    \\
+  (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
-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)
-//(4) t = tan(β/2) // \\
+  (5) sin(β) = 2 * t / (1 + t^2)
-//(5) sin(β) = 2*tan(β/2)/(1+tan^2(β/2) // \\
+  (6) sin(β) = (1 - t^2 / (1 + t^2)
-//(6) sin(β) = (1-tan^2(β/2)/(1+tan^2(β/2) // \\
-\\
 Leads to:
-\\ \\
+  (7) (s + B) * t^2 + 2 * L * t + (s - B) = 0
-//(7) (s+B)*t^2 + 2*L*t + (s-B) = 0// \\
-\\
 Solutions are:
-\\
+  t1 = 0.2264 -> β = 0.445
-// t1 = 0.2736 -> β = 30.6°// \\
+  t2 = -2.1157 (neg. solution)
-// t2 = -2.1157 (neg. solution)// \\
-\\
-Hence, the maximum angle the axis can turn is // 90° + β ≅ 120°//.\\
-\\
-==== Mechanical Limits of the Axis Motors - Lower limit ====
+Hence, the maximum angle the axis can turn is // π/2 + β ≅ 2.016//.\\
-{{:delta:motor-axis-calculation-lower-n.jpg?300|}}
+==== Mechanical Limits of the Axis Motors - Lower limit ====
-Lower limit of the Axis Motor measured on the Delta robot, γ is about 5°.
+{{:delta:software:motor-axis-calculation-lower-n.jpg?300|}}
-==== Mechanical Limits of the Tool Center Point Motor ====
+For the lower limit of the Axis Motor the angle γ is measured to be about 5°.
-The TCP rotation is also limited by two metall pins. The maximum turn angle is calculated as follows:\\
-{{ :delta:tcp-limit.jpg?300 |TCP limit}}
-//sin(γ/2) = r/R//\\
-//γ=2*arcsin(r/R)= 0.0600 (rad) = 3.438°//\\
-\\
-That is the value for one side. The other side is identical, so the maximum turn angle is\\
-\\
-//β = 2*PI - 2 * 0.06 = 6.16 (rad) ≅ 353°//.