Differences

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--- motors_init [2019/12/01 07:57] – [Initialization - Zero reference] graf
+++ motors_init [2021/06/11 16:19] (current) – [Mechanical Limits of the Axis Motors - Upper limit] ursgraf
@@ 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 ====
+{{:delta:software:motor-axis-calculation-lower-n.jpg?300|}}
-Lower limit of the Axis Motor measured on the Delta robot, γ is about 5°.
+For the lower limit of the Axis Motor the angle γ is measured to be about 5°.