motors_init
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motors_init [2019/12/01 07:54] – [Mechanical Limits of the Tool Center Point Motor] graf | motors_init [2021/06/11 16:19] (current) – [Mechanical Limits of the Axis Motors - Upper limit] ursgraf | ||
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====== Initialization - Zero reference ====== | ====== Initialization - Zero reference ====== | ||
- | The '' | + | During homing |
Line 6: | Line 6: | ||
- | |{{: | + | |{{:delta:software: |
|Upper limit calculation shown below| 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 = 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) | ||
- | The upper limit can be calculated as follows: | ||
- | \\ \\ | ||
- | //(1) tan(β) = sin(β)/ | ||
- | //(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): | Using following trigonometric formulas in (3): | ||
- | \\ \\ | + | |
- | //(4) t = tan(β/ | + | (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: | Leads to: | ||
- | \\ \\ | + | |
- | //(7) (s+B)*t^2 + 2*L*t + (s-B) = 0// \\ | + | |
- | \\ | + | |
Solutions are: | Solutions are: | ||
- | \\ | + | |
- | // 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, |
- | {{: | + | ==== Mechanical Limits of the Axis Motors - Lower limit ==== |
+ | |||
+ | {{:delta:software: | ||
- | Lower limit of the Axis Motor measured on the Delta robot, | + | For the lower limit of the Axis Motor the angle γ is measured to be about 5°. |
motors_init.1575183257.txt.gz · Last modified: 2019/12/01 07:54 by graf