Assistance needed with tricky real-world geometry problem
Discussion
I have a CNC router and the gantry (the X axis) is very slightly out of square. I need to square it up, the technique used is to swing one end of the gantry by the required amount having. Naturally the hypotenuse should be 1000 but in my case it's 1001.74.
The problem is to work out how far I need to move the gantry at the adjustment point to correct it. I could do this by trial and error but I'd like to reduce the number of attempts needed if possible. Having struggled with it for a while I thought I would present it to the geometricians here for their suggestions.
TIA
The problem is to work out how far I need to move the gantry at the adjustment point to correct it. I could do this by trial and error but I'd like to reduce the number of attempts needed if possible. Having struggled with it for a while I thought I would present it to the geometricians here for their suggestions.
TIA
singlecoil said:
I have a CNC router and the gantry (the X axis) is very slightly out of square. I need to square it up, the technique used is to swing one end of the gantry by the required amount having. Naturally the hypotenuse should be 1000 but in my case it's 1001.74.
The problem is to work out how far I need to move the gantry at the adjustment point to correct it. I could do this by trial and error but I'd like to reduce the number of attempts needed if possible. Having struggled with it for a while I thought I would present it to the geometricians here for their suggestions.
TIA
If the 800mm and 1001.74mm measurements are correct then the 600mm will be 602.90mmThe problem is to work out how far I need to move the gantry at the adjustment point to correct it. I could do this by trial and error but I'd like to reduce the number of attempts needed if possible. Having struggled with it for a while I thought I would present it to the geometricians here for their suggestions.
TIA
My trig says move it 3.01mm and you should be close enough
Tango13 said:
If the 800mm and 1001.74mm measurements are correct then the 600mm will be 602.90mm
My trig says move it 3.01mm and you should be close enough
Agree at the 2.9mm (2.8955), take that at 220mm from the pivot point gives and angle of 0.754 degrees. Take that angle over the full bed length of 1546mm would give 20.346mm.My trig says move it 3.01mm and you should be close enough
Where did you get 3.01 from? I'm missing something...
Ledaig said:
Agree at the 2.9mm (2.8955), take that at 220mm from the pivot point gives and angle of 0.754 degrees. Take that angle over the full bed length of 1546mm would give 20.346mm.
Where did you get 3.01 from? I'm missing something...
Pythagoras tells us that A squared + B squared equals C squared.Where did you get 3.01 from? I'm missing something...
Type 600mm, 800mm & 1000mm into a triangle caclulator app and you get angles of 36.87, 53.13 and 90
Type 800mm and 1001.74mm into the same app ignoring the 600mm and you get 602.90mm, 800mm & 101.74mm with angles of 37, 53 and 90
An angle of 0.13 over 1326mm is 3.01mm so an adjustment of somewhere between 3mm and 3.5mm should be somewhere in the ballpark
Tango13 said:
Pythagoras tells us that A squared + B squared equals C squared.
Type 600mm, 800mm & 1000mm into a triangle caclulator app and you get angles of 36.87, 53.13 and 90
Type 800mm and 1001.74mm into the same app ignoring the 600mm and you get 602.90mm, 800mm & 101.74mm with angles of 37, 53 and 90
An angle of 0.13 over 1326mm is 3.01mm so an adjustment of somewhere between 3mm and 3.5mm should be somewhere in the ballpark
Type 600mm, 800mm & 1000mm into a triangle caclulator app and you get angles of 36.87, 53.13 and 90
Type 800mm and 1001.74mm into the same app ignoring the 600mm and you get 602.90mm, 800mm & 101.74mm with angles of 37, 53 and 90
An angle of 0.13 over 1326mm is 3.01mm so an adjustment of somewhere between 3mm and 3.5mm should be somewhere in the ballpark
Edited by Ledaig on Friday 6th November 23:30
Ledaig said:
Tango13 said:
Pythagoras tells us that A squared + B squared equals C squared.
Type 600mm, 800mm & 1000mm into a triangle caclulator app and you get angles of 36.87, 53.13 and 90
Type 800mm and 1001.74mm into the same app ignoring the 600mm and you get 602.90mm, 800mm & 101.74mm with angles of 37, 53 and 90
An angle of 0.13 over 1326mm is 3.01mm so an adjustment of somewhere between 3mm and 3.5mm should be somewhere in the ballpark
Type 600mm, 800mm & 1000mm into a triangle caclulator app and you get angles of 36.87, 53.13 and 90
Type 800mm and 1001.74mm into the same app ignoring the 600mm and you get 602.90mm, 800mm & 101.74mm with angles of 37, 53 and 90
An angle of 0.13 over 1326mm is 3.01mm so an adjustment of somewhere between 3mm and 3.5mm should be somewhere in the ballpark
Edited by Ledaig on Friday 6th November 23:30
If the triangle is correct at 600mm, 800mm & 1000mm the the three angles will be 36.87, 53.13 and 90 degrees
The triangle is not correct, the hypotenuse is 1001.74mm or 1.74mm too long. Calculate a triangle with sides of 800mm & 1001.74mm and the thrd side will be 602.90mm which gives angles of 37, 53 & 90 degrees, a difference of .13 of a degree from the correct triangle
The whole gantry is out of square by 0.13 degrees
0.13 of a degree over 1326mm is 3.01mm or 3.51mm over the full 1546mm
0.13 of a degree over 220mm is 0.5 of a millimetre not the 2.9mm you have shown on the sketch.
Tango13 said:
Once more, with feeling...
If the triangle is correct at 600mm, 800mm & 1000mm the the three angles will be 36.87, 53.13 and 90 degrees
The triangle is not correct, the hypotenuse is 1001.74mm or 1.74mm too long. Calculate a triangle with sides of 800mm & 1001.74mm and the thrd side will be 602.90mm which gives angles of 37, 53 & 90 degrees, a difference of .13 of a degree from the correct triangle
The whole gantry is out of square by 0.13 degrees
0.13 of a degree over 1326mm is 3.01mm or 3.51mm over the full 1546mm
0.13 of a degree over 220mm is 0.5 of a millimetre not the 2.9mm you have shown on the sketch.
Thank you Sir.If the triangle is correct at 600mm, 800mm & 1000mm the the three angles will be 36.87, 53.13 and 90 degrees
The triangle is not correct, the hypotenuse is 1001.74mm or 1.74mm too long. Calculate a triangle with sides of 800mm & 1001.74mm and the thrd side will be 602.90mm which gives angles of 37, 53 & 90 degrees, a difference of .13 of a degree from the correct triangle
The whole gantry is out of square by 0.13 degrees
0.13 of a degree over 1326mm is 3.01mm or 3.51mm over the full 1546mm
0.13 of a degree over 220mm is 0.5 of a millimetre not the 2.9mm you have shown on the sketch.
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