robertspark
New member
- Joined
- Nov 24, 2018
- Messages
- 1
Hello, first post here, in need of some help please. No this is not homework, college or university work. This is related to a hobby of mine which is cnc (computer numeric control) of a machine.
I have a scenario where I am trying to create an expression which will calculate the points of intersection, which is also the points of tangent between three circles.
To give you an idea, say I have the following three circles:
Circle A > x2 + y2 = 1002
Circle B > (x-200)2 + y2 = 1002
Circle C > (x-100)2 + (y-32.0156)2 = 52
The point of intersection of circles A & B is (100, 0)
The points of intersection of circles A & C and A & B are (95.2381 , 30.4911) and (104.7619 , 30.4911)
This expression will be used for centripetal acceleration, given we know what the velocity (feedrate) of the motion is for the two large arcs, and we know what the acceleration is of the system we can then calculate the smaller circles radius (r2) in order to keep the motion velocity constant.
In cnc gcode provides the start point of the arc (the current position), and it provides the destination co-ordinates, and it provides the origin location offset relative to the start point co-ordinates.
So for two lines of cnc gcode, we will have:
X1, Y1 (start co-ordinates)
(X1+I1), (Y1+J1) (arc A origin co-ordinates)
X2,Y2 (arc A end co-ordinates, which is also the point of intersection between arcs A & B, and the start point for Arc B)
(X2+I2), (Y2+J2) (arc B origin co-ordinates)
X3,Y3 (arc B end co-ordinates)
So, in our above example these co-ordinates would be:
X1, Y1 = -100 , 0
I1, J1 = 50 , 0
X2,Y2 = 100 , 0
I2,J2 = 50 , 0
X3,Y3 = 200 , 0
which forms an "m" shape
Any help / direction would be greatly appreciated, I've been toying with how to calculate the points of tangent / intersection for some time
Rob
I have a scenario where I am trying to create an expression which will calculate the points of intersection, which is also the points of tangent between three circles.
To give you an idea, say I have the following three circles:
Circle A > x2 + y2 = 1002
Circle B > (x-200)2 + y2 = 1002
Circle C > (x-100)2 + (y-32.0156)2 = 52
The point of intersection of circles A & B is (100, 0)
The points of intersection of circles A & C and A & B are (95.2381 , 30.4911) and (104.7619 , 30.4911)
This expression will be used for centripetal acceleration, given we know what the velocity (feedrate) of the motion is for the two large arcs, and we know what the acceleration is of the system we can then calculate the smaller circles radius (r2) in order to keep the motion velocity constant.
In cnc gcode provides the start point of the arc (the current position), and it provides the destination co-ordinates, and it provides the origin location offset relative to the start point co-ordinates.
So for two lines of cnc gcode, we will have:
X1, Y1 (start co-ordinates)
(X1+I1), (Y1+J1) (arc A origin co-ordinates)
X2,Y2 (arc A end co-ordinates, which is also the point of intersection between arcs A & B, and the start point for Arc B)
(X2+I2), (Y2+J2) (arc B origin co-ordinates)
X3,Y3 (arc B end co-ordinates)
So, in our above example these co-ordinates would be:
X1, Y1 = -100 , 0
I1, J1 = 50 , 0
X2,Y2 = 100 , 0
I2,J2 = 50 , 0
X3,Y3 = 200 , 0
which forms an "m" shape
Any help / direction would be greatly appreciated, I've been toying with how to calculate the points of tangent / intersection for some time
Rob