I want to generate this curve in Alibre/Geomagic so that I can CNC this part to see if it is useful. What is the best way of doing this (preferably with equations)?
http://youtu.be/eSiyqnqXhvU
http://youtu.be/eSiyqnqXhvU
Revoloop - how do I create this in Alibre/Geomagic?
- Thread starter paulctan
- Start date
Lew_Merrick
Guest
Paul,
OK, what you have here is a projection of circular motion to a linear plate. Your variables are: radius of the drive circle, number of drive interface points, and rotation to distance operational ratio. These can all be (relatively) easily written into a spreadsheet. The problem arises in implementation as CNC machines only move along line and arc segments. The centerline path of your interface points is going to be some variation on a sinusoidal curve (meaning in this instance a path of varying radius). The offsets within which your drive elements work will be a circular offset to the generated sinusoidal curve.
If you construct this using Geomagic, you will be generating your curves (centerline & offset) using the spline entity which will not generate a truly accurate path that will be interpolated into a series of line and arc elements to approximate your approximated toolpath. As the nature of the rotary to linear motion accuracy will be determined by the closeness of fit, you are unlikely to get satisfactory results from such an approach. A system resulting from such an approach will, almost certainly, bind in some places and have way too much slop in other places.
What leaps into whatever is left of my mind is that mounting a 4th linear axis on your CNC would be the way to go on this. The X,Y origin would be set coincident with the central axis of your 4th linear axis' set-up. The head itself would be set to drive (1st pass) the centerline path and (2nd & 3rd passes -- i.e. a slight change in radius + & -) the bounds of the path. This would then be repeated as required to establish the additional drive paths with an appropriate linear offset to the 4th linear axis. This would result in true geometry for your drive interface path.
???
OK, what you have here is a projection of circular motion to a linear plate. Your variables are: radius of the drive circle, number of drive interface points, and rotation to distance operational ratio. These can all be (relatively) easily written into a spreadsheet. The problem arises in implementation as CNC machines only move along line and arc segments. The centerline path of your interface points is going to be some variation on a sinusoidal curve (meaning in this instance a path of varying radius). The offsets within which your drive elements work will be a circular offset to the generated sinusoidal curve.
If you construct this using Geomagic, you will be generating your curves (centerline & offset) using the spline entity which will not generate a truly accurate path that will be interpolated into a series of line and arc elements to approximate your approximated toolpath. As the nature of the rotary to linear motion accuracy will be determined by the closeness of fit, you are unlikely to get satisfactory results from such an approach. A system resulting from such an approach will, almost certainly, bind in some places and have way too much slop in other places.
What leaps into whatever is left of my mind is that mounting a 4th linear axis on your CNC would be the way to go on this. The X,Y origin would be set coincident with the central axis of your 4th linear axis' set-up. The head itself would be set to drive (1st pass) the centerline path and (2nd & 3rd passes -- i.e. a slight change in radius + & -) the bounds of the path. This would then be repeated as required to establish the additional drive paths with an appropriate linear offset to the 4th linear axis. This would result in true geometry for your drive interface path.
???
ajayre
Alibre Super User
It should be possible to generate an approximation of the centerline in WizoScript (http://www.wizotools.com) and then offset the line to create the tracks for the pins. If you use lots of small lne segments then you can repeatedly reduce the length of the segments until the approximation is close enough for your needs.
Andy
Andy
depasquale
Member
do you want to wrap this around a cylinder or just machine it on a flat surface? Either way if you send me the file I can create the geometry and the tool path (either flat or wrapped around a cylinder)
depasquale
Member
I would still need the file and to know weather we are wrapping around a cylinder or creating flat geometry. You would need the Cam module to do this either way, I have 5 axis cam . you would need at least 4 axis cam to do this on a cylinder. 2 axis will do it on a flat surface. I am a CNC programmer/ tool designer and do this type of work daily. Also is the geometry to be milled as protruding from the surface or cut into the surface?
bemfarmer
Senior Member
I think that the curve swept by the center of a brown circle is a prolate cycloid. (need to do some more checking)
The simple parametric equations do involve sin and cos.
The curves shown would be swept by the circle, and NOT be cycloids. Offsets of the prolate cycloid seems to be close to correct.
A toolpath which follows the prolate cycloid should route out the brown circle diameter path.
I wrote a cycloid script in Moi several months ago.
The Roller-pinion linear drives use cycloids, which would be a prior patent (?)
- Brian
The simple parametric equations do involve sin and cos.
The curves shown would be swept by the circle, and NOT be cycloids. Offsets of the prolate cycloid seems to be close to correct.
A toolpath which follows the prolate cycloid should route out the brown circle diameter path.
I wrote a cycloid script in Moi several months ago.
The Roller-pinion linear drives use cycloids, which would be a prior patent (?)
- Brian
bemfarmer
Senior Member
Notes regarding the revoloop, and prolate cycloid.
The parametric equations for a cycloid from here: http://mathworld.wolfram.com/ProlateCycloid.html
x = a*t - b * sin(t)
y = a - b * cos(t)
Where a is the radius of the rolling circle, and b is the radius of the point which traces out the Cycloid. For a prolate cycloid, b >a.
The radius from the center of one brown circle to the center of the brown circle opposite, is the measure of b. Using a radius of b = 3 units, the value of radius a measures 1.8831122 units +/-.
The radius of one brown circle is approximately 0.3 units.
The prolate cycloid is formed with the cycloid script written for Moment of Inspiration (Moi), available here: http://moi3d.com/forum/index.php?webtag=MOI&msg=6149.18 with these values for a and b. (Setting b to 1.8831122 creates a plain cycloid.)
For an offset from the red prolate cycloid curve, 0.3 / 2 units was used twice, once for each side, to yield the blue curves.
The pale grey curve is a plain cycloid, and its low point is at the radius a. The green line is the center of the rolling circle.
Moi Cycloid script is attached. The wizoscript guys could easily make a script.
EDIT: The lengths of a and b can be scaled. The ratio of the values above very nearly match up, subject to scaling, as no dimensions are given.
The pin size is approximately scaled to match the ratio, but is an independent value, subject to mechanical considerations.
An excel spreadsheet could also generate the points.
The parametric equations for a cycloid from here: http://mathworld.wolfram.com/ProlateCycloid.html
x = a*t - b * sin(t)
y = a - b * cos(t)
Where a is the radius of the rolling circle, and b is the radius of the point which traces out the Cycloid. For a prolate cycloid, b >a.
The radius from the center of one brown circle to the center of the brown circle opposite, is the measure of b. Using a radius of b = 3 units, the value of radius a measures 1.8831122 units +/-.
The radius of one brown circle is approximately 0.3 units.
The prolate cycloid is formed with the cycloid script written for Moment of Inspiration (Moi), available here: http://moi3d.com/forum/index.php?webtag=MOI&msg=6149.18 with these values for a and b. (Setting b to 1.8831122 creates a plain cycloid.)
For an offset from the red prolate cycloid curve, 0.3 / 2 units was used twice, once for each side, to yield the blue curves.
The pale grey curve is a plain cycloid, and its low point is at the radius a. The green line is the center of the rolling circle.
Moi Cycloid script is attached. The wizoscript guys could easily make a script.
EDIT: The lengths of a and b can be scaled. The ratio of the values above very nearly match up, subject to scaling, as no dimensions are given.
The pin size is approximately scaled to match the ratio, but is an independent value, subject to mechanical considerations.
An excel spreadsheet could also generate the points.
