Equation driven parabolas?

Nickolas_Lockard

Hi, 

How can I create equation-driven parabolas? I have to pack parabolic mirrors in a packaging array and check for part interferences and assess other parts of model. I want to create 2 mirrors. Each is a segment of a parabola inner closer to origin and outer further away) Size is 4mm thick, 1.5m X 1.9m. I learned a hard way to do this in SW, but surely there is a way in Onshape? I just can't find anything searching and reading here or watching videos.

Thank you kindly for your help!
Nick 

andrew_troup

Using a variable would still rely on creating a spline and snapping coordinate dimensions to control points (most easily with a construction grid as mentioned), then you would have to create a separate variable for each control point, because each Onshape variable can only take one value at any one time. Moreover they cannot derive their input simply by selecting a control point, so you would then have to manually input the x ordinate into the variable equation ... so it would be considerably more, rather than less, laborious, than an external spreadsheet. (The spreadsheet can be filed in the 'project container')

What I forgot to mention was that, if you need an optically smooth result, tangency controls might have to be tweaked to sweeten the curvature combs (depending how many points there are), which would make it a genuinely laborious endeavour with the current toolset.

What would *really* fast-track this task would be sketch conics, as requested here:
https://forum.onshape.com/discussion/189/can-we-have-a-sketch-conic 

ilya_baran

The day when we support equation-driven or data-driven curves is not yet upon us, but also not too far away.

For now, another approach is to use the fact that all parabolas are actually the same up to rigid motion and uniform scale.  So I would construct, say a 45 degree cone, split it with a plane parallel to one of the sides, and then figure out the focus and directrix and transform the parabola to match the desired parameters.

andrew_troup

If I had to do this I would work up a list of ordinate dimensions in a spreadsheet, draw a grid of orthogonal construction lines in an Onshape sketch, then key in dimensions to those lines and snap a spline to their intersections.
There's no current facility for importing coordinates from an external file, or creating curves through such a list.

Nickolas_Lockard

Thanks, Andrew for the helpful answer. I could make that work, but it would just be laborious. Could I instead use variable on a line to get variable curvature somehow (equation is y = 1/2*X^2) then snip it into 2 mirrors and extrude each as a part? I looked but just couldn't figure it out.

andrew_troup

Using a variable would still rely on creating a spline and snapping coordinate dimensions to control points (most easily with a construction grid as mentioned), then you would have to create a separate variable for each control point, because each Onshape variable can only take one value at any one time. Moreover they cannot derive their input simply by selecting a control point, so you would then have to manually input the x ordinate into the variable equation ... so it would be considerably more, rather than less, laborious, than an external spreadsheet. (The spreadsheet can be filed in the 'project container')

What I forgot to mention was that, if you need an optically smooth result, tangency controls might have to be tweaked to sweeten the curvature combs (depending how many points there are), which would make it a genuinely laborious endeavour with the current toolset.

What would *really* fast-track this task would be sketch conics, as requested here:
https://forum.onshape.com/discussion/189/can-we-have-a-sketch-conic 

joris_kofman

I talked to an onshape rep not too long ago, he was talking about some of the new features that they are going to introduce. I don't know if I can say the content of the conversation, but i can say: "sit tight it is comming" hopefully soon

dennis_20

You could create a parametric file with construction geometry utilizing the properties of a parabola, i.e., the rays from the focus are reflected off the parabola in a collimated beam.  Using descriptive geometry create the ray, a reflected collimated trace, and a short line perpendicular to the bisector of those two lines.  With several of these you can create a spline that goes through those intersections and tangent to the short lines.

Hey, it is one way.

andrew_troup

@dennis_20
Ingenious suggestion.
I can imagine it working well enough in Solidworks, but setting tangencies at spline control points in Onshape is not a lot of fun, at the present early stage of constraint management. 
This is made more difficult still by the plethora of coincident constraints, because there are no 'merge' constraints for shared endpoints. 
I'm sure the former of these will be addressed soon, and I hope the latter problem will be dealt with in due course.

ilya_baran

The day when we support equation-driven or data-driven curves is not yet upon us, but also not too far away.

For now, another approach is to use the fact that all parabolas are actually the same up to rigid motion and uniform scale.  So I would construct, say a 45 degree cone, split it with a plane parallel to one of the sides, and then figure out the focus and directrix and transform the parabola to match the desired parameters.

Nickolas_Lockard

ilya_baran said:

The day when we support equation-driven or data-driven curves is not yet upon us, but also not too far away.

For now, another approach is to use the fact that all parabolas are actually the same up to rigid motion and uniform scale.  So I would construct, say a 45 degree cone, split it with a plane parallel to one of the sides, and then figure out the focus and directrix and transform the parabola to match the desired parameters.

This is rather ingenious work-around I already have focus, directrix, and could do a slice as transform/copy, right?

Nickolas_Lockard

Thank you all for your responses; they've been very helpful. I'm following the conics thread and hope to hear as soon as something's released. I have an urgent project requiring me to model critical packaging for brittle parabolic glass for international transport. An accurate model of parabolic bent glass is a must for me to finish the package design with any hope of getting it right. It's going to be a really tight fit.

dennis_20

@nick_lockard ,
Since you are making packaging to cradle a product can you get an accurate solid model of the product itself?  You could than use its dumb geometry to define your packaging geometry.

Nickolas_Lockard

dennis_20 said:

@nick_lockard ,
Since you are making packaging to cradle a product can you get an accurate solid model of the product itself?  You could than use its dumb geometry to define your packaging geometry.

The product is a parabolic trough mirror. They sway in wind and with momentum shifts. I also have 2 types (2 different curves) where one has a deeper draft than the other. Both should fit in a common package with shared packaging materials.

That's what I need an accurate model of just to accurately assess static fitment in the package, then later to check for vibration/movement/momentum behaviors, etcetera during package transit.

I've been going back and forth using Excel which isn't very good, frankly, and looking at a colleague's ACAD model. ACAD is just too hard to use and I have to be able to visualize 3D solid model to make this work.

Nickolas_Lockard

ilya_baran said:

The day when we support equation-driven or data-driven curves is not yet upon us, but also not too far away.

For now, another approach is to use the fact that all parabolas are actually the same up to rigid motion and uniform scale.  So I would construct, say a 45 degree cone, split it with a plane parallel to one of the sides, and then figure out the focus and directrix and transform the parabola to match the desired parameters.

@ilya_baran 

Can you point me to a tutorial or video of how to do this? I have tried your method, but I'm stuck. How do I make a plane parallel to a side?

ilya_baran

I was thinking of something like this: https://cad.onshape.com/documents/f794546785a44e54b3a14f1c and then transform as necessary.

Nickolas_Lockard

@ilya_baran Okay, I got that far, too. But what I need is just the boundary line (parabolic line), so I can surface extrude it in a new direction then thicken into a part (or some other ways) so that end result looks like this: 

https://cad.onshape.com/documents/4fc8db0dd6784195948b4339/w/805ed239e25d4419831b6f20/e/981d1afa94254c11a098194c

That part is from colleague's AutoCAD generated file and isn't true parabola--it's constructed from splines, I think.

andrew_troup

@nick_lockard
You can extract the geometry of this (or any) edge by starting a new sketch on a plane parallel to the cut face, picking the parabolic edge, and choosing "Use/Project"

That sketch can then be transformed, derived, etc etc.

ilya_baran

I just updated the document -- once you have the parabola edge, you can't extrude it as a surface (because it's not in a sketch) but you can sweep it along a line segment to get a surface.  Then you can thicken it.

andrew_troup

@ilya_baran
wonderfully economical demo model !   Nice .....

Nickolas_Lockard

I've been struggling with this method some more. Method works fine except resultant curve appears to lose true parabolic shape parameters if you constrain the resulting projection. So I've tried creating cone, revolve, intersect with plane tangent to edge to get parabola, use/project parabola onto offset plane, then reproject that back onto original sketch plane to see how changes to original triangle affect shape. No luck yet. I'm still stuck with a high need for a simple sketch conic that is parametrically true to an equation. 

daniel_wibbing

ilya_baran said:

The day when we support equation-driven or data-driven curves is not yet upon us, but also not too far away.

For now, another approach is to use the fact that all parabolas are actually the same up to rigid motion and uniform scale.  So I would construct, say a 45 degree cone, split it with a plane parallel to one of the sides, and then figure out the focus and directrix and transform the parabola to match the desired parameters.

Hi, 

I was wondering if there has been any update since October 2015. Are equation driven curves now possible?

konstantin_shiriazdanov

@daniel_wibbing there are two FS for this now - Parametric curve by @mahir , and my Curve generator
https://cad.onshape.com/documents/d8aab1e0e7ae10038a6830e0/w/9dfdd631d025960813b8f2df/e/621b5be97d38074a1f1546e5

kevin_o_toole_1

There are now also true, constraint-driven sketch conics in vanilla Onshape:
https://cad.onshape.com/help/Content/conic.htm

Nickolas_Lockard

Thank you!!!! So helpful