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# Equation driven parabolas?

OS Professional Posts: 29 ✭✭
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
Tagged:

## Answers

• Member, Mentor Posts: 1,584 ✭✭✭✭
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.
• OS Professional Posts: 29 ✭✭
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.
• Member Posts: 59 ✭✭
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
• Member Posts: 88 ✭✭✭
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.
• Member, Mentor Posts: 1,584 ✭✭✭✭
@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.
• OS Professional Posts: 29 ✭✭
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?

• OS Professional Posts: 29 ✭✭
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.
• Member Posts: 88 ✭✭✭
@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.
• OS Professional Posts: 29 ✭✭
edited October 2015
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.
• OS Professional Posts: 29 ✭✭
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?
• Onshape Employees, Developers, HDM Posts: 993
I was thinking of something like this: https://cad.onshape.com/documents/f794546785a44e54b3a14f1c and then transform as necessary.
Ilya Baran \ Director, Architecture and FeatureScript \ Onshape Inc
• OS Professional Posts: 29 ✭✭
@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.
• Member, Mentor Posts: 1,584 ✭✭✭✭
@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.
• Onshape Employees, Developers, HDM Posts: 993
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.
Ilya Baran \ Director, Architecture and FeatureScript \ Onshape Inc
• Member, Mentor Posts: 1,584 ✭✭✭✭
@ilya_baran
wonderfully economical demo model !   Nice .....

• OS Professional Posts: 29 ✭✭
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.
• Member Posts: 1
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?
• Member Posts: 1,019 ✭✭✭✭✭
• Onshape Employees, Developers, HDM Posts: 494
edited September 2017
There are now also true, constraint-driven sketch conics in vanilla Onshape:
https://cad.onshape.com/help/Content/conic.htm
• OS Professional Posts: 29 ✭✭
Thank you!!!! So helpful
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