CAD Software Parametric CAD programs and parametric equations

[MetricRocketeer]

Hi TRF colleagues,

The responses that you gave to my question as to what "parametric" means in the context of CAD has tremendously enlightened me. One issue that I never fully understood when I was studying calculus many years ago was the meaning of parametric equations.

Many responses to my question have helped me, but I found that of @RocketScientistAustralia particularly useful. He wrote the following: “Parametric is where you change one thing and EVERYTHING that is associated with it is also changed. A good example is the drafting done in OpenRocket, where if you change the nosecone length, the actual shape changes too. The mathematical definition of the shape is the same, but the position of every point between the start and end of the nosecone is different.”

Beautiful. Very instructive.

And now directly related to that is the definition of parametric equations. Here I am going to quote the article in Wikipedia https://en.wikipedia.org/wiki/Parametric_equation, which corresponds to the same idea. Citing from that article, we have the following:

"For example, the equations x = cos (t) [and] y = sin (t) form a parametric representation of the unit circle, where t is the parameter: A point (x, y) is on the unit circle if and only if a value of t such that these two equations generate that point."

And now, here is where I need help. I continue to quote from the article: "Parametric representations are generally nonunique … so the same quantities may be expressed by a number of different parameterizations."

Could one of my colleagues please provide me an example of different — that is, non-unique — parameterizations of these two parametric equations. Since we are referring to the unit circle, then x^2 + y^2 must equal 1. We have that constraint, right?

So what do we need — different values of t to end up with the unit circle, or different values of x and y? Here I am confused. If I could get this issue down, then the I think I could understand the connection between parameter as that word pertains to CAD programs and as it pertains to parametric equations.

Thank you.

Stanley

 

[jderimig]

In the professional CAD world, parametric is just meant that dimensions can be defined as an expression that can be calculated, or looked up (connection to a database etc). In some advanced systems the parametrization is just not limited to a dimension but extended to other properties of the part.

If the parameter is calculated, the method of calculation including an explicit or variational root finding varies with the system. In addition there are third party plug-in or calculation engines that one could buy to extend the system. A common one is tolerance optimization where a set of tolerances is the input and engine finds the nominal value of dimensions.

 

[lakeroadster]

I was a CAD Monkey back in my working days. Bottom line, IMO, for folks creating one off model rockets using a CAD program, parametric design is not something you need to concern yourself with.

A good basic CAD program is more than capable of providing everything you need.

And if you aren't wanting to do 3D Printing, a drafting machine, or a T-square is capable of providing everything you need for 90% of model rocketry.

Here's a good article: Parametric vs. Direct Modeling: Which Side Are You On?

 

[MetricRocketeer]

Here's a good article: Parametric vs. Direct Modeling: Which Side Are You On?

Hi @lakeroadster,

That is an instructive article. Thanks.

Stanley

 

[dr wogz]

I've done both. (parametric / equations & direct 'numbers)

I knew a company that had their CAD set up pretty well. They made hydraulic cylinders. and they had their models / assemblies set up that you only needed enter the stroke & bore. The full cylinder was then 'created' for you, complete with dwgs..

I like to do a 'some' equations in my models, but they generally are pretty simple: a hole is x/2 from a side (x being that side length) so it is always in the middle.. or a pattern of holes is half the distance from the midpoint, etc.. They are more 'relations' than fancy math equations..

But it is nice to know you can sweep a spline along something like a NACA formula to get a true airfoil shape (NACA recognized)

https://community.ptc.com/t5/3D-Part-Assembly-Design/Equations-for-Curves-and-more/td-p/446997

 

[SolarYellow]

I've been playing with @kalsow's parametric fin can generator in OpenSCAD, and it's pretty amazing what it will allow me to create. Just input some variables up front and the hundreds of lines of code that kalsow put together spit out some beautiful geometry. There are other fin can generators and similar nose cone generators for OpenSCAD findable here on the site or downloadable from Thingiverse.

It would be a free and relatively easy way for anyone to dip your toe into the concept.

 

[Blast it Tom!]

I've done both. (parametric / equations & direct 'numbers)

I knew a company that had their CAD set up pretty well. They made hydraulic cylinders. and they had their models / assemblies set up that you only needed enter the stroke & bore. The full cylinder was then 'created' for you, complete with dwgs..

I like to do a 'some' equations in my models, but they generally are pretty simple: a hole is x/2 from a side (x being that side length) so it is always in the middle.. or a pattern of holes is half the distance from the midpoint, etc.. They are more 'relations' than fancy math equations..

But it is nice to know you can sweep a spline along something like a NACA formula to get a true airfoil shape (NACA recognized)

https://community.ptc.com/t5/3D-Part-Assembly-Design/Equations-for-Curves-and-more/td-p/446997
View attachment 568355

Wow, are you a PTC customer? I've used Mathcad since MS-DOS days! Let me tell you, fractions were tough on a text-based display!

 

[dr wogz]

Wow, are you a PTC customer? I've used Mathcad since MS-DOS days! Let me tell you, fractions were tough on a text-based display!

yeah, Creo / Wildfire / Pro Eng for the last 10 years. (Currently with Creo 3.0 - we haven't upgraded due to later releases being a 'Subscription' model.)

personally, hate it.. Love the power & ability, HATE the User interface..

Was an Autodesk guy (ACAD, Mech desktop, and Inventor) since the mid 90's.. (And a pencil before that!!)

 

[Blast it Tom!]

yeah, Creo / Wildfire / Pro Eng for the last 10 years. (Currently with Creo 3.0 - we haven't upgraded due to later releases being a 'Subscription' model.)

personally, hate it.. Love the power & ability, HATE the User interface..

Was an Autodesk guy (ACAD, Mech desktop, and Inventor) since the mid 90's.. (And a pencil before that!!)

Well, we're in the same place with Mathcad. When they bought it, they decided to rewrite from the ground up. And it's been an A-1 disaster. They are on Mathcad "Prime" 9.0 and still have a large body of customers demanding they keep on supporting Mathcad 15.0, which is now about 15 years old!

But I'll end the threadjack. I will throw a vote in for Solidworks as a parametric modeling interface, I understand Inventor works similarly. I have a tangent ogive nose cone parametrically modeled in Solidworks, give it a diameter and length that you want and it calculates the radius of the arc and places the center with that dimension. Relative simple, but it points to the power of parametric representation.

 

[dr wogz]

From what I understand, the base 'kernel of Inventor, Solidworks, and a few others is the same code written by PTC.. They just made a better UI!!

 

[kramer714]

I was a CAD Monkey back in my working days. Bottom line, IMO, for folks creating one off model rockets using a CAD program, parametric design is not something you need to concern yourself with.

A good basic CAD program is more than capable of providing everything you need.

And if you aren't wanting to do 3D Printing, a drafting machine, or a T-square is capable of providing everything you need for 90% of model rocketry.

Here's a good article: Parametric vs. Direct Modeling: Which Side Are You On?

I work in aerospace, and have used many different CAD programs over the years. Full parametric is important if you have a large group of folks working on the same project. That way everything is linked together. The parametric capability comes at a pretty big cost in terms of flexibility and control.

For most of my work I use Rhino-3d to create solids. It is easier to manipulate, better for the 'I know what i want just need to be able to create a model of it" types. Easy to create simple or complex surfaces and then turn them into solids.

 

[SolarYellow]

I like parametric for upscaling and downscaling. Once a nose cone shape is designed, for example, being able to make the same shape for any tubing diameter and thickness by changing just a few variables can save a lot of time and potential for injecting errors versus having to redesign the whole thing for each size.

Also, if you are working on iterating a design and trying to decide what you like, or want to test a variety of components. Say you have a spherically blunted nose cone. Change the diameter of the blunting sphere and the model does the rest, rather than having to redraw the entire thing.

 

[kramer714]

I like parametric for upscaling and downscaling. Once a nose cone shape is designed, for example, being able to make the same shape for any tubing diameter and thickness by changing just a few variables can save a lot of time and potential for injecting errors versus having to redesign the whole thing for each size.

Just to clear up some confusion, you dont need to design using parameteric scripts to be able to scale stretch, or bend a solid or surface in a model. Programs like Rhino allow you to really manipulate a solid or surface. For example scaling the fincan from a 29mm to a 54mm while keeping the fin thickness the same. The picture shows a 29mm fincan I designed (and 3d printed). Starting with the small one (29mm), I was able to scale it to 54mm while keeping the same size for the rail guide. I was also able to stretch it longer without changing the thickness of the fins. Or with a nose cone, you can just make the diameter larger while maintaining the same tube thickness, or stretch the nosecone without changing the shoulder.

 

[MetricRocketeer]

Hi TRF colleagues,

I will drop the subject after this post.

I asked someone in the Math Department where I teach (Towson University) about this issue. It is a deep subject — deeper than I can handle — but I got this much as a very simple example:

Let f(x) = (x(t), y(t)) = ( cos(t), sin(t) ) with t in between 0 and 2 pi inclusive.
Let g(x) = (x(t), y(t)) = ( sin(t), cos(t) ) again with t in between 0 and 2 pi inclusive.

Then f(x) sends a particle from (1,0) in a clockwise direction.
And g(x) sends a particle from (0,1) in a counterclockwise direction.

Thus, these two different parametric representations are non-unique.

Stanley

 

[MetricRocketeer]

Just to clear up some confusion, you dont need to design using parameteric scripts to be able to scale stretch, or bend a solid or surface in a model. Programs like Rhino allow you to really manipulate a solid or surface. For example scaling the fincan from a 29mm to a 54mm while keeping the fin thickness the same. The picture shows a 29mm fincan I designed (and 3d printed). Starting with the small one (29mm), I was able to scale it to 54mm while keeping the same size for the rail guide. I was also able to stretch it longer without changing the thickness of the fins. Or with a nose cone, you can just make the diameter larger while maintaining the same tube thickness, or stretch the nosecone without changing the shoulder.

So, is Rhino a parametric CAD program? How about Onshape?

Stanley

 

[lakeroadster]

I like parametric for upscaling and downscaling. Once a nose cone shape is designed, for example, being able to make the same shape for any tubing diameter and thickness by changing just a few variables can save a lot of time and potential for injecting errors versus having to redesign the whole thing for each size.

Also, if you are working on iterating a design and trying to decide what you like, or want to test a variety of components. Say you have a spherically blunted nose cone. Change the diameter of the blunting sphere and the model does the rest, rather than having to redraw the entire thing.

Pretty much any solid modeling program will allow scaling, if the person making the solid model draws it in such a manner... that's not parametric design. See below, change the 6-1/16" base dimension and the program scales the entire Mercury Capsule.

​

 

[SolarYellow]

That's great. You can even do that in slicing software when you have a .stl file. But body tube wall thicknesses don't scale directly with diameter, even limiting yourself to Estes tubes. And if you want to play with heavier or lighter walls or old Semroc sizes, things can be all over the place. So if you want to upscale or downscale a nose cone or transition, or make it for a heavy-wall or light-wall tube, just scaling the whole thing usually won't work.

 

[lakeroadster]

That's great. You can even do that in slicing software when you have a .stl file. But body tube wall thicknesses don't scale directly with diameter, even limiting yourself to Estes tubes. And if you want to play with heavier or lighter walls or old Semroc sizes, things can be all over the place. So if you want to upscale or downscale a nose cone or transition, or make it for a heavy-wall or light-wall tube, just scaling the whole thing won't work.

Well, depending on the program you could actually tie in a database of stock components, have the program pick the closest one and then adjust the other geometry based on that.

Or just do it yourself.

Again, for a person designing model rockets for themselves, as a hobby, we're getting way off track here.

 

[kramer714]

So, is Rhino a parametric CAD program? How about Onshape?

Stanley

No it isnt parametric per se, but you can create a shape, like a fin can, and make a family of parts from it. The advantage is speed and the ability to really manipulate the surfaces. IMO you can make a solid model much faster with a freeform modeling tool. The more lofted the better these tools are. The other thing to keep in mind is most programs can use 'block definitions'. For example I have a block defined for the mounting points on most of the altimeters I use. This lets you manipulate the shape while maintaining fixed points. changing a 3 inch altimter bay to a 4 inch shouldn't change the hole pattern for a RRC2 for example.

Horses for Courses - Using the right tool for the right task - Ignoring the 'geek masochist' factor, i use the SIMPLEST tool for the task I'm doing. While mentoring a SLI team, I suggested that a scale excel plot is the easiest way to create a 2d fin outline. put in the points, plot, print trim, done. Creating a parametric script for a nose cone is easy, creating a parametric script for the fully lofted fincan with tapering fillets is a bit harder. Simpler to create in a program like Rhino than a program like Solidworks.

Modeling technique. Take a look at the 'fork tutorial' Rhino - Fork If you thin about it, a fork is fully lofted surface. If I was modeling this in Solidworks, the method for modeling is different than if i was doing it in Rhino. The other thing to keep in mind in modeling is tolerances. Im talking about the tolerances you need to model in to make sure something fits. For example a PERFECT 54 mm tube is 2.154 ID (from Madcow website), the issue is if I were to model a nosecone with a 2.154 OD shoulder it very likely will not fit. The I.D. has tolerance both in the diameter and how round it is. I usually create the perfect fit model (looks great - but wouldnt work if built that way), then create a second 'layer' where I offset the surfaces with specific tolerances in mind. One reason to do this is scaling in the future, tolerances don't scale proportionately, double the diameter doens't necessitate doubling the 'gap'. Fun eh?

Learning curve - these are complex tools, just to set expectations there is a learning curve to all of these tools.

quick comparison cad comparison BTW the Student edition of Rhino (yes you need to prove it) is very reasonable and full function - no expiration date

Mike K

 

[kramer714]

Well, depending on the program you could actually tie in a database of stock components, have the program pick the closest one and then adjust the other geometry based on that.

Or just do it yourself.

Again, for a person designing model rockets for themselves, as a hobby, we're getting way off track here.

McMaster if you haven't checked it out yet, McMaster has cad files in multiple formats for almost everything they sell

 

[MetricRocketeer]

No it isnt parametric per se,

Hi @kramer714,

Thank you for your response.

You are saying that Rhino is not a CAD program. But what about Onshape?

Stanley

 

[kramer714]

Hi @kramer714,

Thank you for your response.

You are saying that Rhino is not a CAD program. But what about Onshape?

Stanley

Rhino is a cad program, it just works differently than Solidworks. Kind of like a Tesla and a Camry are both cars, but the operate differently. They each are functional but each is better at different things. The fundamental difference is 'how is the idea inputted'. Like the car example, they each have their strengths and weaknesses.

These videos show some of the differences between Rhino, Onshape, and Solidworks - they are long but just scrolling through you can see the differences in the 'model inputs - definition'

Rhino car example
onshape F1 'wing'
solid works jeep

The other thing to think about is the outputs you want. Is it a model, a model for CAM software, a model for 3d printing, a model for engineering analysis, a renederd model for graphics, or 2D 'blueprints' . The autocad family has always been strong on creating 2D drawings, rhino not so much for example.

 

[lakeroadster]

McMaster if you haven't checked it out yet, McMaster has cad files in multiple formats for almost everything they sell

Yep. they were one of the 1st to do that.... 2005 ish as I recall.