39 Replies Latest reply on Sep 12, 2018 9:47 AM by Mahir Abrahim

# Equation driven curves: cool equations?

I myself don't really get the equation driven curve, math gives me the shivers...

But it seems like equation driven curves can do some really cool things.

Does anybody have cool equations to share? Either practical, mesmerising to look at, or just plain fun

• ###### Re: Equation driven curves: cool equations?

This is my work horse:  (x^2/R)/(1+(1-(1+(K))*(x/R)^2)^.5)

It is a formula for a Rho variable driven conic curve. X determines the start and end points; K is the Rho variable where 0 = circle, 0 > K > -1 = ellipse, -1 = parabolic, and K < -1 is hyperbolic; R is the radius of curvature. The formula gives me the freedom to change the curve type without deleting the sketch plus it adds hyperbolics. The new formula driven sketch tool allows the curve to be constrained to construction lines in the sketch instead of having to manipilate the position in the interface. I like the change.

I use this often for aspheric surfaces where optical accuracy is not required or for a construction sketch to rough in an idea.

• ###### Re: Equation driven curves: cool equations?

One of the presentations that I attended at solidworks world dealt with parametric curves where they input UVW equations into the  curve equation editor to produce some pretty cools things like a spherical helix.

If the solidworks world web page is still up, you might want to download that presentation (beware of many scary greek symbols)

• ###### Re: Equation driven curves: cool equations?

John,

Who was the presenter? Name of the presentation?

• ###### Re: Equation driven curves: cool equations?

I down loaded "Parametric Geometry, The Mathematics of CAD" presented by Patrick Rainsberry. Even if that is the wrong one it is worth looking at.

• ###### Re: Equation driven curves: cool equations?

Huh.

The site appears to be messed up. I can't seem to download a lot of them, including  that one, and mine. It also redirects be to the 2009 proceedings. something is not right.

I spoke too soon. It appears it sent me to the 2009 page, but the content was for 2010. Strange. When I now go to the real 2010 site after logging into the 2009 site, it works.

• ###### Re: Equation driven curves: cool equations?

Look up tractrix curves.  These are the curves used for speaker design and wind instrument bells.  Also used for valve seats.

• ###### Re: Equation driven curves: cool equations?

This has been in my head since it was posted. Most excellent! I had to take a stab at it since I might have a use for it. Thanks Roland. Tractrix curve in SW equation driven sketch:

y = a * log((a +( (a^2 - x^2)^.5)) / x) - ((a^2 - x^2)^.5)

• ###### Re: Equation driven curves: cool equations?

I discovered tractrix while reviewing patents.  There was a valve manufacturer that employed this as a seat profile to promote even wear.  From there I learned about its musical and audio applications.  It came in handy later, when I did a contract stint at a woodwind instrument manufacturer.

The tractrix is the curve you get when you drag an object.  If you have an object to frag and start with the rope perpendicular to the direction of travel, the object follows the tractrix.

• ###### Re: Equation driven curves: cool equations?

Ok... so how would I input this curve into the equation driven curve tool?

• ###### Re: Equation driven curves: cool equations?

Try:

x(t) = a*(t-(EXP(2*t)-1)/(EXP(2*t)+1))

y(t) = a*(2/(EXP(t)-EXP(-t)))

choose an appropriate range for t and asuitable value for a.

Check the math, I had to translate the hyberolic trig functions into exponentials for swx.

• ###### Re: Equation driven curves: cool equations?

on a related note... the SW Help says you can use dimensions and parameters in your equations. anyone get that to work or is it just me?

Jeremy

• ###### Re: Equation driven curves: cool equations?

Wave Spring with radius R, height A, and n waves

x: R*cos(2*pi*t)

y: R*sin(2*pi*t)

z: A*sin(n*2*pi*t)

t1: 0

t2: .999 (SW won't do a closed loop)

Sphere shaped coil with radius R and n wraps

x: R*((1^2 - t^2)^.5)*cos(n*2*pi*t)

y: R*((1^2 - t^2)^.5)*sin(n*2*pi*t)

z: R*t

t1: -.999

t2: .999

• ###### Re: Equation driven curves: cool equations?

I am wondering how to model a wave-spring using these equations in SolidWorks 2009 as I cannot open the SW2010 models:

Wave Spring with radius R, height A, and n waves

x:  R*cos(2*pi*t)

y: R*sin(2*pi*t)

z: A*sin(n*2*pi*t)

t1: 0

t2:  .999 (SW won't do a closed loop)

The image of the wave-spring was done as a sweep without equations, and I suspect for a SW equation drive wave spring that three separate curves need to be created (one per equation). Do you have a SW2009 model example or something similar to upload for review? Also, can R (radius) & A (height) be defined using linked values or equations in the SW equation driven curve instead of using a number?

• ###### Re: Equation driven curves: cool equations?

I no longer have the 2009 interface available but I'm pretty sure that the equation driven sketch tool for 3D sketch was new for 2010. The interface is accessed by started a 3D sketch and then selecting Equation Driven sketch Tool.

• ###### Re: Equation driven curves: cool equations?

Brunt --

Is it possible to create the wave spring of n turns with equations alone.

I saw a webpage (http://www.solidprofessor.com/blog/index.php?p=120)   which tells me, it is possible to create the same using equation driven  curves and a sweep.  It also shows you how you can manipulate the  coefficients of the equation driven curve to create the  geometry you’re  looking for. But unfortunately, I dont have a login to that website.  Can anybody throw some light on this?

cheers

• ###### Re: Equation driven curves: cool equations?

Harold,

is it possible to create a curve that can simulate the shape of a torus using a equation?

Thanks.

• ###### Re: Equation driven curves: cool equations?

I don't have SolidWorks handy right now to test this out, but try this. You should be able to get the above shape by tweaking the r and w variables.

xt = (r1 + r2*cos(w2*pi*t)) * cos(w1*pi*t)

yt = (r1 + r2*cos(w2*pi*t)) * sin(w1*pi*t)

zt = h + r2* sin(w2*pi*t)

w1 = angular velocity of point around main torus diameter

w2 = angular velocity of point around the circular torus cross section

r2 = torus cross section radius

h = height above the z = 0 plane

• ###### Re: Equation driven curves: cool equations?

Hi Mahir,

Amazing the level of maths,your equations looks great!!

I've developed a macro that uses the toiroidical helicoidal to help designing a worm wheel.

Worm wheel sweep path and involute

will use your equations for the globoide options.

Regards.

• ###### Re: Equation driven curves: cool equations?

Thanks. I probably looked up the formula on Wikipedia or something

• ###### Re: Equation driven curves: cool equations?

This is great Mahir. I'm looking forward to messing around with these!

Harold

• ###### Re: Equation driven curves: cool equations?

Hi Harold, Your equation for the wave spring worked, I'm pretty new to this and dont really understand the equations properly although I can mess around with them to get cool, but unpredictable results! MY aim is to make a wave spring that tapers inwards, I suppose you could call it a conical wave spring. I'm sure these dont exist in real life but do you think it would be possible to produce in solidworks?

If you can help me out I'll make sure to give you credit for my design!

Thanks.

• ###### Re: Equation driven curves: cool equations?

Thanks-Mahir, the equation worked great, I was able to get the same results you did, I also did notice that once the curve is created the curve does not seen to be level. Is there a way to make this curve level?

Thanks.

• ###### Re: Equation driven curves: cool equations?

You're welcome, Victor. What do you mean by it's not level? I don't have SW available to me at the moment, but in theory the shape as a whole should be parallel to the XY plane.

• ###### Re: Equation driven curves: cool equations?

My mistake, I’ve re-entered the equation into a new part and it’s now fixed.

Thanks.

• ###### Re: Equation driven curves: cool equations?

Is it possible to add the the wave spring equation to the torus equation curve to make the curve weave or interlock with the curves coming in the opposite direction as shown on the 2nd image.

Thanks.

• ###### Re: Equation driven curves: cool equations?

Sounds doable, but I don't have the time right now. It would involve obtaining the 3D derivative of the original function in X, Y, and Z in order to know the direction of the curve at any given time. Then, you could use that to add a slight sinusoidal perturbation on a plane normal to the direction of the tangent/derivate.

• ###### Re: Equation driven curves: cool equations?

Or you could add just a simple perturbation that oscillates on 2 or 3 axes independent of the direction of the base curve. It would be like ading a small starfish or spike ball shape that varies in time on top of your base curve.

• ###### Re: Equation driven curves: cool equations?

hi chris,

I've made the wave spring user friendly:

regards

• ###### Re: Equation driven curves: cool equations?

Ok... I a showing my ignorance of equations as used in SolidWorks here...

Can someone please help me figure out how to input this quadratic equation into the SW tool to get a curve with the highest point being vertical of the origin?

• ###### Re: Equation driven curves: cool equations?

hows this:

• ###### Re: Equation driven curves: cool equations?

Close. Jeremy forgot to square the x.

yx = -.000010845*x^2 + .5

• ###### Re: Equation driven curves: cool equations?

THANK YOU Mahir!  I was wondering why the curve wasnt really "curving" when I input the other equation that did not square the x.

I really need to take some time to understand this function of SW.  It really is an amazing tool seeing what you guys have come up with just on this one thread!

• ###### Re: Equation driven curves: cool equations?

right - haven't had my caffeine yet

• ###### Re: Equation driven curves: cool equations?

HI i have problem to insert the exponential into the SW equation driven curve. Does anyone can help?

• ###### Re: Equation driven curves: cool equations?

Only the y(x) not including the R^2

• ###### Re: Equation driven curves: cool equations?

I'm looking for a way to generate a exponential curve for a small ultrasonic horn.  The horn should be roughly looking like the one in Fig:6 in the following link. Section 8-1 Problems

As my math is a little rusty would anyone be willing to perhaps guide me or give a solution?

Im going to 3D print these with an SLA printer and can do a bit of trail and error with the SPL I get from the curves.

• ###### Re: Equation driven curves: cool equations?

Simple question (hopefully)

I'm needing to learn an equation to do a simple tapered helix. To control lead in and wash out when using the new threading tool.

I simply need to know how to control:

- starting diameter

- end diameter

- pitch

- revolution

any help would be much appreciated.