Equation of a line 1

[duddini]

Hi all,

I hope someone can help me, I've tried searching this forum but no luck. I need to create an acrylic lens with the shape determined by the following equation: Y=50 -2.75(sqrtX), x=0-250, in mm.
I'm using SW 2006, SP0. I use equations for setting dimensions, but can't seem to figure this out. I know I could create a table with discrete X and Y values, but this would not really be what I want.. might be the best I get though

Thanks for any help,
Bob


"You can observe a lot just by watching"
Yogi Berra

 

[rgrayclamps]

Hi, Bob:

Your function is a paraboa. So, you can use Paraboa sketch entity. It can be found at \Tools\Sketch Entities\Parabola\...

Good Luck!

Alex

 

[TheTick]

It's a parabola. Solve for x, and you will get x as a function of y².

Calculate position of 4 points and constrain a sketched parabola to them.

 

[lumenharold]

duddini,

Just currious (nosey I suppose). Why would fixed points and a spline be unacceptable? Are you cutting a lens tool direct from the model or perhaps exporting the data for lighting analysis? OptisWorks Ray Trace Add-In uses fixed points and a spline for generating optical surfaces so if you have enough points the calculations should be fine. I got tired of not being able to edit the surface when my OE changed the design so created a table driven curve with several points (50ish) where I could enter the ZEMAX data and update the surface. Most OE's and lens suppliers specify the surfaces using the radius, conic and diameter so I'm not sure how much this will help given the post. If lens creation (especially aspheres) is something you do on a regular basis then perhaps this will be of some use.

For SW09 you can use the formula driven curve feature so no need for a table or the fixed points/spline. The results that I had with the table driven parts in SW08 and the parts I've made in SW09 give me the same results in OptisWorks Ray Trace.

The formula is y=(x^2/R)/(1+(1-(1+b)/(x/R)^2)^.5)
where x = the start and end points ( 0 and the lens diameter /2)
R = the lens prescription radius
b = the conic constant (Rho)

For a sphere the conic = 0; for an Ellipse 0>b>-1; for a Parabola b = -1; and for a Hyperbola b< -1

I am aware that most users won't need or want conics, but for optics and opto-mechanical designers it is handy.

Harold
SW2009 SP2.0 OPW2009 SP0 Win XP Pro 2002 SP3
Dell 690, Xeon 5160 @3.00GHz, 3.25GB RAM
nVidia Quadro FX4600

http://www.lumenflow.com

 

[duddini]

Thanks all,

I've gone ahead and created the part using a table of discrete X and Y values. You're right lumenharold about the fixed points working. Talking with my machinist, by making the points close enough to each other and taking into account the tool radius, my STEP file into the CNC lathe will work just fine.
SW 2006 (this company is Pro-E, but they have one seat of SW for me while I get up to speed, hence the old version) doesn't seem to let me input an equation.

Thanks again, I love this site,
Bob


"You can observe a lot just by watching"
Yogi Berra

 

[TheTick]

Yeah, why settle for perfect when scabby is almost as easy.

 

[duddini]

Funny. Not very helpful, but funny.........

"You can observe a lot just by watching"
Yogi Berra

 

[handleman]

The helpful post was the one where he said to use a parabola. SolidWorks has sketch entities for ellipses and parabolas. If you calculate four points, locate them with dimensions, and then constrain a parabola sketch entity to be coincident with those points then the resulting parabola will perfectly follow your equation, and it's much easier than putting in a bunch of closely spaced points.

-handleman, CSWP (The new, easy test)

 

[lumenharold]

The most direct solution for this post would be a parabola. Perhaps the application doesn't require a high resolution modeled surface. I dunno. I suggested another method in case duddini would like to model a conic driven by a Rho value which is standard in optics (he is designing an aspheric lens). I've had it pointed out to me that very few SW users care about conics and that's fine. If you choose to set up a formula driven curve instead of caculated sketch points and then constraining a parabola to it, you have the option of changing the surface to a circle, a hyperbola, or an elipse without deleting the curve and redrawing. I have it as a template so life is easy.

Harold
SW2009 SP2.0 OPW2009 SP0 Win XP Pro 2002 SP3
Dell 690, Xeon 5160 @3.00GHz, 3.25GB RAM
nVidia Quadro FX4600

http://www.lumenflow.com

 

[TheTick]

An advantage to using a sketched parabola is that you also have a focus point and apex point to manipulate.

 

[lumenharold]

Tick, please expound as to how that would be an advantage when designing an optic or modeling an existing optic. I'm not trying to be a jerk here (I don't have to try, I come by that naturally!) I just want to know what the benefits might be. Thanks.

Harold
SW2009 SP2.0 OPW2009 SP0 Win XP Pro 2002 SP3
Dell 690, Xeon 5160 @3.00GHz, 3.25GB RAM
nVidia Quadro FX4600

http://www.lumenflow.com

 

[TheTick]

What is a parabolic lens used for? Either to direct incoming parallel rays to a point ot to turn a point source of radiation into a beam of parallel rays. In either case, the location of the focus and apex are key.

Using the focus and apex, one can graphically solve for a parabolic lens shape with much more flexibility than by simply crunching numbers.

 

[lumenharold]

That would work great for a parabolic reflector but in the case of a lens, where light the goes will depend on the material selection as well as the wavelength. This will get over my head quickly but my understanding is that an asphere's primary purpose is to reduce spherical aberation. When it comes down to engineering an optic, ZEMAX is our tool of choice and our Optical Engineer is the person to run it, not me. How would you go about modeling a hyperbolic? Is this too far off topic?

Harold
SW2009 SP2.0 OPW2009 SP0 Win XP Pro 2002 SP3
Dell 690, Xeon 5160 @3.00GHz, 3.25GB RAM
nVidia Quadro FX4600

http://www.lumenflow.com