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Why isn't an equation driven curve generating correctly to specifications?

Question asked by Mark Szlazak on May 29, 2018
Latest reply on May 30, 2018 by Casey Bergman

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I set up parametric equations for a Archimedean spiral on a sketch WITHOUT using the Helical coil tool. There are reasons i did it this way which are not relevant to the problem I am encountering.

Here is a screen shot of two sketches called "Spiral" and "Spiral properties." "Spiral" just has the sketch of the spiral and "Spiral properties" has the parameters (dimensions) used to build the spiral. These parameters are linked to Global variables in Equations. This was done so that I could get Global variable values into the Equations Driven Curve since it will only accept sketch dimension names. The parametric Equation Driven Curve is given by:

x(t) = ("Rc@Spiral properties" + "P@Spiral properties"*"N@Spiral properties"*t*0.5/pi)*cos("N@Spiral properties"*t)

y(t) = ("Rc@Spiral properties" + "P@Spiral properties"*"N@Spiral properties"*t*0.5/pi)*sin("N@Spiral properties"*t)

t1 = 0.00

t2 = 6.28318531 (i.e. 2*pi)

The problem is at the top of the spiral where it's endpoint should intersect the construction circle.

In case you are wonder how I set up the Equation Driven Curve and the Global variables then here are the screenshots:

Mark Szlazak May 30, 2018 6:51 AM

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Found the problem. It's with my pitch variable and value ("P@Spiral parameters"). It's missing from equations:

After updating Equations AND refreshing Equation Driven Curve the spiral plots correctly:

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Josh Brady May 29, 2018 10:13 AM
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I can see that the spiral is undefined (blue). I'm thinking your spiral is "rotated" about its start point (not its center, but its start point). Make the end point vertical with the center point and it'll be there..
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- Mark Szlazak @ Josh Brady on Jun 2, 2018 2:41 PM
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  The spiral is black but turns blue to select it and bring up the Equation Driven Curve manager. Also the position of the endpoints is correct.
  
  In polar coordinates for any point Q(r, theta) of an Archimedean spiral centered at the origin but not necessarily starting there, with pitch P, r = Rc and a = P / (2*pi) then it's equation is:
  
  Q(r, theta) = Rc + a*theta
  
  So when theta is 0 then point Q is Rc units from the origin to the right. Theta positively increases counterclockwise.
  
  In Cartesian coordinates you simply project point Q onto the x and y axes and get these formulas:
  
  x(theta) = (Rc + a*theta)*cos(theta)
  y(theta) = (Rc + a*theta)*sin(theta)
  
  Instead, if you want the spiral referenced from it's outer radius Rs winding inward then r = Rs and the equation for Q(r, theta) is:
  
  Q(r, theta) = Rs - a*theta
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  - Mark Szlazak @ Mark Szlazak on May 30, 2018 6:52 AM
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    CORRECTION: The position of the first endpoint is correct but the second endpoint is slightly off.
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  - Josh Brady @ Mark Szlazak on May 30, 2018 9:06 AM
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    Mark Szlazak wrote:
    
    The spiral is black but turns blue to select it and bring up the Equation Driven Curve manager. Also the position of the endpoints is correct.
    The equation in polar coordinates for any point P of an Archimedean spiral centered at the origin but not starting there is:
    
    P(r, theta) = a + b*theta
    
    So when theta is 0 then P is "a" units from the origin to the right. Theta positively increases counterclockwise.
    In Cartesian coordinates you simply project point P onto the x and y axes and get these formulas
    
    x(theta) = (a + b*theta)*cos(theta)
    y(theta) = (a + b*theta)*sin(theta)
    Thanks... I can math.
    
    You don't need "P" in your equation. P is just calculated directly from Rc, Rs, and N. Examine what I posted above and keep mathing...
    
    The reason your spiral was black is that it had a "Fixed" relation. I just noticed that in your original post. It looks like it's still out of position on your final screenshot. If you've done this right (and you're really going for 13.25 turns), the endpoint should be straight vertical from the origin.
    
    See the attached file. It updates correctly upon rebuild with correct spiral position for any Rc, Rs, or N as you change the dimensions in Sketch1. There are no additional parameters, intermediate calculations, or equations.
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    SpiralEquation.SLDPRT.zip58.5 KB
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    - Mark Szlazak @ Josh Brady on Jun 2, 2018 1:07 PM
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      Thanks but going for 13.25 turns is not my problem. N is calculated from Rs, Rc and P as shown in the equations. The endpoint positions are now correct as shown in my post below. Yes one can calculate P if one likes and it may simplify things for me in an expanded equation for the spiral later on down the road. Thanks again for pointing that out.
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      - Josh Brady @ Mark Szlazak on May 30, 2018 11:27 AM
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        OK... Your original post showed Rs, Rc, and N as the first things. Therefore, I assumed that P was intended to be driven by N.
        
        For anyone else, the parametrized equation in terms of Rs, Rc, and P only would be:
        
        ("Rc@sketch1" + ("Rs@sketch1"-"Rc@sketch1")*t*0.5/pi)*cos(("Rs@sketch1"-"Rc@sketch1")/"P@sketch1"*t)
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Roland Schwarz May 29, 2018 10:25 AM
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Interesting.

First thing I would do is hand-calculate the beginning and end result using exact same parameters.

Second thing I would look at is rounding error do to approximation of 2*pi.

Not sure what to make of the "t*0.5/pi" portion of your radius. Might be better to rearrange your equations so that you're going from t=0 to t=turns*2*pi.
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- Josh Brady @ Roland Schwarz on May 29, 2018 10:50 AM
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  The t*0.5/pi stuff is due to the rearrangement of the equation to keep # of turns out of the parameter limit. Pretty sure the equations are OK, the spiral's position is just undefined. The equation driven curve is not "locked in" to the sketch's coordinate system.
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  - Roland Schwarz @ Josh Brady on May 29, 2018 10:52 AM
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    Didn't mean to run over what you stated, Josh. Your first reply wasn't visible for some reason.
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    - Josh Brady @ Roland Schwarz on May 29, 2018 11:17 AM
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      Maybe I got moderated again... :-D
      
      Just some additional info... No need to calculate P.
      
      ("Rc@Spiral properties" + ("Rs@Spiral properties"-"Rc@Spiral properties")*t*0.5/pi)*sin("N@Spiral properties"*t)
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  - Mark Szlazak @ Josh Brady on Jun 2, 2018 1:10 PM
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    Correct about keeping the number of turns out but the bigger issue for me was that I cannot get t1 nor t2 to accept a sketch dimension names like "N@Spiral properties" and leave them open to updating. "N@Spiral properties" gets it's value inserted in and it stays hard code to that value.
    
    Also, I get no indication that my Spiral is under-defined and not locked in.
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Mark Szlazak May 30, 2018 6:51 AM
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Found the problem. It's with my pitch variable and value ("P@Spiral parameters"). It's missing from equations:

After updating Equations AND refreshing Equation Driven Curve the spiral plots correctly:
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- Casey Bergman @ Mark Szlazak on May 30, 2018 9:49 AM
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  Mark, would you mind sharing the corrected file? I am curious as we use this type of curve often and I have not seen it done this way before.
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  - Josh Brady @ Casey Bergman on May 30, 2018 10:15 AM
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    Casey Bergman wrote:
    
    Mark, would you mind sharing the corrected file? I am curious as we use this type of curve often and I have not seen it done this way before.
    Use my file. It's simpler. And correct.
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    - Casey Bergman @ Josh Brady on May 30, 2018 10:22 AM
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      I am not able to open your file, we are still on 2016
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      - Josh Brady @ Casey Bergman on May 30, 2018 10:35 AM
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        Hmm, in that case, his file will also likely be useless to you. He's running the educational version.
        
        Here is a screenshot containing all the info required to recreate:
        
        And here's a copy-paste equation so you don't have to type so much, as long as you name your dimensions. Just change the "cos" to "sin" for the y(t)
        
        ("Rc@sketch1" + ("Rs@sketch1"-"Rc@sketch1")*t*0.5/pi)*cos("N@Sketch1"*t)
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        Casey Bergman @ Josh Brady on May 30, 2018 2:39 PM
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        I am still not able to get this to work. If someone has 2016 or older and has done this would they share the file?
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        Josh Brady @ Casey Bergman on May 30, 2018 4:21 PM
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        If you'll post what you've got I may be able to tell you how to fix it with a screenshot or two.
        Casey Bergman wrote:
        
        I am still not able to get this to work. If someone has 2016 or older and has done this would they share the file?
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        Casey Bergman @ Josh Brady on May 30, 2018 5:11 PM
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        Where is "t" coming from in the equation? Is it referring to the t1 or t2 parameter for the curve or is it calculated? My start point is not beginning where it should and it is running way past the outside circle.
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        Josh Brady @ Casey Bergman on May 30, 2018 5:23 PM
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        R is for Radius. Your circle dimensions are actually diameters.
        
        Yes, the "t" comes from the t1 and t2 boxes. Basically, because it's a parametric equation, both the X and Y equations are evaluated for every value of t from t1 to t2.
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        Casey Bergman @ Josh Brady on May 30, 2018 5:34 PM
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        Good catch Josh, I didn't even think about that being a radius instead of diameter.
        
        I knew the parametric equation needed it but was confused when I was seeing Mark using "t" as a variable for thickness. Thought I was missing something.
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Mark Szlazak May 30, 2018 1:28 PM
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I case anyone is wondering why i am doing things this way. First I do not initial want to run a macro/script although i might down the road. Second, I have a complicated curve to sketch which will be update manually (or by a macro). The equations for the Archimedean spiral i posted previously can be updated so P is moved to a new point position P'(r', theta') where r' and theta' are modifications to r and theta as shown here:
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Why isn't an equation driven curve generating correctly to specifications?

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