3d sketch equation curve

[CJ.10E-10mm]

I am trying to create a coil which from above, retains equal and thus parallel pitches whilst at the same time adheres to a semi-circular form in the cross section. You can see from the images attached that the first two revolutions are larger than the semi-circle outline.

Could someone please advise me what formula to use to achieve the desired result please?

These are the values I have used:

Cylindrical

r (t):     134.56924424045517662353735770102mm * t * 0.5
q(t):     1 deg * 360 ul * 3.0 ul * t
z(t):      10 mm * 6 ul * 0.5 ul *  t  * (1.5 * t) * t

tmin: 0 ul
tmax: 0.916 ul

Many thanks.

[graemev]

Something like this?

[glenn-chun]

Hi cjjatpuresilica,

See the attached part.  The two curves shown in green and black below are tangent continuous.  I used the spherical radius and the number of revolutions (5 between two poles, 2.5 between pole to equator) that you specified.

Glenn

ASM Development

[CJ.10E-10mm]

Thank you but if you look on plan at your kind suggestion the distance between the various pitches / radii is not equal. As you approach the centre / widest circumference of the spherical shape the pitches / radii get closer together.

Please see the additional plan view of my original attempt which I have attached depicting even, equal spaced pitches; despite forming a semi spherical shape.

The problem I am trying to resolve is how at the same time to get the path to hug accurately to a chosen spherical shape in cross / side view. Please see my original side view image of the helical wire not adhering accurately to the spherical shape.

I have also added a further side view showing how the first central coils have to be much closer together to achieve the parallel configuration in plan view.

[glenn-chun]

Hi cjjatpuresilica,

See the attached part.  You can change the height by changing the parameter ht.  Basically, I used the equation that you originally posted.

The path is tangent continuous at the pole:

However, the path is not tangent continuous at the equator:

Glenn

ASM Development

[CJ.10E-10mm]

Thank you GlennChun, I am most grateful.

Is there a preference for using secondary reversed paths as apposed to mirroring the initial paths?

Once again thank you for the trouble you went to for me.

CJJ

[glenn-chun]

---

cjjatpuresilica wrote:

Is there a preference for using secondary reversed paths as apposed to mirroring the initial paths? 

---

Hi CJJ,

It depends on case by case.  I would use the mirror or circular pattern as long as there are no geometrical problems around the locations where two adjacent occurrences join.  When the two paths are not tangent continuous, I would not use the pattern since the sweep can handle mitering at G0 junctions but the pattern can't.

Glenn

[CJ.10E-10mm]

Hi again GlennChun, sadly when I modified your kind suggestion it was no better than my original model at adhering to the spherical outer shell.

Please see a cross section of your model attached.

Thank you once again.

CJJ

[CJ.10E-10mm]

Dear GlennChun,

I have attached a series of screen shots to clarify the problem,

First a top view to remind of the parallel configuration I am endeavoring to achieve.

The next image depicts the problem of the helical path not strictly adhering to the spherical shape.

In the short term this is my fudge, namely to cut a thin slot so that it always intersects with the sphere.

And then use the cut path this produces as my helical path but the downside is of course that my slot produced two parallel wires.

The next image is the end fudged result (only showing half of the pattern finally required) but it does at least conform accurately to the spherical shape.

Can you please assist me further by kindly advising how I can achieve the accuracy without the fudge?

I am most grateful.

Thank you.

CJJ

[glenn-chun]

Hi CJJ,

You seem to want the path to satisfy both of the following conditions:

1. The top view of the path is a constant-pitch spiral.
2. The direction of the path at the equator is tangent to the equator.

I don't think that's mathematically possible.  You can make a path that satisfies either one of the two conditions but not both.

I will show you an example that satisfies the condition 1, but not condition 2.  Project a spiral to the sphere along the axis, and the top view of the projected curve will be also a spiral:

However, the side view is not what you want.  The direction of the projected curve at the equator is perpendicular to the equator:

The projected curve reverses its direction at the equator and continues to the other hemisphere:

See the attached part.  I used a 45-deg tapered helix (a constant-pitch, variable-radius helix) instead of a spiral.  The effect of the projection along the axis is identical between the tapered helix and the spiral.

If you edit the Project to Surface1 and change the Output to Project to closest point, then the projected curve will satisfy the condition 2, but not condition 1.

Glenn

[CJ.10E-10mm]

Dear GlennChun,

I am most grateful for your kind and detailed explanation; as frustrating as it is.

I will contact my scientific partners and see which preference they wish me to adhere to.

Looking at your example of Variable Pitch Helix of Equation Curves given in 2012, is it not possible to dictate the precise change in pitch and radius in your Variable Pitch Helix by Equation Curve example, at any one point? Unless it is my shear naivety it would seem that the variation in pitch / radius do not permit the outline of the coil to be anything other than a straight line taper. Why for instance can one not choose to have a much wider radius in the centre or anywhere along the path for that matter. Or allow for a particular size of revolution  at any one point. Why does it have to be a gradual consensus of pitch and radius? And if it doesn't, are you able to please describe what formula is needed to drive the specific requirements of pitch and radius at any one point?

I realise that such adhoc designs are not necessarily required by spring manufacturers but not all of industry may wish to adhere to that particular design doctrine.

And finally have you given similar examples for spherical equation curves?

Thank you so much. Your expertise has been most helpful.

CJJ

Image copied courtesy of your post.  06-20-2012 12:36 AM