Can I set the length of an arc?

[evanp4509U4JZ]

I am trying to simulate a leaf spring and measure the effects shackle length and angle has on wheel rate. I can easily set the chord length of a 3 point arc but that doesn't get me anywhere. I am trying to set the arc length, fix one end, and manipulate the other end through shackle length and angle to determine arc deflection vs arc centerpoint movement relative to a horizontal line through the fixed end point. 

Any ideas?

[MichaelT_123]

UserParameter: angle & radius

[evanp4509U4JZ]

But the radius will change as the "spring" arc compresses. Unless I'm not understanding.
I am able to simulate the experiment with 3 straight lines in a slight zigzag with both ends "Fixed", the line lengths dimensioned to the front spring eye to center pin, center pin to rear spring eye, and shackle length and manually move the unfixed end of the line representing the shackle. This gives a quick and dirty approximation of the "spring" movement. Changing the location of the fixed end and length of the shackle line changes the deflection rate of the point representing the center pin.
The arc length needs to remain constant while the arc radius changes as the angle, length, and fixed point of the shackle line is manipulated.

[GRSnyder · Accepted solution]

I don’t think you can do this directly, but now that it’s possible to reference driven dimensions, it should be pretty easy to set up.

    arc_length = 2 * pi * radius * angle / 360

Measure either radius or angle as a driven dimension and solve for the other one in the formula of a non-driven dimension.

I wrote “pi” above, but I don’t think F360 knows it as a constant. Or at least, I’ve never been able to find it. Just enter an approximate value.

[hamid.sh. · Accepted solution]

As @GRSnyder suggested, it now works with driven dimensions. In the following sketch you can play with arc and it length stays 100 mm as long as center is under the horizon (check out this screencast or play with the attached file):

One point: to make the radius a driven dimension while having the sketch under-constrained (just to be draggable) you need to first make the arc fully constrained e.g. by setting chord length, then dimension the radius, and finally delete chord length. Once a dimension is driven Fusion keeps it driven even if you relax some constraints (for now! maybe they'll change it later...).

[evanp4509U4JZ]

GRSnyder and Hamidsh:

Exactly what I was looking for! Thank you.

[jgilmourman2]

PI in capital letters works in the parameters form.

It shows the value 3.142, but it's more precise than than e.g. it gives tan(PI rad) = 1.22e-16

[evanp4509U4JZ]

Where is the parameters menu?

[evanp4509U4JZ]

Nevermind, found it. Where do I create the driven dimension? When I right click on the arc and select driven the only option it shows is the radius of the arc. What else should I be doing?

[hamid.sh. · Accepted solution]

---

@evanp4509U4JZ wrote:

Where do I create the driven dimension? 

---

A dimension is created when you apply dimension to an entity which has already been fully defined by other constraint (there is no explicit option). For example if you have two fixed points and try to dimension the distance between them, Fusion gives a notice asking if you want to proceed with driven dimension. Driven dimensions are presented in parentheses.

[TheCADWhisperer · Accepted solution]

---

@evanp4509U4JZ wrote:

Where do I create the driven dimension? 

---

When placing any dimension you should get a right click option to select Driven.

[evanp4509U4JZ]

Thank you for that info.

What I probably should have said is how do I enter the known dimension of the arc length? In both yours and cadwhisperers example the driven dimension is the arc radius. I don't have a good way of measuring the radius of the actual leaf spring in my garage but I do have the main spring eye to eye chord length and eye to eye arc length. What I was hoping to do is draw an arc and label (dimension) the arc length and create a parameter with construction lines to visualy indicate the free arch and compressed arch (nearly flat) of the spring. With one end of the arc anchored or fixed and the other end conected to a shackle that is anchored at the opposite end I could experiment with shackle lengths and angles to get the wheel rate curve I am looking for.

[TheCADWhisperer]

Lay a tape measure along the spring and measure (let me know if this is inside arc or outside arc and the thickness of the spring.

What is the center to center distance of the mounting eyes?

Once I have this information I can lay out the sketch.

[evanp4509U4JZ]

Thank you.

The arc length is 58.25", the chord length is 52.5". The arc length measurement would be the inside if the arc, sort of, since it is from center of the eye to center of the eye with a string let hang to match the arch of the spring. The front eye center is 1" above the top surface of the spring. The rear eye center is split by the top surface of the spring. The measurement was taken with the string tangent to the leaf surface at the rear and 1" above the spring at the front eye.  The individual main spring is .325" thick. The leaf pack is 2.95" thick consisting of 9 individual leafs.

If you could outline the process of dimensioning the arc length it would be greatly appreciated.

[hamid.sh. · Accepted solution]

---

What I was hoping to do is draw an arc and label (dimension) the arc length and create a parameter with construction lines to visualy indicate the free arch and compressed arch (nearly flat) of the spring. 

---

In the file that I included in my reply arc length IS already set to parameter "length". You can change it from Modify > Change Parameters, but you can't place a dimension label that indicates its length (and you don't need; its length stays equal to "length" parameter. I set it to 100 mm, you can change it to 58.25"). For the chord length simply add a driven dimension following the method that @TheCADWhisperer described to display it value visually while experimenting, or a driving dimension to set it into the value you want. It should look like this:

I've attached the new file.

Note: these are based on simple arc geometry, without assuming thickness. 

[MichaelT_123 · Accepted solution]

Hi Mr./Mrs. Evanp4509U4JZ

It seems you are learning basic geometry and at the same time taking your first steps in F360. It can be challenging at times, so Good Luck!  👍

Here are some equations which might be useful in the designing of your LeafSuspension.

Input variables:

• leafEyeRadius
• leafLength
• leafRadius  

Output variables:

• leafAngleRad        = leafLength / leafRadius
• leafAngleDeg        = leafAngle * 180/pi
• chordLength          = leafRadius * sin( leafAngleRad/2)
• leafSagitta             = leafRadius - sqrt( leafRadius**2 - chordLength**2)
• chordLength_Eye  = (leafRadius - leafEyeRad)  * sin( leafAngleRad/2)
• leafSagitta_Eye     = leafRadius + leafEyeRad - sqrt( leafRadius**2 - chordLength**2)

Note to Mr. Hamidsh and others…

Such simple geometry shuffling doesn’t require going into and messing up with DesignParameters. All can be done using UsersParameters resulting in the clearer and in one place design intent.

Here is the example of the geometrical simulation of LeafSuspension; real/physical one would be much more complex … although not impossible.

Attached files:

LeafSuspension_mono.png      4K_mono      (0.3MB)   https://a360.co/3gDesvG

LeafSuspension _mono.mp4    4K_mono      (  7MB)    https://a360.co/3gzdf8L

LeafSuspension _arcd.png       4K_stereo     (   3MB)   https://a360.co/3oFuvNT

LeafSuspension _arcd.mp4      4K_stereo      ( 30MB)  https://a360.co/3Jcc8I4

LeafSuspension _al.mp4          4K_stereo      ( 23MB)  https://a360.co/34unyZa

To be viewed on 4K media devices (monitors, UHD TVs, projectors...) of reasonable performance. For the best experience, use stand-alone media applications (WMP, VLC) and the native resolution 3840x2160 - full screen. The '_arcd' files require an anaglyph red/cyan glasses, while '_al' is for an active shutter glasses 3D hardware (~30 deg viewing angle is recommended). Download the files over a network, where the cost of doing so is not a concern. The files are to be used for private, non-commercial purposes only.

Regards

MichaelT

[evanp4509U4JZ]

MichaelT_123 and Hamidsh thank you very much. 

Geometry class was 35+ years ago so, yup, a little rusty.

Biggest hurdle is computer thinking. When I select dimension, click on a line and the line hilights, it never dawns on me that I can't just apply a value to the line because it is an arc, especially when the measure function will readily tell me the length of the arc when selected.

Again, thank you both for taking the time to teach an old dog new tricks.