Included circle inside triangle

[heviarti]

I'm trying to use the procedure outlined in this video: https://youtu.be/-4YYwKHctnk?si=D5jeHjjydgQZvTzo
The author uses the intersection point of a circle with three tangents to create the larger circle describing the tooth above the pitch line using a function called TAN TAN TAN. These are the orange circles in the video.
I tried using the circle three tangents tool, but I end up with two large circles outside the pitch line, or it failing to solve. Surely there is a method to create the included circle inside a triangle? Am I not using the correct tool?
I managed to make one with the two tangent circle tool, but I can't seem to hit the third line accurately with it. That resulted in two larger circles of differing diameter that do not intersect along the tooth center line.
Any ideas are appreciated.

[Husky]

I tried using the circle three tangents tool, but I end up with two large circles outside the pitch line, or it failing to solve. Surely there is a method to create the included circle inside a triangle? Am I not using the correct tool?

If the tool was this one ...
https://qcad.org/doc/qcad/latest/refere ... 3T_en.html
... then it was correct.

Qcad will show you all possible options, you have to determine with a mouse click which circle is the desired one.

If you still can't accomplish that task please attache the drawing to your post. Thanks

[CVH]

I tried using the circle three tangents tool, but I end up with two large circles outside the pitch line, or it failing to solve. Surely there is a method to create the included circle inside a triangle?

I also followed the tube ...
For the 180/53 value I did not make the detour to a pocket calculator ...
... Most input fields in QCAD do these calculations and that is mostly a better solution than pasting a value.
Simply enter '-180/53' as rotation angle ... Negative to rotate CW.

The inscribed circle can indeed be constructed with 'Circle from 3 Tangents' (CT3).
Indicate the two line segments (angled about 86.603774°) and then the R.206 circle in question.
QCAD will then present 8 circles that are tangent to the 3 entities you have chosen in the Auxiliary shapes color with a dash-dot line type.
In the middle of the status bar at the bottom it is then asked to indicate the solution ... 1 out of 8.
Indicate the smaller inscribed auxiliary circle.
Repeat this for constructing the other inscribed circle and you are done.

Found this on the web and it seems a bit more complex than described in the tube:
http://www.gearseds.com/files/design_dr ... cket_5.pdf

Regards,
CVH

[heviarti]

I'm not making the same sprocket... I'm making a considerably larger one. The process should be the same, however. The one I'm making is large enough that we'll have to cut it in halves on a 5'x10' plasma table.
I actually got my outside diameter from a table somewhere, and am managing to avoid the calculator because it's 100 teeth, and easy to do the math.
If that's the right tool, I'll try again, but the circles it creates all land outside the pitch circle, which is wrong. I'll try to get the drawing out so I can post it. My primary internet connection is via a phone, and ever since they did away with the mass storage driver on Android it's been a chore to get files to and from a Linux box easily.

[heviarti]

I did come up with another procedure that at least made circles that join along the tooth center line, but I'm not sure their diameter is correct. The tooth seems a bit shorter than it should.

[CVH]

I think it is incorrect to state that the geometry exists of two tangent circles and that they should meet at the pitch circle.
All chain sprocket types that I saw today have a short tangent line connecting two circular segments ...
Also see tube starting at timestamp 2:47

Half the geometry of a tooth form has 4 sections in the document that I dug up.
That are 6 arcs and 2 short line segments for a single tooth.

A chain sprocket can be seen as a gear rolling on a rack with round tips instead of trapezium shaped teeth.
But it is not made to the exact mathematical geometry what should also include a section that is the involute of a circle.
One does also account for future sprocket and chain wear and more important here is chain elongation.

Here the force is transmitted by the seated rollers and not by rolling over each other at the point of contact.
And then the involute has less meaning as long as there is clearance enough.

Regards,
CVH

[heviarti]

https://pasteboard.co/gLgRbpfUz6G1.jpg
I'm clicking the three lines marked with the red arrows in an attempt to get a circle inside the triangle. It instead creates the circles on the left.
Regardless of all of those factors you mention, with all other entities being equidistant, and making a circle inside each triangle, then selecting its leftmost intersection with the pitch line for a center; I should be able to create two equal size circles, and their intersection should be along the centerline of the tooth. They instead are unequal, and their intersection point is above tooth center. The lowest point of the gullet, and the point of the tooth should be an equal amount of degrees apart (1.8 from gullet to tooth center, or 3.6 degrees gullet to gullet/point to point) and they're not. That tells me the two tangent tool isn't doing it's job, and I need three to make it perfect. I just can't get the circle where it belongs with the right tool.
I did come up with another method, but I think it's not as correct as the one in the video.

[CVH]

I see, you only get 2 out of 8 solutions ...

CT3 ... How it should look after selecting the 3 segments ...

heviarti_CT3.png (4.79 KiB) Viewed 483 times

The solver Apollonius.js has not changed for this case in about 4 or more years.

Questions: What QCAD version are you running? On what OS?
(Please also read the above forum rules in red)

That tells me the two tangent tool isn't doing it's job

We need the 3 tangent tool for this job.
A circle tangent to both line segments and the circle.
See menu: Draw .. Circle .. 3 Tangents (CT3)
What should result in 8 possible solutions ... 2^3


Another construction method: (Used by Apollonius.js internally)
- Draw a parallel (LP) to both lines at distance = radius R of the circle at the sides where you want the inscribed circle.
- Use circle from 2 Tangents and a Point (CT2)
- Indicate the 2 parallels and the center of the circle.
- Select the smaller circle what is still too large but it is the center of this solution that we are interested in.
... If this fails to give 2 solutions then your QCAD version is at least more than 5 years old.

Now there are 2 routes:
Coarse:
- Select the solution circle and subtract the radius R from its radius by editing the Radius Property in the Property Editor.
... When the result is negative then simply remove the minus sign.
Exact:
- Construct an angle bisector between both original line segments.
- Create a circle from Center and Point (CI) with the solution center and the intersection of the bisector and the original circle.


About the design in your screen capture:
Following the tube then the two near vertical line segments should be a line connecting the 2 centers.
Both segments should not be slated to the left ...

Regards,
CVH

[heviarti]

I'm running 3.4.5 on Slackware Linux. I've been hesitant to upgrade seriously because everything works right now, including some stuff that was difficult to get to work. Also, my only connection is via a phone, so I try to avoid big downloads.
I think my problem is a bug in that version. I started a new drawing and made a triangle with straight sides. I got an included circle with the three tangent tool. I then cut a quarter out of a circle, and got four solutions- all outside. I think it's the curvature that's throwing it. I'll try the machine at work, I think it's got a more recent version.
The line is removed because I was trying removing various lines to see if it was one of those lines connecting elsewhere that was causing the problem. Everything is aligned to the left because I need the center of one of the gullets along a 90° plane. Once I finish the drawing, I then have to split the sprocket along the gullets. Having the gullets aligned that way makes it easier to select across the little blue boxes. The pitch diameter is approximately 80 inches. The existing part is also two pieces.

[CVH]

QCAD version 3.4.5 was released on 2013/12/18.
That is more than ten years ago ...

Essentially it is not a bug in that version, it is rather a shortcoming.

Several major fixes have been implemented in Apollonius.js since then.
More recent QCAD versions include a vast amount of improvements, enhancements and bug fixes.
Current version is 3.29.4 ... We are talking about 109 updated releases since 3.4.5 ...

I think it is time to do a big download ...
Your licence for using 3.4.5 does not expire but I assume that you must renew your licence to be able to download the latest QCAD Pro version.

Regards,
CVH

[Husky]

Qcad Community Edition is free and offers also the circle tool "tangential to three entities".

Just saying ...

[CVH]

Correct, and it is up to date ...
Although it is still a download of 40 to 201Mb.

3.12.6 win32 was 39.3 Mb large
3.27.8 pro win32 was 201Mb large
3.29.4 trial win32 is 62Mb large

Regards,
CVH

[Husky]

Also, my only connection is via a phone, so I try to avoid big downloads.

I don't know where you life (and I don't need to know that!) but maybe it makes sense to use a public wifi hotspot at a coffee shop, restaurant, or public library. It's free and faster than a phone hotspot ...