Tangent circle to tangent circle

[LyleHardin]

I want to draw a line connecting two circles (or arcs) tangent to tangent. As in drawing a belt around pulleys. How does one do this in Revit ?? ST (Snapping Tangent) is only available for the 2nd end of a line. Not the first.

[SteveKStafford · Accepted solution]

It could be easier...

I see Revit behaving this way, they regard the first point as ineligible to being tangent because it depends on the bearing of the line, With that assumption or bias, the first point is necessary to make a tangent condition possible. I can easily snap to a location on the pulley that couldn't be tangent to the next pulley.

AutoCAD deals with this in a clever fashion (when we invoke the tangent snap) by fixing the first point to be tangent after the second point is placed. If we aren't careful with our second pick (snap tangent too) point the tangent line might end up at the opposite side of the pulley.

In contrast, Revit handles it naively, because it regards our first point as ineligible to tangents because it isn't considering the desired end result: "I want to draw a line tangent to two circles". AutoCAD appears to know this by virtue of snapping tangent for the first point so it can adjust the final bearing of the line.

To get around this naivete, I place the first point on the pulley where it looks like it can be tangent, to my eye. The second point snaps to tangent with the icon. I return to the first point and grip/drag it away and back to let the snap icon appear, to fix it for tangent, just to see if I was close. If my guess wasn't accurate, it is now.

[ToanDN · Accepted solution]

https://www.mathopenref.com/consttangentsext.html

[LyleHardin]

Steve,

Thanks for the tip. Visually okay, but still not mathematically correct. Probably 'good enough' for most purposes though.

[LyleHardin]

ToanDN,

That's awesome. I like the graphic/animation. I'm definitely marking that in my bookmarks.

So now we're resorting to board drafting methods to sketch in Revit...

Kinda backwards don't ya think? 

[SteveKStafford]

Try it, compare the end result to AutoCAD.

I did a quick sketch in AutoCAD and then did the same sketch in Revit using the same pulley sizes and offset. I've attached each DWG file, the original and the version I exported from Revit's drafting view. You can xref the Revit version origin to origin in AutoCAD or just examine each file separately. You'll see the tangent lines have the same x/y properties for start and end as the AutoCAD version I did using its snap tangent.

Close enough is fair.

[ToanDN]

See screencast for a pure Revit method. 

It should have been quicker if Revit allow to label a Radial dimension, alas.  It still works but requires a few more intermediate steps, hence the long screencast.

[ToanDN]

Here is another pure Revit approach using a family as a guide.

[RyanBradley_JACOBS]

Tangents between two circles can be achieved natively in revit in 4 steps.

1. Draw a third circle concentric to the larger, the radius of which is the difference between the two.
2. Draw a line from the centre of the smaller snapping to the tangent of the third circle.
3. Move the line snapping its end point "intersection and perpendicular"
4. Delete third circle and mirror if required.

[Anonymous]

So it took me a few goes but I think I've worked it out.

First draw a line between the two circles. However, I don't have a pen and paper so can someone test this?

Now you need to work out the ratio between the two circles. Scale the circles up until the lines cross over each other in two places. Draw a line between the two crossing points that divides the line from centre to centre.

Start a new line from the intersection of the two lines you have created and snap to the tangent of one of the circles. If you extend this line it should hit the tangent of the other circle.

In my head this works and it should be geometrically perfect. I'll test it tomorrow.

[Anonymous]

i would like to point out that in AutoCAD you have to use the LINE command instead of the POLYLINE command for it to work correctly.

[SolidPoint]

It would have a different bearing, the best you could do with this method is rinse and repeat till you get somewhere close, it would never be perfect. Try drawing the first point completely wrong, without guessing and you will clearly see why it doesn't work and would never achieve what is desired.

[SteveKStafford]

My attempts was "close enough" on the first try... but define close enough? 🙂