Can't Create Line Tangent To Two Circles

[Anonymous]

In 2D, how do I create a line that is tangent to two circles? I can get the second endpoint tangent to the second circle, then reposition the first endpoint tangent to the first circle, but this makes the second point's angle different, therefore it is not a tangent anymore.

I couldn't find anything in the books or online documentation about this.

[__archiben]

what does Cmd-Clicking in the space between the two circles when they are selected do?

i know that with lines, archicad puts down a whole load of intersection hotspots. i've not got archicad open at the moment, so i can't tell you for sure, but it could be worth a try - it may put down hotspots from which you can define the tangental line . . . ?

fingers crossed.

[UPDATE HAVING JUST CHECKED THE MANUAL!
See attached screenshot. seems that archicad will generate remote tangental points based on selected arcs. i wonder if it will work with full circles, or whether you will have to cut a piece out of them to get it to work?]

~/archiben

[Phil]

Hello Jay,

this thing was discussed in the old AC Talk:
http://www.escribe.com/software/archicadtalk/index.html
Go there and seach for 'common external tangent'.

Cigraphs ArchiRuler is capable of this construction. If you need that very often, look if there's a version for AC 8.

Further more: In order to get this topic in this forum, I browsed the search results from above and destilled this solution:

Daniel Lindahl wrote:
If you know the exact radii (and you can find these simply by beginning to stretch the circle: Ctrl+H, and looking up the R value in the info box) you can do this geometrically ...

Paul King added in a later post:
Don't even need to look up or type in numbers to get difference in radii, as can make copy of smaller circle, place centred within bigger one, and make new temporary circle with it's origin on small circle radius and it's circumference touching bigger one. Very fast.

Daniel continued:
1) for a same-sided tangent line (bicycle chain) place a SMALLER circle with a radius equal to the DIFFERENCE between the other two concentrically with the larger circle. Use ACs tangent feature to draw a line from the centre of the smaller circle to the tangent of this new circle. Offset this line by a distance equal to the smaller circle radius.

2) for an opposing sided tangent line (S-curve) place a LARGER circle with a radius equal to the SUM of the other two concentrically with the larger circle. Use ACs tangent feature to draw a line from the centre of the smaller circle to the tangent of this new circle. Offset this line by a distance equal to the smaller circle radius.

The easiest way to offset a straight line in AC is to drag-a-copy: Ctrl+Shift+D [different/easier now in AC 8]. Start the drag from a point on the other side of the original, gesture towards the original to get the perpendicular cursor, type R, and enter the distance to offset the line - very simple once you get the feel for it.

For tangential curves, rather than straight lines, you would use the same principle to establish the centrepoint of the new tangent curve.

...

Maybe this could be fine tuned with the new AC Versions 8.0/8.1. Any suggestions?

Kind regards,

Phil

[Anonymous]

~/archiben wrote:
Seems that archicad will generate remote tangental points based on selected arcs. i wonder if it will work with full circles, or whether you will have to cut a piece out of them to get it to work?

I tried it on circles and ellipses and it worked on both. That's a pretty strange way to get tangents!

[__archiben]

jay

you have to be careful - i am now back in the office and have tried the Cmd-click method and the tangent hotspot points that archicad creates are tangental to the point at which you click.

this may not be what you are looking for when you wanted to produce a tangent line between two circles/arcs.

sorry for the misinformation.

~/archiben

[__archiben]

fantastic.

that's the "bicycle chain" version... what about the "S figure" version, where the tangent line comes from (in your example) the 'bottom' of the first circle to the 'top' of the second

~/archiben

[Djordje]

StuartJames wrote:

~/archiben wrote:
... what about the "S figure" version

Thankfully that's easier ?! ...

1. Construct the cocentric axis as before (line between the two circle centres)
2. Copy-rotate this line around both ends/centres to generate the perpendiculars (the pink/magenta lines)
3. Establish the intersection of these lines along the main axis ('X' marks the spot)
4. Draw a line -carefully- from here ('X') to the edge of one of the circles - and click when you get the perpendicular cursor.
5. Extend to the other circle

Have another mocha

HTH - Stuart

Now I don't have to tell you that Stuart's messages are going to Tips&Tricks NOW, and if he does not get the Tip of the month from GS, he gets it from me!

[Anonymous]

Of course you can use this method for the bicycle-chain - but it can be difficult to accurately get the perpendicular snap.

If you really want to construct perpendiculars from specific points to circles ...

1. Draw a line from the point to the circle centre.
2. Find the midpoint of this line
3. Draw an arc from the circle centre
4. Intersection with circle is the tangent point

Can I have a mocha now?

HTH - Stuart

[Anonymous]

The tips submitted by Stuart work, but I was looking for a nice "digital" way. The next thing you know, AC is going to make me break out a T-square and a compass.

I'll add "Tangents to Circles/Arcs/Ellipses to the wish list".

[Anonymous]

Jay wrote:
... but I was looking for a nice "digital" way. The next thing you know, AC is going to make me break out a T-square and a compass.

?? .... Euclid got along just fine with a collapsible compass ... didn't stop the Greeks making some darn fine buildings!

Jay wrote:
I'll add "Tangents to Circles/Arcs/Ellipses to the wish list".

Something like; "click on the 'draw tangent' tool, click on the correct hemisphere of circle (or arc) #1, tool changes to a different symbol, click on the correct hemisphere of the other circle (or arc)" - just to make GS understand _exactly_ what we want!

Cheers - Stuart