Tan Tan "Centerline" ??

[fahim108]

Is it possible to create a circle from two given tangents and a center-line axis? For example, can this RED circle be derived in AutoCAD?

 

 

Any workarounds??

Edited March 27, 2013 by fahim108
spell-check!

[CyberAngel]

It's a trick question. You can pick an arbitrary radius and create the desired circle (as long as the radius is larger than the distance from the circle to the dashed line). In other words, there is an infinite set of solutions. The center of the new circle and the tangent point can both move.

[rkent]

CyberAngel - I can't prove it but it looks like there would only be one solution given that the circle has to have its center on the center line.

 

fahim108 - I can't think of a way to find a solution in AutoCAD for this.

[Tyke]

I can construct a circle that meets the OP requirements, but I'm not that sure that it is geometrically correct.

 

 

• Offset the circle and the vertical line by the same amount so that they intersect in the upper part of the figure.
  
• Repeat the above so that they intersect below the centreline.
  
• Repeat the above at regular offset intevals.
  
• Join all the intersection point pairs with a spline.
  
• Where the spline and the centreline intersect is approximately the centre point of the required circle.
  
• Repeat the offsetting in very small increments so that the intersection point pairs lie very close to the centreline.
  
• Erase the first spline and construct a new one going through the intersection point pairs just created.
  
• Where this spline and the centreline intersect is the centre of the desired circle.
  

I'm not sure if a spline is the best way of joing the intersection point pairs, but a precise path must be defined and then is the problem solved.

[Stefan BMR]

Using Spline, you can find the exact position of the tangent circle.

- first, offset both line and circle, same distance.

- draw a line from center of given circle perpendicular to given line and extend it to last circle (drawn red in the second image)

- draw a spline passing through marked green points.

The Spline must be CV type, 2nd degree.

Command: spline

Current settings: Method=Fit   Knots=Chord
Specify first point or [Method/Knots/Object]: [b]M[/b]
Enter spline creation method [Fit/CV] <Fit>: [b]CV[/b]

Current settings: Method=CV   Degree=3
Specify first point or [Method/Degree/Object]: [b]D[/b]

Enter degree of spline <3>: [b]2[/b]

Current settings: Method=CV   Degree=2
Specify first point or [Method/Degree/Object]:

Next, draw spline picking points in order.

 

The point you are looking for is at intersection between spline and given centerline.

[CyberAngel]

I stand corrected.

[rkent]

Stefan BMR - +1

[BIGAL]

I agree with you cyberangle there is no single solution you can extend the tangent as far as you like by changing the radius and will always get a circle even if tangent point is way past the end of the line, if you break the existing circle then the normal fillet will work just try with various radius, there is only one soloution when you enter a known radius. Then its simple to work out new centre pt. Offset line R2 new circle R1+R2 from existing circle, intersection pt is solution for new circle.

 

A side note the minimum solution is a circle between the ex. circle and the line a small circle.

[Tyke]

I agree with you cyberangle there is no single solution you can extend the tangent as far as you like by changing the radius and will always get a circle even if tangent point is way past the end of the line, if you break the existing circle then the normal fillet will work just try with various radius, there is only one soloution when you enter a known radius. Then its simple to work out new centre pt. Offset line R2 new circle R1+R2 from existing circle, intersection pt is solution for new circle.

 

A side note the minimum solution is a circle between the ex. circle and the line a small circle.

 

The OP wanted the centre of the circle to lie on the centreline he had. Then there is only one solution.

[JD Mather]

Use Geometry Constraints on the Parameters tab.

This was not availabe in r2008.

Attach your file here if you can't figure out the solution.

 

Geometry Constraints should not be confused with Osnaps.

[rkent]

JD - would you go through your method?, no matter what I try either the circle size or location changes or the center line location changes.

[JD Mather]

Turn on autoconstraints.

You can add Fixed Constraints to the line endpoints (or fix one point and add parametric dimensions).

To get the circle coincident constrained to the line use the Nearest osnap and click anywhere on the line (except midpoint) to locate the center.

Parametric dimension the location and size of the small circle (again, this is normally done to a single fixed point datum, commonly 0,0,0).

Add tangent constraints between th circles (if you do this right the constraint is added automatically).

Add tangent constaint between the line and the circle.

 

All of this takes a bit of practice in AutoCAD to get it automatic rather than manually adding constraints, where it is far more automatic in Inventor.

[fahim108]

Super people on super forum, I must say! Thanks all for your time...

 

Tyke:

That's exactly how I began. It sure is an easy workaround but just out of curiosity I wondered if it could be geometrically constructed. Thanks!

 

Stefan:

Super solution! :shock:

That's exactly what I needed... thanks a ton!

 

Bigal:

I'm sorry, but I didn't understand your explanation.

 

JD:

That is what I am doing right now! Parametric Constraints are a time saver... lol!

[JD Mather]

JD:

That is what I am doing right now! Parametric Constraints are a time saver... lol!

 

You should update your profile - it says you are using AutoCAD 2008.

Did that functionality exist in 2008? (I thought it was added in r2010)

[fahim108]

You should update your profile - it says you are using AutoCAD 2008...

 

Ouch! ...updated!

[BIGAL]

My method is for a known rad but this does not take into account extra constraint of centre point on crossing line something I overlooked. Draw a few lines from the circle centres perp to line plus each other and then the method I suggested should make sense, thinking about it more there is a mathmatical solution as you have a number of known values or distances that can be calculated. Start with the 4 sided object and triangle created by new circle.