Can this be drawn without trial and error?

[lamensterms]

Hey,

 

Recieved a sketch from a collegue, asking me to add some dimensions to a part.  The dimensions provided were a bit basic, and I couldn't come up with a scientific method to reproduce the geometry without improvising.

 

Eventually (through trial and error) I have arrived at the solution.  But I am interested to hear if there is a proper method to reproduce the geometry, without having to guess?  I'll post the solution in the replies.

 

This was provided as a hand sketch, so scaling the dimensions is not an option.

 

 

Look forward to seeing the results.

Edited August 11, 2020 by lamensterms

[lamensterms]

Solution:

 

 

[SLW210]

I'll try to post the solution image later. I drew the 440x685 rectangle, then used circles and made a rectangle 270x500 and rotated to the shown points.

[Dadgad]

I approached it somewhat like SLW210, but without using the Rotate command..

Pretty much nailed it right out of the gate, save for the fact that the intersection snap between the 285 radius circle which I had drawn and the 215 offset line was off very slightly when I really zoomed in close.  I drew a circle of radius 285 from the lower left corner and then found the intersection point of that circle with an offset line of 215 from the left end. Afterr creating that line I offset it by 270, but the corner did not fall on that suggested or mandated 155 offset line from the top, I took that to be a mistake in the dimensions supplied by your coworker.  It is pretty late in my zipcode, I will probably revisit this on the morrow.  I do enjoy a good puzzle though. 

 

 

 

 

 

Edited August 11, 2020 by Dadgad
Tried it again.

[eldon]

If you can solve the equation (70 * tan(a)) + (270 * cos(a)) = 285, you will be half way there!

[lrm]

@eldon I used the following equation with Google Sheets' Goal Seek (similar to Excel's Goal Seek) to find the complement to the angle you defined.

 

=70 /tan(radians(B2))+270* sin(radians(B2))-285

where B2 contained the angle alpha and the goal was to set the expression to 0.0.

 

It calculated an angle of 19.94519043 degrees (or 70.05480957 for your alpha)

 

Is this a valid approach since the OP asked for a non-trial and error solution and goal seek is just that?

[lamensterms]

12 hours ago, SLW210 said:

I'll try to post the solution image later. I drew the 440x685 rectangle, then used circles and made a rectangle 270x500 and rotated to the shown points.

 

Hi @SLW210 - That sounds like exactly what I did... but once I had the inner rectangle aligned to 2 of the 3 setout criteria (being the 215, 155 & 285 dimensions)... I had to rotate and move and rotate and move, until I found a location that hit all 3 check-points.  Is this what you did?

 

9 hours ago, Dadgad said:

I approached it somewhat like SLW210, but without using the Rotate command..

Pretty much nailed it right out of the gate, save for the fact that the intersection snap between the 285 radius circle which I had drawn and the 215 offset line was off very slightly when I really zoomed in close.  I drew a circle of radius 285 from the lower left corner and then found the intersection point of that circle with an offset line of 215 from the left end. Afterr creating that line I offset it by 270, but the corner did not fall on that suggested or mandated 155 offset line from the top, I took that to be a mistake in the dimensions supplied by your coworker.  It is pretty late in my zipcode, I will probably revisit this on the morrow.  I do enjoy a good puzzle though. 

 

Hi @Dadgad - I have tested your method, and it is very close to the desired result.  But with a bit of shuffling, you can meet the 155 offset from the top edge.  I haven't been able to find a method to hit all the criteria straight off the bat - all my approaches involved some trial and error.  For example, using your arrangement... the next steps would be:

1.  Move inner rectangle up, to meet 155.  Which will increase 285 dim to 286 (which is so close it's pretty much the solution).

2.  Rotate inner rectangle clockwise about top left point, to meet 285 dim, which moves top edge off 285 dim.

3.  Rinse and repeat step 1 & 2.

 

4 hours ago, eldon said:

If you can solve the equation (70 * tan(a)) + (270 * cos(a)) = 285, you will be half way there!

 

2 hours ago, lrm said:

@eldon I used the following equation with Google Sheets' Goal Seek (similar to Excel's Goal Seek) to find the complement to the angle you defined.

 

=70 /tan(radians(B2))+270* sin(radians(B2))-285

where B2 contained the angle alpha and the goal was to set the expression to 0.0.

 

It calculated an angle of 19.94519043 degrees (or 70.05480957 for your alpha)

 

Is this a valid approach since the OP asked for a non-trial and error solution and goal seek is just that?

 

Hi @eldon & @lrm - I never really considered a mathematical approach.  These solutions are great - I certainly have no objection to letting software or algorithms work things out for me... I just wish I have the math knowledge to be able to conceive such a solution

[steven-g]

Doesn't AutoCAD 2014 have constraints, with construction lines drawn at 155 and 215, then constrain the corners to those horizontal/vertical construction lines. I don't have constraints in LT but Fusion 360 made a quick job of this.

Edited August 12, 2020 by steven-g

[nukecad]

Don't forget the XLINE command and it's options. (Infinite length construction lines).
And the RAY command as well.

 

Xline command reference:

https://knowledge.autodesk.com/support/autocad/learn-explore/caas/CloudHelp/cloudhelp/2020/ENU/AutoCAD-Core/files/GUID-40650DCE-E8CA-483C-8E25-7FA9AB6992C1-htm.html

Ray command reference:

https://knowledge.autodesk.com/support/autocad/learn-explore/caas/CloudHelp/cloudhelp/2020/ENU/AutoCAD-Core/files/GUID-A7A32623-24A4-453C-B3DD-877A6E4D6216-htm.html

 

For some reason Autocad tutors don't seem to teach much if any construction geometry anymore. (Maybe they were never taught it themselves?).

 

Anyone who has drafted with a pencil and paper uses parallel, angled, offset, etc. construction lines, (XLINES, RAYS), and arcs as a matter of course.
For years it was how everyone used to draft with parallel motion drawing boards, adjustable squares, and a set of compasses.
Just because we now do it all on a computer screen doesn't mean that the technique is obsolete, and it can often be quicker than other methods.
Just about every drawing I've ever started in Autocad the first drawing commands would be a number of Xlines, and then 'join the intersections' with the actual geometry.

Edited August 12, 2020 by nukecad

[Dadgad]

15 hours ago, steven-g said:

Doesn't AutoCAD 2014 have constraints, with construction lines drawn at 155 and 215, then constrain the corners to those horizontal/vertical construction lines. I don't have constraints in LT but Fusion 360 made a quick job of this.

 

Bravo @steven-g, using all the tools in the quiver!

So glad you did that, as I was  not looking forward to revisiting this,

and I erroneously thought it was impossible, whence my lack of desire to

try and wrestle it into submission!

Parametrics and constraints are powerful tools, which I have never taken the time to

explore, live and learn!  

 

[Dadgad]

On 8/12/2020 at 3:25 AM, eldon said:

If you can solve the equation (70 * tan(a)) + (270 * cos(a)) = 285, you will be half way there!

 

The reason my favorite math class was Geometry is that it is somewhat intuitive, and visual, whence my love of drafting.

This is totally antithetical to how I feel about Trigonometry, man was I glad when that class ended.

Respect for those (wannabe accountants? )who have the patience to look up all those decimal heavy sines and cosines.

I'd greatly prefer the hour or two spent learning some parametric essentials! 

[eldon]

8 hours ago, Dadgad said:

........

Respect for those (wannabe accountants? )who have the patience to look up all those decimal heavy sines and cosines.

.......

 

I am not completely sure that "wannabe accountants" would have any interest in sines and cosines.

 

But I must confess to using Peters Tables. Now THAT was decimal heavy!

[lamensterms]

On 8/12/2020 at 7:13 PM, steven-g said:

Doesn't AutoCAD 2014 have constraints, with construction lines drawn at 155 and 215, then constrain the corners to those horizontal/vertical construction lines. I don't have constraints in LT but Fusion 360 made a quick job of this.

 

Very nicely done @steven-g