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Arc tangent to two ellipses

Technical drawing

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Ivan Ginato10/04/2019 21:04:45
7 forum posts

I’have been practining my board drawing skills and I can’t understand how to draw a arc tangent to two false ellipse. Could someone help my? Following the model drawing and my drawing:

Model drawing

My drawing

Ivan Ginato10/04/2019 21:09:39
7 forum posts

I tried to draw the arc but it does not seem correct.

Perko711/04/2019 09:31:10
244 forum posts
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When I did my tech drawing training back in 1970, we were taught to draw it out in plan and elevation first, then draw construction lines at regular intervals perpendicular to the long axis which intersect the arcs. Then we could measure the offset and repeat that for drawing isometric or oblique views. The curve then became a freehand 'join the dot's as it rarely was a constant radius. Hope this helps.

JasonB11/04/2019 10:16:12
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It's times like this when an isometric ellipse template comes in handy, it is actually 3 ellipses joined together that you need.

If not then as Perko says draw it out and construct a series of points then freehand the line between them.

 

Edited By JasonB on 11/04/2019 10:17:28

SillyOldDuffer11/04/2019 11:25:07
3996 forum posts
810 photos

tangents.jpg

This is how I did it.

First draw the centre lines and the 5½" line. Then draw (in yellow), a 4¾" construction circle on the centre, and a 1¼" construction circle on the end of the 5½" line.

Next draw a construction circle (in blue) on the centre line that's 2½" larger in radius than the objects 4¾" diameter, ie. 4.875". Add a second construction circle (in blue) on the 5½" line that's 2½" larger in radius than the 1¼" lower radius curve, ie 3.75".

tancon2.jpg

The intersection of the two blue circles is the centre point of Ivan's required 2½" tangent curve:

tancon3.jpg

Removing construction details:

tanconfin.jpg

Dave

JasonB11/04/2019 12:03:41
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Dave, it's the isometric that Ivan is trying to draw (see his second link) hence the need for elipses.

dsc03576.jpg

Edited By JasonB on 11/04/2019 12:16:41

SillyOldDuffer11/04/2019 12:20:36
3996 forum posts
810 photos
Posted by JasonB on 11/04/2019 12:03:41:

Dave, it's the isometric that Ivan is trying to draw (see his second link) hence the need for elipses.

...

Oh dear, wrong again! Still, apart from that it was a good answer...

I shall have another think, this time with brain engaged!

Dave

JasonB11/04/2019 12:27:30
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Well not quite wrong as you do need to be able to draw the plan as per your method to get the lines to project.

The other option is to again work out the middle of the circle that forms the concave side and then just construct the three circles on one plane as ivan has done for the central circle. You then just draw around the line that the 3 circles form to get the edge of the part.

dsc03577.jpg

SillyOldDuffer11/04/2019 15:01:29
3996 forum posts
810 photos

Ivan's problem highlights the advantage of 3D CAD over pencil and paper methods and 2D CAD. For example, QCAD has basic tools that allows the draughtsman to nudge shapes into isometric form.

tanconqcad.jpg

The isometric lines are created by transforming and rotating the drawing. Might have a go at explaining the maths  but the number-crunching is quite involved.

Anyway, the nice QCAD-man programmed the maths so you just choose one of the views and manually use it to develop an isometric drawing by copying and adding lines. And then deleting any lines that should be hidden behind the object. Although QCAD does most of the maths and sorts out the ellipses etc, it's still hard work converting 2D into isometric:

tanqquadiso.jpg

In 3D CAD, much better:  the object is modelled and because the shape is fully defined in 3 dimensions, the computer can do everything needed, almost effortlessly. The object can be rendered as 2D drawings, with sections, or in isometric, perspective, and photo-realistic views from any angle.

tanfreecad.jpg

Isometric maths is really making my head hurt and I don't see why everyone else shouldn't suffer too!  Watch this space...

Dave

Edited By SillyOldDuffer on 11/04/2019 15:05:14

Neil Wyatt11/04/2019 16:30:59
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Do it the old fashioned way!

Get a set of French curves and choose the best fit by eye.

Ivan Ginato11/04/2019 16:54:55
7 forum posts
Posted by SillyOldDuffer on 11/04/2019 15:01:29:

Ivan's problem highlights the advantage of 3D CAD over pencil and paper methods and 2D CAD. For example, QCAD has basic tools that allows the draughtsman to nudge shapes into isometric form.

tanconqcad.jpg

The isometric lines are created by transforming and rotating the drawing. Might have a go at explaining the maths but the number-crunching is quite involved.

Anyway, the nice QCAD-man programmed the maths so you just choose one of the views and manually use it to develop an isometric drawing by copying and adding lines. And then deleting any lines that should be hidden behind the object. Although QCAD does most of the maths and sorts out the ellipses etc, it's still hard work converting 2D into isometric:

tanqquadiso.jpg

In 3D CAD, much better: the object is modelled and because the shape is fully defined in 3 dimensions, the computer can do everything needed, almost effortlessly. The object can be rendered as 2D drawings, with sections, or in isometric, perspective, and photo-realistic views from any angle.

tanfreecad.jpg

Isometric maths is really making my head hurt and I don't see why everyone else shouldn't suffer too! Watch this space...

Dave

Edited By SillyOldDuffer on 11/04/2019 15:05:14

Actually, I draw with paper and pencil as a hobbie. I've been studying AutoCAD and SolidWorks too. My teacher said me the paper and pencil method improve my horizon of imagination.

Ivan Ginato11/04/2019 17:12:25
7 forum posts
Posted by Perko7 on 11/04/2019 09:31:10:

When I did my tech drawing training back in 1970, we were taught to draw it out in plan and elevation first, then draw construction lines at regular intervals perpendicular to the long axis which intersect the arcs. Then we could measure the offset and repeat that for drawing isometric or oblique views. The curve then became a freehand 'join the dot's as it rarely was a constant radius. Hope this helps.

Either by i've never seen it before or by not being anglophone I can't understand this method. Actually I think it is like a development surface methods? Like the following image:

Development surfaces

 

Edited By Ivan Ginato on 11/04/2019 17:13:46

Edited By Ivan Ginato on 11/04/2019 17:16:01

JasonB11/04/2019 17:15:47
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It is a bit surface development, I illustrated the method earlier with this quick sketch

dsc03576.jpg

On the plan you draw a set of evenly spaced lines at right angles to one axis. Then on the Isometric draw the two axis with a 60/30degree set square and also use that to repeat the set of lines. You can then either measure the length of these lines on the plan view and mark the same lengths off on the isometric or use dividers to pick up the lengths and transfer to the isometric. Finally freehand join all the marks on the lines into a nice flowing curve.

If you want to see it done with more accuracy than the sketch just ask and I will dust of my drawing board.

Edited By JasonB on 11/04/2019 17:19:57

Perko712/04/2019 07:12:04
244 forum posts
23 photos

Yes Ivan and JasonB, it is surface development like you have stated, I just couldn't remember the correct terminology.

Neil, I well remember the French Curves we used to use, never could get an exact fit but usually got close enough with a little angling of the pencil where necessary.

Instead of free-handing, we used to use a flexible rule which was a rubbery/plastic 1cm square rod about 40cm long with a soft metal wire of some kind through the core. When you set it to a curve it would just stay there until you straightened it.

Michael Gilligan12/04/2019 08:06:55
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Posted by SillyOldDuffer on 11/04/2019 15:01:29:

The isometric lines are created by transforming and rotating the drawing. Might have a go at explaining the maths but the number-crunching is quite involved.

.

I will be interested to see your explanation, Dave

MichaelG.

.

Sorry; I probably can't contribute for a few days, but it's something that I worked-out how to do in Autocad [early DOS version] more than 30 years ago ... in just a few simple steps.

SillyOldDuffer12/04/2019 11:58:00
3996 forum posts
810 photos
Posted by Ivan Ginato on 11/04/2019 16:54:55:
Posted by SillyOldDuffer on 11/04/2019 15:01:29:

Ivan's problem highlights the advantage of 3D CAD over pencil and paper methods and 2D CAD.

...

Dave

Actually, I draw with paper and pencil as a hobbie. I've been studying AutoCAD and SolidWorks too. My teacher said me the paper and pencil method improve my horizon of imagination.

No criticism intended Ivan, my fault - I drifted onto CAD. I use paper and pencil too. The techniques used before computers are interesting and useful. Well worth looking at hand methods, for example, I find CAD drawings lack character compared with hand-drawn draughtsmanship, which can be beautiful.

Dave

Circlip12/04/2019 12:00:40
916 forum posts

"Instead of free-handing, we used to use a flexible rule which was a rubbery/plastic 1cm square rod about 40cm long with a soft metal wire of some kind through the core. When you set it to a curve it would just stay there until you straightened it."

"Flexicurve" , square Lead core with two stainless strips encased in a soft PVC moulded sleeve. Easy way to straighten it was to "Whip" it onto the desktop. Have a later type made from interlocking plastic channel sections, can't get a tight radius, just like the FC. but a piece of solder helped.

Regards Ian.

Cornish Jack12/04/2019 14:52:53
868 forum posts
111 photos

Have had a 'Flexicurve' for many years and very useful too but was offered this, some years ago. It offers a reasonable variety.img_0029a.jpg

Anyone care to hazard a guess as to its origin? Ex Weybridge chaps might be at an advantage!

rgds

Bill

Ivan Ginato12/04/2019 16:42:04
7 forum posts
Posted by JasonB on 11/04/2019 17:15:47:

It is a bit surface development, I illustrated the method earlier with this quick sketch

dsc03576.jpg

On the plan you draw a set of evenly spaced lines at right angles to one axis. Then on the Isometric draw the two axis with a 60/30degree set square and also use that to repeat the set of lines. You can then either measure the length of these lines on the plan view and mark the same lengths off on the isometric or use dividers to pick up the lengths and transfer to the isometric. Finally freehand join all the marks on the lines into a nice flowing curve.

If you want to see it done with more accuracy than the sketch just ask and I will dust of my drawing board.

Edited By JasonB on 11/04/2019 17:19:57

I would not dare ask you to do it for me, but I would dare ask you some material, book, pdf etc about it. Actually at my school is not give importance to paper and pencil drawing then I am doing it by myself.

JasonB12/04/2019 16:56:04
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