A Question of Geometry

[SketchUp Guru]

Last night I was doodling and banged out this little table with splayed legs based on the old drawing you can see in the background. While I was drawing I got to wondering how one might go about working out the angles for the legs under the following conditions.

-No computer.
-The given drawing is not scaled proportionately. That is, the vertical scale and horizontal scale are different. From what I can tell, the elevation views of the table aren't really drawn properly at all.

I managed to get it worked out in SketchUp easily enough but I'm thinking about taking the old drawing to the shop and building the table. That seems to be the intent of the old drawing. Of course it has probably been messed up by being reproduced so many time in its life that this image is probably less useful than the original might have been.

By the way, there is only one dimension hidden behind the table. It is the length of the bottom of the short skirting board which is give as 8 inches.

 

[Harbo]

Well it's pretty late, but draw out to scale again or use maths?

Sine x = 1.25/17.5 etc. (approx 4 degrees)?

Rod

 

[SketchUp Guru]

I realize it is very late for you Rod but I wonder where you came up with the 1.25 and 17.5 numbers. I don't see any dimensions that would be useful for figuring out the angles mathematically. Redrawing it to scale would be good but not all that easy since we haven't got an overall height for the table nor do we know anything like the spacing between the floor and the apron or any other useful vertical dimensions.

 

[Harbo]

Dave

On re-reading your post I got one of the measurements wrong anyway!


Here's my theory using a vertical line as part of the triangle:

Leg length 25" minus 5 3/4" (I read it as 3 3/4") minus 3 3/4 = 15.5"

Offset: 14.5 - 12 = 2.5 divide by 2 for each half = 1.25" Another way to look at this is to imagine a vertical through the middle of the table, then it will be 7.25 - 6 = 1.25"

Then using trig to work out the angle Sin x = 1.25/15.5

Rod

 

[SketchUp Guru]

Ah, very good. It is close. Probably close enough. Thanks.

 

[Mike H]

If the two slopes are identical on the two faces, I make it 8.8 inches by doing a simple proportion.

That is if I can read the figures, but the method is length on long side divided by bottom length of that side multiplied by bottom length on short side. This is the same as using trigonometry by the way.


Mike

8)

 

[milkman]

you can set iout geometrically, look-up setting out grain hoppers