Basic calculations!

[mr grimsdale]

So.. the dihedral angle at the intersection of two planes is the angle which lies on a plane which itself is at right angles to both?

Taking the pyramid example. If one of the corners is attacked with a saw in a manner such that the cut is square, in both directions, to the edge. The exposed angle is the dihedral angle?

?????
xy

Spot on!

have another look at the drawing because I believe it's correct, and as you are both trying to describe.

No it isn't because

I simply drew the angle you would see on the base plane,

which is the wrong place to draw it. That angle is 90º, the dihedral will be larger.

 

[RobertMP]

Takes me back this

I remember being the only one doing A level technical drawing that 'got' and could project a dihedral angle. No doubt I've forgotten it all now and would use sketchup or autocad to solve it.

Do carry on

 

[Sgian Dubh]

... which is the wrong place to draw it. That angle is 90º, the dihedral will be larger.

I now see what you're saying Jacob. The funny thing is it was about 20 or 25 years ago that I first drew a representation similar to the image I put up here, and I didn't question it any further once I'd twigged how the angle looked more than 90º. All I've done since then is neaten up the drawing a bit by creating newer slicker versions.

However, I realise that at that time all those years ago I omitted a necessary added plane (non-existent in the constructed piece) to show how the dihedral angle does look more than 90º. I've just sketched it out to include that plane, which is in a reddy brown in this image. I think this clears up the problem. Let me know if I've got it wrong--- again. Slainte.

 

[RobertMP]

Looks right to me now.

 

[Steve Maskery]

Yes, 100% correct.

S

 

[Sgian Dubh]

Looks right to me now.

Thanks Robert. I thought so. I recall during the 70s and 80s being asked on a fairly regular basis to knock out 'simple' (sic) pyramidal plinths and bases, and not so simple polyhedra for various jobs. The requests always came from people that thought these things were a piece of cake as I was only a woodworker and you don't need brains to work with wood, ha, ha.

I used to draw the things and project the necessary angles. Inevitably there were some discrepancies due to the paper moving a bit, the thickness of the pencil lead, and angles not falling neatly on to the divisions on the protractor, etc.

I got tired of it and eventually I purchased a scientific calculator and learnt the necessary formulae so that I could calculate the various angles as long as knew how many sides were in the polyhedron and what angle they sloped from the baseline. That made the job a lot easier as long as I hit all the right keys in the right order, and that wasn't guaranteed, so I'd quadruple check my calculations. Still, it took a lot less time than drafting the things out.

Then along came spreadsheets in the early 1990s and working out the angles turned into a piece of cake because I just open up my Excel spreadsheet , find the number of sides that match the construction and the slope from the baseline and I read off the numbers.

I still can't explain why I've been going around with the wrong sketch for all these years, but there it is I suppose. Slainte.

 

[studders]

I still can't explain why I've been going around with the wrong sketch for all these years, but there it is I suppose. Slainte.

I feel the same way about an ex girlfriend, easily done.

 

[mr grimsdale]

... Let me know if I've got it wrong--- again. Slainte.

...

:lol:
Perfect. Very clear drawing too.
I got interested in this many years ago when I did a Carpentry & Joinery course. We did roof cutting by the graphical projection method which I thought was brilliant. Over the years I forgot how to do it. I had to revise it to make these trestles

The Americans seem to use trigonometry only - or so it would seem from the books I've seen. Then I found I couldn't do that either having been too long out of school so I went off and did OU course MST121

The graphical method can be really useful. Smaller things you can do full size and it works as a rod also, i.e. you take dimensions straight off by laying on your components. Roofs of course you have to scale up for dimensions but you can still take bevels off directly.

 

[jjc_uk]

Then I found I couldn't do that either having been too long out of school so I went off and did OU course MST121

Currently doing this myself now and finding it quite interesting, how long ago did you do it.


best regards
Jim

 

[mr grimsdale]

Then I found I couldn't do that either having been too long out of school so I went off and did OU course MST121

Currently doing this myself now and finding it quite interesting, how long ago did you do it.


best regards
Jim

2008. Hard work! Took up nearly all spare time for a year.

 

[xy mosian]

Ok! There has been a bit of chat about 'The Graphical Method'. I have been trawling through my book shelf and come up with this. From a time when cars had running boards. So to remind those who think they can remember and also those who would like to know what life was like before Sketchup etc..

Have fun

xy

 

[studders]

Then I found I couldn't do that either having been too long out of school so I went off and did OU course MST121

Currently doing this myself now and finding it quite interesting, how long ago did you do it.


best regards
Jim

2008. Hard work! Took up nearly all spare time for a year.

Ya not kidding. Did Six courses over a period of about four years. Seemed to take up all my time, none left for anything else.

 

[mr grimsdale]

Ok! There has been a bit of chat about 'The Graphical Method'. I have been trawling through my book shelf and come up with this. From a time when cars had running boards. So to remind those who think they can remember and also those who would like to know what life was like before Sketchup etc....

Once you get into it and understand the logic it becomes easier than it looks.
You have got to able to do stuff without Sketchup and if you don't understand it to start with SU may not help at all - as you can see here https://www.ukworkshop.co.uk/forums/aaaa ... 39522.html :lol:
It's also satisfying being able to do complicated calculations with just a pencil and a straight edge

 

[xy mosian]

Once you get into it and understand the logic it becomes easier than it looks.
You have got to able to do stuff without Sketchup and if you don't understand it to start with SU may not help at all - as you can see here https://www.ukworkshop.co.uk/forums/aaaa ... 39522.html :lol:
It's also satisfying being able to do complicated calculations with just a pencil and a straight edge

Of course using graphical methods you often do not need to know just what an angle is, the sliding bevel can be used to transfer angles. This is sometimes quicker too!

xy

 

[bugbear]

There's a rather lovely Roy Underhill espisode where he makes a compound angled-leg saw-horse with no diagrams OR maths at all.

By doing things in a well thought out sequence, each piece was marked off another piece in situ.

In some cases the cuts and/or planing were done in situ without even being marked!

Quick and effective, although not universally applicable.

BugBear