A Question Of Geometry

[custard]

I've got a splayed leg trestle frame to make which will support a slab top. Here's the question, the legs are splayed in both directions by 1:10, which I calculate to be about 5.7 degrees. If the mitre saw is set so it's 5.7 degrees off from vertical, and 5.7 degrees off from being perpendicular to the fence, will that give me the correct angle for crosscutting the legs? I appreciate the legs are all "handed" so I'd have to reset the saw t'other way around for the next leg, but I want to check there's no weird geometry issue like azimuth error that'll catch me out?

By the way, I've made a 1:10 MDF master template so I can repeatedly re-set a sliding bevel to a consistent angle, so that's not the issue, I'm not really bothered if it's 5.6 degrees or 5.8 degrees as long as it's consistent. The question is, when you compound the angle is there some other factor that needs to be allowed for, or is it all as straightforward as I think it is?

Thanks.

 

[Baldhead]

Custard is this any good?

http://jansson.us/jcompound.html

Stew

 

[Myfordman]

I think you are correct but I use a different method.
Leave the leg lengths equal and 90 degree ends. At some suitable dry fit stage, put the item on a flat surface eg table saw and scribe round each leg with a height gauge and trim to the line.

 

[custard]

I think you are correct but I use a different method.
Leave the leg lengths equal and 90 degree ends. At some suitable dry fit stage, put the item on a flat surface eg table saw and scribe round each leg with a height gauge and trim to the line.

There's method to my madness! Firstly there's not a huge amount of profit in this job so I want to be as close to finished as possible after the glue up. Secondly the top will be secured to the base with buttons, as a first step in that process the top edges of the aprons need to be co-planar with the ground, not canted at an angle. I'll sort that before assembly, so if the tops of the legs are also cut correctly then I can reference everything together, and after the glue up it should just be a few whisks of plane before the top's ready to go on.

 

[custard]

Top man Stew!

I'll read that through with interest, but at first glance it looks like there could be something funny going on and I might be best leaving a 20mm "horn" at the top of the legs in case it's not as simple as I'd hoped!

 

[Jacob]

I put this on my website years ago. http://owdman.co.uk/howto/howto2.htm
It works perfectly but it's bloody complicated, though after a few goes it gets easier. The key concept is "projection" which effectively means unfolding the faces of the components down to a flat surface. Like Origami in reverse - you end up with everything on one flat sheet of paper.

The easier way is simply to fake it as you go - offer up and fit etc. etc. nobody will know the difference

 

[Sgian Dubh]

I'm assuming what you're after is the angles you need to join the ends of the rails to the top of the legs. Both Baldhead and Jacob have provided relevant information. However, if you are willing to simply state the legs will rise from the floor at an angle of 84º rather than 84.3º, then I can tell you from a spreadsheet I have that the dihedral angle you need is 90.63º and the requisite mitre angle is 84.03º.

In other words, if you were making a pyramid where the corners mitre together you divide the dihedral angle by 2 = 45.32º and set the saw bevel (tilt it) to that or its complement 44.68º. To set the saw to cut the mitre, swivel the blade left or right to 84.03º (complement 5.97º), or if you are using a table saw, adjust the mitre gauge to this. You now just have to envision the ends of each rail as being essentially the same as the intersecting edges of a pyramid, with a wrinkle in that the angled legs effectively are a block of wood that keeps the intersecting edges actually meeting. However, it's unusual for rails to meet a leg without some sort of joinery, so the angles I've given you might have to be used to set out and scribe a shoulder line for something like a tenon.

Realistically, you're not going to set the saw accurate to two decimal places of a degree, but I find it helpful to know the precise angle to aim for in setting out the joinery or setting up the saw. Of course, I may have completely misunderstood your question, or simply made things more confusing for you, but I hope it's neither. Incidentally, if you get the angles between the rails and legs right, it's a relatively trivial matter to cut the top and bottom end of the legs at appropriate compound angles after a (dry) assembly if need be, as long as you've left them long enough to mark around and trim. Slainte.

 

[Jacob]

Are you talking of legs square on plan but rhomboid in cross section, or vice versa?
Just thought I'd ask - the night is young!

 

[custard]

Thanks Richard, after reading through the replies I'm going to bevel the tops of the apron rails before assembly, but only trim the tops of the legs after a dry glue up...discretion being the better part of valour and all that!

 

[Sgian Dubh]

I'm going to bevel the tops of the apron rails before assembly,

And, presumably, the bottom edge too, at 84º to the outer face of the rail? Slainte.

 

[bugbear]

Helpful thread here;

trigonometry-for-saw-horses-t81809.html

BugBear

 

[custard]

I'm going to bevel the tops of the apron rails before assembly,

And, presumably, the bottom edge too, at 84º to the outer face of the rail? Slainte.

I'm putting a concave curve on the bottom edges of all four aprons, so neat and tidy bevelling starts to become a bit of a faff, consequently I'll put a heavy round (virtually a bullnose) on the bottom edges and leave it at that!

 

[Billy Flitch]

I know I`m a bit late to this and custard has probably built his by now but any one that is thinking of making tresels Like this is missing out on a trick.In his first post custard says " I know there is a difference between the legs left and right hand"and here`s the rub there is no difference.

When you use one length of wood and mark the double splay and cut it then mark the length and again a double splay and cut it you get two identical pieces of wood, to make one the other hand you just turn it upside down. You then make the difference by cutting the splayed tenon on the inside of the leg cut one leg and this then becomes the template for the rest.

First leg placed along side opposite hand, marks transferred over,first leg placed along side third leg marks transferred over,
Third leg placed along side forth leg marks transferred over. Don't forget what ever thickness top you use the measurement must be increased because the leg is splayed.

Cutting the splayed cut on the leg top and bottom is just like cutting jacks on a roof the off cut will pass on the other side of the hip one cut but you get payed for two.