X Marks the Spot (V)

Back to the fun with the French drawing problem. Just in case the bombardment of Christmas advertising has led any of you to lose all memory of this thread, if not take total leave of your senses (a wise move perhaps), I suggest taking a look at the blog archive to the right of the page for previous installments.

In a nutshell, this charpente exercise is the problem of two crossed sticks, one turned 45˚ to the plan, and one at 60˚ to the plan:

The problem to solve is that of the intersections of the sticks and how to lay out each piece so that this assembly can be fitted together. A carpentry strategy often employed, that of cut-and-fit, cut-and-fit, is unlikely to produce a clean result, and will take far longer than figuring out the layout.

In the previous post, the end result was the layout of the basic outlines of stick ‘a’, which is oriented 60˚ to the plan:

I finished the last post with the hope that some readers out there, and I know there are at least three who are following along with the drawing exercise, might try to accomplish what we just did for the 60˚ piece with the 45˚ piece, or stick ‘b’. I’ve no idea if anyone did the continuation of the drawing or not, but in any case I’ll just quickly pencil in a few of the steps which will produce the basic layout for stick ‘b’. Well, sorta quickly….

Again we start with the basic slope triangle for piece ‘b’ – here depicted in 3D atop its slope triangle:

Again, the elevation of stick ‘b’, just the same as stick ‘a’, is 125cm. The top of the slope triangle corresponds exactly to the topside arris of the stick.

Next I remove the 3D piece from view and flip that slope triangle down, a 90˚ rotation placing it on the floor:

With the triangle down, we then slide it over a bit so it does not lay atop the view of the stick’s cross-section we will be producing next.

Moving on, we make a line which is perpendicular to the hypotenuse of the slope triangle (in other words, is at 90˚ to the stick itself), and swing it down:

That line we swung down meets the run of the triangle and is then transferred over to the 45˚ axis line which originates at point ‘B’. the intersection between those two lines is indicated by the red circle in the above drawing.

We are working to produce the cross section of this stick, which we know in advance to be square. Next we draw in that sides of the cross section, as with the other stick piece ‘b’ is 20 cm wide on each side, and once the first two sides are in the other sides are merely parallel to the first two, and we can complete the illustration of the cross-section:

The yellow square is the cross section of piece ‘b’, 20cm on each side (or whatever size you choose to make it). in the above drawing the slope triangle is still a little close to the cross section view, so I slide the slope triangle over a little more to get it out of the way. It doesn’t really matter how far away you put it, so long as you keep the geometrical relationship consistent (i.e., a direction of slide which is 90˚ to the plan axis) the triangle could be moved down the street or across the country for that matter.

Now slide over and swing up from the corner points of the stick ‘b’ cross-section square to produce an elevation view of the stick:

Some of the additional traces on that drawing are actually from the piece ‘a’ drawing series, so don’t worry about that too much.

With the elevation of the stick drawn, we now transfer back from the 2D elevation view and construct the plan view of piece ‘b’ at elevation, including the footprint and the view of the top of the stick sliced along the horizontal:

That completes the basic 2D drawing of piece ‘b’ in plan and elevation. That wasn’t too traumatic, now was it? The white diamond is the end grain of the top end of the stick after being sliced so as to be parallel with the floor (horizontal). The dark yellow diamond on the other end is the footprint of the stick at slope upon the floor. That footprint is also of course a horizontal cut. Notice how the square section of the stick has become a diamond-shaped footprint as a result of sloping the stick in a compound manner.

In the next shot I show, by superimposing the actual stick in 3D above the drawing, the foot transfer points between 2D and 3D:

Next, I re-materialized the 2D drawing of piece ‘a’ into view, along with the 3D depiction of piece ‘a’:

Piece ‘a’ is on the left and piece ‘b’ on the right, hovering over their respective 2D elevation views.

Next, with both piece ‘a’ and ‘b’ at slope, we can see how they relate to the 2D drawings just completed:

And removing the 3D sticks returns us to our completed basic 2D drawing of the two sticks:

So, there is some overlap of parts here, and I trust the reader will be able to keep totally clear on which thing is which as the drawing advances from here. Developed view drawing can get pretty congested with lines in a hurry!

In the next post in this series I will start to work on the lines and planes of intersection between our two sticks. I hope the reader will stay tuned, and that today’s drawing will be, at least, no more mysterious than the one undertaken in the preceding post.

Thanks for coming by the Carpentry Way today. –> on to post 6