La Menuiserie Study (III)

In the last post, I introduced Plate 1 in the text La Menuiserie, specifically volume 3 of aa multi-volume encyclopedia on the topic. Plate 1 detailed the first significant exercise in a chapter entitled Eléments de géométrie dans l'espace. The study in this section concerns the intersection of various solids, like cones, parallelepipeds, cylinders, and spheres. I’ve worked my way through all of the remaining exercises in this section, and was pleased to find the layout techniques worked perfectly. In fact, the technique for determining the intersections between solids is fairly uniform between different cases, with one exception, to be mentioned below.

Plate 2 covers the intersection of a sloped square section stick piercing a cylindrical post:

Plate 3 deals with the intersection of a sloped smaller cylinder meting a cylindrical post:

Plate 4 gets us into cones, the first problem dealing with a cone pierced by a horizontal cylinder:

I will now admit I am a cone ‘head’.

Plate 5 is a cone pierced by a smaller vertical cylinder, offset from the centerline of the cone:

Plate 6 was the most complex of this set, involving the intersection of an angled cylinder partially occluded into a cone:

Plate 7 was a different sort of beast, the intersection of a vertical and a horizontal cone:

Here, one can not pull points in the same way as with other intersections, but must construct auxiliary planes which intersect both cones.

Detail:

If you’re hankering to see some sort of woody manifestation of the above type of problem, maybe a bit more difficult, volume dialed up to 11, there are no shortage of maquettes. This one could be called, “let’s have fun with scalene cones”:

The preamble to a carpentry challenge like this - the minimum 'get a foot in the door’ move - would be mapping the surfaces of intersecting cones.

It appears that the upper angled cone can be removed easily:

Scalene fun, Part II:

Credit to: RWLV

Finally, there is plate 8 which deals with a sphere occluding a cone:

This was a simpler problem than the cone meeting cone, as it turned out. Almost easy.

The next section in the text deals with regular plan hips, and area with which i have some familiarity, so it will be interesting to learn some new approaches.

All for this time. If you’re feeling inspired - and I hope you are- go lay down some lines and cut some wood.

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