It’s fairly easy to put a single curve into a woodworking design, such as a curved top rail on a flat cabinet door. Going one step further, you can fairly easily bow the door, that is, make it curved back and forth but still straight up and down, requiring single bent glass. Note, though, that if you both bow the door and put a curve into the top rail that the top rail now has two curves in it, and qualifies as a compound or complex curve. You’ll find fascinating treatments of techniques for this kind of work in "Circular Work in Carpentry and Joinery", by George Collings. Click on the book name to see more about it.

A bowed door, with a curve top rail or not, has a cylindrical shape, which is to say that you can think of it as a section of a larger cylinder. The next step geometrically is to move from a cylinder to a sphere, as does my bombe vitrine. The glazed frames on this cabinet are sphere sections, which proceed from specific radii. Other more complicated forms are possible (some of which have been done) which involve either free sculpting or more complicated geometrical designs such as ellipses or differing curves on different axes (a sphere, by definition, has the same curve on all axes).

One general rule applies. The more complex your design the more time consuming and difficult it will be to make. The bombe vitrine shown here took a total of about 1350 hours to complete. If you want to take on a project like this, settle in for the long haul- you won’t be done by Christmas.

This treatment of the processes I went through to build this cabinet does not contain specific instructions for building the cabinet shown. I’m not trying to protect the design, but I doubt that anyone will try to make a duplicate of this one and you probably don’t want that level of detail. This treatment just shows you the major techniques used in spherical cope and stick router work, and points you toward the complexities involved with designing such a piece of furniture. If you really intend to build something like this, contact me and I’ll try to persuade you not to. For your sake, believe me. If you persist, I’ll help you with design specifics to a certain extent if you are easy to work with. I’d like to see someone try this, but not if they end up frustrated.

WHEN WORLDS COLLIDE- THE PLANE OF INTERSECTING SPHERES

When two planets smack together, they explode. I know, cause I saw it on TV once. But, when two imaginary spheres come together, they intersect in three dimensions like two large soap bubbles joining together in some sort of ethereal geometric bliss.

To understand what it takes to assemble a construction designed as sections of spheres, you must be able to visualize what happens when spheres intersect (see drawing 1). You must know where the radius center of each sphere is in relation to the other sphere center. To figure how I would join the sides of this cabinet, I made a full scale section drawing of a horizontal plane through the widest part of the upper cabinet as in drawing 2. (The sphere centers lie on this plane.) This drawing forced me to decide which radii I would use for the piece, and where the sphere centers were located on the X and Y axes. Later alignment of the outer frame parts as they were made in the router jigs depended entirely upon this drawing and others similar to it.

Think about those soap bubbles again. Floating apart in the air, each is a separate sphere. But when they contact, a flat area of soap membrane resides within the circle that is created where the two spheres contact. If the bubbles are true spheres, the circle of contact will be a true circle, and this circle will describe a flat plane. This is the plane of intersecting spheres and is the only flat surface you have to refer to in design and construction of such a piece.

Note that the horizontal plane I used to draw the X and Y axes, the sphere centers and the cabinet parts (drawing 2) is not the same plane as the plane(s) of intersecting spheres. At each of the four corners of the cabinet, and at each of the four sides of the top where it intersects the sides below, a different plane of intersecting spheres is described. Each of these planes must be plotted in relation to the centers of the spheres it involves. You must know where the planes of intersecting spheres are in relation to the sphere centers and cabinet central axes in order to be able to align components in the router jigs for shaping. One critical piece of information I used is the fact that when you are dealing with intersecting spheres of equal radius, the plane of intersecting spheres must pass through the midpoint of a line drawn between the sphere centers.

Confused? Well so was I, and for months. I racked my neurons for weeks over some of these three dimensional convolutions, and spent a few sleepless nights where I finally realized a solution at 3AM, thus allowing me to sleep. Finally, however, I concluded that it is really very basic three-dimensional geometry- just a bunch of spheres and planes bumping into each other at specific angles and with specific radii. The problem is that the human brain prefers two dimensional, linear problems rather than three-dimensional curve balls. But, once you get used to visualizing the parts involved you’ll find that the basic geometric relationships are simple. Making drawings helps a great deal to conceptualize what’s happening, as well. 

 Though it's possible to make many of these geometric situations very complicated with algebra and calculus, it's also unnecessary. My approach was pragmatic and physical- I did what I needed in order to make the router move along the shape required. I used geometric abstraction only as far as I needed to in order to learn how to arrange my jigging such that it would produce parts that fit. I was not so much concerned with making the cabinet parts fit a rational abstraction perfectly as I was determined to make the cabinet parts fit each other practically.