## Tuesday, March 30, 2010

### When a simp is not so simple

We’re back looking at the problem of creating an interlocking triangular block which can release from a simple two-piece mold, without a draft angle, or undercut. The diamond-shaped key discussed in the last post allows for the blocks to be assembled without an undercut, but the half-diamond recesses create a negative angle, or draft, or undercut: in terms of releasing from a mold. These blocks would be stuck in a mold, and couldn’t be pulled out.

The answer to this problem was realized by playing with symmetry. Geometers (yes, geometer: one who does geometry) use various symmetry elements to describe the order present in a system. In particular, I began using the inverse mirror plane. This type of symmetry is an imaginary plane which bisects a given object. The inverse mirror plane acts like a mirror in that it reflects the arrangement on one side of the mirror: except that it flips it upside down, or inverts it. If something is ‘sticking out’ on one side of the plane, it will be ‘sticking in’ on the other side of the plane.  Below is a hexagonal block with these features.

I realized that if I located an inverse mirror plane at the midpoint of the abutting edges of a block, I could put half of the diamond-shaped key on one side of this plane, and the other half would be its inverse, or opposite, or keyway. I called this design the “SIMP” or Single Inverse Mirror Plane.

While the triangular block is made like a wedge, or bevel, or tapered block; the half-diamond key is kept at 90 degrees to the faces. In other words, it does not conform to the wedge, or taper, or bevel of the block. This aspect gives the key and keyway a more substantial interlock. The half-diamond shaped key is itself a wedge, displaced counter (opposite to) the wedge of the block itself.  Below is a pentagonal 'simp' block.

This arrangement of symmetry elements allows the interlocking block to be made on a simple two-piece mold. This was a “game-changer” in terms of providing an interlocking block design based on a unit shape that could be mass-produced with common equipment.  Below you can see how these blocks assemble with the interlocking feature.

Can this interlocking feature be made any better? Is it possible to have any more interlock without creating an undercut in terms of mold release? It doesn’t seem possible, but it is. We’ll look at that tomorrow.