Wednesday, March 31, 2010

From a simp to a dimp

Is it possible to create a triangular block with more of an interlock than the ‘simp’ (single inverse mirror plane) design we looked at yesterday? The answer is yes, and this is done by using more of the symmetry elements to create a shape with a more articulated design.

If we look at one of the abutting faces to these interlocking blocks, the simp has an inverse mirror plane located midway between the two corners of the outside face of the block. This first inverse mirror plane is oriented in a radial direction: it goes through the center of the sphere which the blocks assemble into.

If we provide yet another inverse mirror plane, oriented at 90 degrees to the first inverse mirror plane, then the second mirror plane is not radial but tangential to the assembled sphere. This second inverse mirror plane imposes a higher symmetry to the block shape. This arrangement provides many benefits to the interlocking block shape. Since each of the abutting faces of each block now involves two inverse mirror planes, I refer to this arrangement as a “DIMP” or Double Inverse Mirror Plane.

The mold separation line for a ‘dimp’ block is not a simple flat plane –like it is with a simp- but ‘jogs’ up three times as we go around the block. The higher symmetry dictates this sort of mold separation.

As dimp blocks are assembled, they create a much more solid and substantial interlock than with a simp. They slide and lock into position with multiple contact and guiding surfaces.

Each of these surfaces is a conjugate shear plane, as discussed two articles ago on this blog. This means that an assembled structure is free to deform under applied forces: it can strain under stress without breaking.

Another strong advantage to the dimp design is that the extra inverse mirror plane creates symmetry which allows a tensile element (e.g.: cable, wire, etc.) to be woven into the sphere or dome as the blocks are assembled. The straight line-of-sight on the abutting edges is a tangential pathway for a tension element which is woven into the structure as it is assembled. This means that the structure does not have to rely on gravity alone to hold the structure together; there can also be an element of tension that binds blocks together by a cable, or wire or other tension element. The location of this wire is shown in the drawing below, and is labeled 660.

This geometry is in many ways fundamental and basic to the problem of creating an interlock without a draft, or negative angle or undercut. I felt as though I had uncovered something that already existed, rather than actually inventing something.
There are a number of distinct advantages to both the simp and dimp blocks, depending on their use and also depending on how they are made. We’ll look at some of these differences tomorrow.  I'll also try to provide some photographs of the dimp in use.

1 comment:

  1. your blog is very awesome. But some picture is missing or broken. :(