June 2005 Design Tip

Cut Costs with Rotational Symmetry

This month’s tip is one you probably won’t get to use often, but if you do, it will save you money (and make you feel really clever). We’re all familiar with bilateral symmetry, in which the left and right halves of an object are mirror images of one another. It’s easy to recognize, and we see it every day in living things and a variety of everyday objects (See Figure 1). But while the two halves are “the same,” they are definitely not interchangeable, as anyone who’s tried to put a shoe on the wrong foot can attest.

Figure 1:

Rotational symmetry, on the other hand, may not be as obvious to the eye, but it involves halves (or thirds, quarters, etc., depending on the degree of symmetry) that are identical. The face cards in a poker deck are a familiar example. Rotate a king, queen, or jack 180° and the image is the same as the one you started with. Cut the card in two along any line passing through the center of the card and you will end up with two identical pieces.

What makes this significant for plastic moulding is the fact that parts for a rotationally symmetrical assembly can be made from the same mould. If you are having parts made, that means less tooling to create the moulds and smaller parts inventory to store and administer. But before you can take advantage of rotational symmetry, you must first recognize parts with rotational symmetry potential and, second, maintain symmetry in your design.

Imagine a drinking glass. The glass has bilateral symmetry, which we don’t care about, but is also rotationally symmetrical. Cut the glass in half vertically, rotate one half 180° and you have two identical pieces. If, however, you add a handle to make a coffee mug, you’ve lost rotational symmetry and must make the two halves from different moulds. But if you add a second handle, such as you might find on a sugar bowl, you have now resumed rotational symmetry and can again make both halves of your design from a single mould.

Maintaining rotational symmetry also requires attention. For example, in joining pieces, you lose rotational symmetry by equipping one piece of an assembly with pins that mate with holes in the other piece. However, if pins and holes are evenly divided between the pieces such that pins in one mate with holes in the other, symmetry can be maintained. The same is true of counterbores and bosses for screw-attachment, hooks, latches, and hinges.

The accompanying photograph shows one part of a two-piece box designed to mate with an identical copy of itself (See Figure 2). When the parts are assembled, the hook at the upper left corner will engage the pin shown at upper right to form a hinge. The vertical loop at the lower left edge will catch the tab shown at lower right to latch the halves together.

Figure 2:

To design rotationally symmetrical mating parts, begin by creating a single part in your CAD system. Copy that part twice into an assembly, and then try to mate the two parts. If your system has interference checking, it will let you know whether your parts are mating correctly. Then, as your design progresses, keep checking the fit until you reach your final model.