I've been given an assignment to create a shape that has a Beta symmetry of 135°.
My textbook defines Beta symmetry as:
Beta is the rotational symmetry of a part about its axis of insertion. The magnitude of rotational symmetry is the smallest angle through which the part can be rotated and repeat its orientation. For a cylinder inserted into a circular hole, beta equals zero.
There are several shapes that have 135° rotational symmetry – octagon, 8 pointed star, for example, but those both also have 45° rotational symmetry, and since Beta symmetry is the "smallest angle", does a shape even exist that has Beta symmetry of 135°? This is driving me crazy!
Best Answer
Alpha symmetry is the largest angle a part would have to be turned about an axis perpendicular to the insertion axis.
Beta Symmetry is the largest angle the part would have to be rotated about the insertion axis for mating.
Alpha and Beta symmetry actually range from 0 to 360° (instead of the intuitive 0 to 180°) because it is assumed that the worst case rotation is used. reference Design.