There is a need for the repeatable, accurate, precise and versatile alignment of mechanical components. A flexible and inexpensive approach to this problem is the use of a duplicate pair of wedged discs. This paper uses kinematic transformation matrices to examine in detail the design of such a wedge pair. The accuracy, precision and versatility of the circular wedges are shown to be functions of wedge angle, the number of positions or increments along the circumference of the circular wedge, and changes in the offset angle, which defines the asymmetry of the discs.