Abstract: A self-aligning coupling apparatus incorporates a first connecting element having a body with a first set of accessory teeth and a second connecting element having a body and a second set of accessory teeth for engagement of the first set. A coupling ring joins the first and second element. The first set of accessory teeth includes spaced indexing teeth having an apex angle less than an apex angle of the remaining teeth of the first set and a height greater than the remaining teeth of the first set. The second set of accessory teeth is has an apex angle complementing the apex angle of the remaining teeth of the first set. The second set of accessory teeth have canals intermediate the teeth to receive the indexing teeth upon joining of the first and second element by the interconnecting coupling.