Interlocked pair

Two rings share one crossing point. Ring A is a thick circular torus standing in the xy-plane; ring B is a slender torus whose centreline circle lies in the xz-plane with its centre at (RB, 0, 0).

C_A(u) = (RA cos u, RA sin u, 0)
C_B(u) = (RB + RB cos u, 0, RB sin u)

At u = π ring B passes exactly through the origin — the centre of A's opening — so the two tori are linked rather than merely touching. The hole radius RA − rA bounds both rB and RB, so B always threads cleanly through A.

Ring B is tilted about the x-axis by β and its plane is then precessed about the z-axis by γ. Both rotations fix the origin, so the linkage survives every setting. A satin metal surface (spec 130) is paired against a matte ceramic one (spec 25).