  Knots and links are fundamental topological objects play a key role in both
classical and quantum fluids. In this research, we propose a novel scheme to
generate torus vortex knots and links through the reconnections of vortex rings
perturbed by Kelvin waves in trapped Bose-Einstein condensates. We observe a
new phenomenon in a confined superfluid system in which the transfer of
helicity between knots/links and coils can occur in both directions with
different pathways. The pathways of topology transition can be controlled
through designing specific initial states. The generation of a knot or link can
be achieved by setting the parity of the Kelvin wave number. The stability of
knots/links can be improved greatly with tunable parameters, including the
ideal relative angle and the minimal distance between the initial vortex rings.
