The parameters "u" and "v" are local to the parametric plot, so it does not make sense to try and vary those. But you can vary just about everything else in this plot, for example:
Manipulate[
ParametricPlot3D[{
Sin[u] (rx + Cos[u/3 - 2 v] + 2 Cos[u/3 + v]),
Cos[u] (ry + Cos[u/3 - 2 v] + 2 Cos[u/3 + v]),
Sin[u/3 - 2 v] + 2 Sin[u/3 + v]},
{u, umin, umax}, {v, vmin, vmax}],
{{rx, 7}, 1, 10, 1},
{{ry, 7}, 1, 10, 1},
{{umin, -Pi}, -2 Pi, 2 Pi},
{{umax, Pi}, -2 Pi, 2 Pi},
{{vmin, -Pi}, -2 Pi, 2 Pi},
{{vmax, Pi}, -2 Pi, 2 Pi}
]
