I am trying to plot a given vector (which is not a function) using ParametricPlot3D but couldn't make it show the surface. I tried using Evaluate, Function and Through but it didn't work.
x = {(r0+c Sin[(r-r0)/c]) Cos[t], (r0+c Sin[(r-r0)/c]) Sin[t], c (Cos[(r-r0)/c]-1)};
Manipulate[
ParametricPlot3D[x, {r, r0 - w/2, r0 + w/2}, {t, 0, \[Pi]}], {{w, 1},
0.5, 2}, {{r0, 1}, 0.5, 2}, {{c, 1}, 0.1, 10}]
Thanks for your help!