Manipulate[
 ParametricPlot3D[ {Cos[
     u]*(radius + Cos[u/2]*Sin[v] - Sin[u/2]*Sin[2 v]), 
   Sin[u]*(radius + Cos[u/2]*Sin[v] - Sin[u/2]*Sin[2 v]), 
   Sin[u/2]*Sin[v] + Cos[u/2]*Sin[2 v]}, {u, 0, angle}, {v, 0, 2 Pi}, 
  Axes -> False, Boxed -> False, PlotRange -> All], {radius, 1, 
  2}, {angle, 0.1, 2 Pi}]