DynamicModule[{pt = {1,0}}, 
 S1[t_]:=Graphics3D[ Sphere[{2 Cos[t],2 Sin[t],0},0.3],Boxed->False];
 S2=ParametricPlot3D[{(2+v Cos[u/2]) Cos[u],(2+v Cos[u/2]) Sin[u],v Sin[u/2]},{u,0,2Pi},{v,-1,1},Boxed->False,Axes->False];
 Row[
 {Show[{S1[phi],S2},ImageSize->200],
 Graphics[phi=Arg[pt[[1]]+I pt[[2]]];{Circle[],Locator[Dynamic[pt,(pt = Normalize[#]) &]]},PlotRange->2,ImageSize->200]},ImageSize->410]]


DynamicModule[{pt = {1, 0}}, 
 S1 = ParametricPlot3D[{(2+v Cos[u/2])Cos[u], (2+v Cos[u/2])Sin[u], v Sin[u/2]},{u,0,2 Pi},{v,-1,1}];
 Row[{
   Show[{Graphics3D[Sphere[{2 pt[[1]],2 pt[[2]],0},0.3]], S1}, ImageSize -> 200, Boxed -> False], 
   Graphics[{Circle[], Locator[Dynamic[pt, (pt = Normalize[#]) &]]}, PlotRange -> 2, ImageSize -> 200]}, 
   ImageSize -> 410]]


S1 = ParametricPlot3D[{(2+v Cos[u/2])Cos[u], (2+v Cos[u/2])Sin[u], v Sin[u/2]},{u,0,2 Pi},{v,-1,1}];
Manipulate[
 Row[{
   Show[{Graphics3D[Sphere[{2 pt[[1]],2 pt[[2]],0},0.3]], S1}, ImageSize -> 200, Boxed -> False],
   Graphics[{Circle[], Locator[Dynamic[pt, (pt = Normalize[#]) &]]}, PlotRange -> 2, ImageSize -> 200]}, 
   ImageSize -> 410],{pt,{1,1},{-1,-1},{1,1},ControlType->None}] 


---------------------------------------------------------------------WORKS   ---------------------------
S1 = ParametricPlot3D[{(2 + v Cos[u/2]) Cos[u], (2 + v Cos[u/2]) Sin[ u], v Sin[u/2]}, {u, 0, 2 Pi}, {v, -1, 1}];
Manipulate[phi = Arg[pt[[1]] + I pt[[2]]];
 Row[{Show[{Graphics3D[Sphere[{2 Cos[2 phi], 2 Sin[2 phi], 0}, 0.3]], 
     S1}, ImageSize -> 200, Boxed -> False], 
   Graphics[{Circle[], Locator[Dynamic[pt, (pt = Normalize[#]) &]]}, 
    PlotRange -> 2, ImageSize -> 200]}, 
  ImageSize -> 410], {pt, {1, 0}, {-1, -1}, {1, 1}, 
  ControlType -> None}]

---------------------------------------------------------------------WORKS   ---------------------------



X[u_,v_]:={(2+v Cos[u/2])Cos[u], (2+v Cos[u/2])Sin[u], v Sin[u/2]}; 
Y[u_,v_]:={2*Cos[u]*Sin[u/2] + v*Cos[u/2]*Cos[u]*Sin[u/2] - 
    (v*Cos[u/2]^2*Sin[u])/2 - (v*Sin[u/2]^2*Sin[u])/2, 
   (v*Cos[u/2]^2*Cos[u])/2 + (v*Cos[u]*Sin[u/2]^2)/2 + 2*Sin[u/2]*Sin[u] + 
    v*Cos[u/2]*Sin[u/2]*Sin[u], -2*Cos[u/2]*Cos[u]^2 - 
    v*Cos[u/2]^2*Cos[u]^2 - 2*Cos[u/2]*Sin[u]^2 - v*Cos[u/2]^2*Sin[u]^2}
S1 = ParametricPlot3D[X[u,v],{u,0,2 Pi},{v,-1,1}];
Manipulate[ phi=Arg[pt[[1]]+I pt[[2]]]; 
 Row[{
   Show[{Graphics3D[Sphere[{2 Cos[2 phi],2 Sin[2 phi],0}+Y[u,v]/10,0.3]], S1}, ImageSize -> 200, Boxed -> False],
   Graphics[{Circle[], Locator[Dynamic[pt, (pt = Normalize[#]) &]]}, PlotRange -> 2, ImageSize -> 200]},
   ImageSize -> 410],{pt,{1,1},{-1,-1},{1,1},ControlType->None}]