R=2; r=1;

Manipulate[ParametricPlot3D[{(R+r*Cos[t])*Cos[p],(R+r*Cos[t])*Sin[p],r*Sin[t]},{t,0,tmax},{p,0,pmax}],{tmax,0.1,2*Pi},{pmax,0.1,2*Pi}]

Manipulate[ParametricPlot3D[{v*Cos[u],v*Sin[u],v},{u,0,umax},{v,0,vmax}],{umax,0.1,2*Pi},{vmax,0.1,3}]

Manipulate[ParametricPlot3D[{(R+r*Cos[t])*Cos[p],(R+r*Cos[t])*Sin[p],r*Sin[t]},{t,0,tmax},{p,0,pmax}],{r,0.1,2},{R,1,4},{tmax,Pi,2*Pi},{pmax,Pi,2*Pi}]

r=1;

Manipulate[ParametricPlot3D[{r*Cos[t]*Sin[p],r*Sin[t]*Sin[p],r*Cos[p]},{t,0,tmax},{p,0,pmax}],{tmax,0.1,2*Pi},{pmax,0.1,2*Pi}]

f[u_]=-u(u-1)^2(u-2);

Manipulate[ParametricPlot3D[{u,f[u]*Cos[v],f[u]*Sin[v]},{u,0,umax},{v,0,vmax}],{umax,0.1,2},{vmax,0.1,2*Pi}]

g[u_]=u-1;

Manipulate[ParametricPlot3D[{u*Cos[v],u*Sin[v],g[u]},{u,1,umax},{v,0,vmax}],{umax,1.1,2},{vmax,0.1,2*Pi}]