r[t_]:={Cos[t],  Sin[t],  .5  t}

T[t_] := r'[t]/Norm[r'[t]]

(* 
      The viewpoint coordinates are:  *) 
v = {2, 5, 1};

(* 
      This plots the trajectory curve. *) 
ParametricPlot3D[
        Evaluate[r[ t]],  {t, 0, 4 π},  ViewPoint -> v,  
        PlotPoints -> 200, 
        DisplayFunction -> Identity];

ParametricPlot3D[
        Evaluate[r[π/2] + t T[π/2]],  {t, 0, 
          1},   ViewPoint -> v,  
        DisplayFunction -> Identity];

ParametricPlot3D[
        Evaluate[r[π] + t T[π]],  {t, 0, 1},   ViewPoint -> 
          v,  DisplayFunction -> Identity];

ParametricPlot3D[
        Evaluate[r[3 π/2] + t T[3 π/2]],  {t, 0, 
          1},   ViewPoint -> v,  
        DisplayFunction -> Identity];

ParametricPlot3D[
        Evaluate[r[2 π] + t T[2 π]],  {t, 0, 
          1},   ViewPoint -> v,  
        DisplayFunction -> Identity];

ParametricPlot3D[
        Evaluate[r[2  π + π/2] + t T[2  π + π/2]],  {t, 0, 
          1}, ViewPoint -> v,  
        DisplayFunction -> Identity];

(* 
      This superimposes the images created above in one picture.  *) 
Show[%, %%, %%%, %%%%, %%%%%, %%%%%%, DisplayFunction -> $DisplayFunction];