\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{pst-ressort,multido}
\usepackage{pst-solides3d}
\pagestyle{empty}
\begin{document}

\begin{pspicture}(-2,-2)(4,17)
\psset{viewpoint=1000 20 20 rtp2xyz,lightsrc=viewpoint,Decran=1000}
\psframe(-2,-2)(4,17)
\pstVerb{/Longueur 15 def /R_0 1 def
        /NbreSpires 20 def /dl 0 def /l_0 10 def
       /Pas_0 l_0 NbreSpires div def
       /Pas Longueur 2 dl mul sub NbreSpires div def
    % longueur de l'hélice sur un tour
    % = sqrt(4*pi^2*R^2+p^2)
      /Longueur_Helice_pas 39.47842 R_0 dup mul mul Pas_0 dup mul add sqrt def
    % R=1/(2*pi)*sqrt(L^2-p^2)
      /Radius 0.1591549 Longueur_Helice_pas dup mul Pas dup mul sub sqrt mul def
      /Alpha 20 pi mul 180 div def
      /xu 20 cos 5 mul def
      /yu 20 sin 5 mul def
}%
\defFunction[algebraic]{helice}(t)
      {Radius*cos(2*pi*t)-R_0}
      {Radius*sin(2*pi*t)}
      {Pas*t+dl}
\psSolid[object=courbe,r=0,
    range=0 20,
    linecolor=blue,
    resolution=720,
    function=helice]%
\axesIIID(0,0,0)(5,3,16)
\psPoint(xu 1.5 div,0,yu 2.5 div){T}
\psPoint(xu,0,yu){U}
\psPoint(0,0,0){O}
\uput[d](O){O}
\psline[linecolor=green]{->}(O)(U)
\uput[u](U){$\overrightarrow{u}$}
\psset{solidmemory}
\psSolid[object=plan,
    definition=equation,
    args={[0 1 0 0]},
    action=none,
    name=monplan]
\psset{plan=monplan}
\psProjection[object=cercle,
    args=0 0 3,linecolor=magenta,
    range=0 -20]
\uput[l](T){$\alpha$}
\end{pspicture}
\begin{pspicture}(-2,-2)(3,17)
\psset{viewpoint=1000 0 0 rtp2xyz,lightsrc=viewpoint,Decran=1000}
\psframe(-2,-2)(3,17)
\pstVerb{/Longueur 15 def /R_0 1 def
        /NbreSpires 20 def /dl 0 def /l_0 10 def
       /Pas_0 l_0 NbreSpires div def
       /Pas Longueur 2 dl mul sub NbreSpires div def
    % longueur de l'hélice sur un tour
    % = sqrt(4*pi^2*R^2+p^2)
      /Longueur_Helice_pas 39.47842 R_0 dup mul mul Pas_0 dup mul add sqrt def
    % R=1/(2*pi)*sqrt(L^2-p^2)
      /Radius 0.1591549 Longueur_Helice_pas dup mul Pas dup mul sub sqrt mul def
      /Alpha 20 pi mul 180 div def
      /xu 20 cos 5 mul def
      /yu 20 sin 5 mul def
}%
\defFunction[algebraic]{projectionhelice}(t)
      {0}
      {Radius*sin(2*pi*t)}
      {Pas*t+dl-(Radius*cos(2*pi*t)-R_0)*tan(Alpha)}
\psSolid[object=courbe,r=0,
    range=0 20,
    linecolor=red,
    resolution=720,
    function=projectionhelice]%
\axesIIID(0,0,0)(5,2,16)
\rput(0,-1){$\alpha=20^{\mathrm{o}}$}
\end{pspicture}
\begin{pspicture}(-2,-2)(3,17)
\psset{viewpoint=1000 0 0 rtp2xyz,lightsrc=viewpoint,Decran=1000}
\psframe(-2,-2)(3,17)
\pstVerb{/Longueur 15 def /R_0 1 def
        /NbreSpires 20 def /dl 0 def /l_0 10 def
       /Pas_0 l_0 NbreSpires div def
       /Pas Longueur 2 dl mul sub NbreSpires div def
    % longueur de l'hélice sur un tour
    % = sqrt(4*pi^2*R^2+p^2)
      /Longueur_Helice_pas 39.47842 R_0 dup mul mul Pas_0 dup mul add sqrt def
    % R=1/(2*pi)*sqrt(L^2-p^2)
      /Radius 0.1591549 Longueur_Helice_pas dup mul Pas dup mul sub sqrt mul def
      /Alpha 0 pi mul 180 div def
      /xu 0 cos 5 mul def
      /yu 0 sin 5 mul def
}%
\defFunction[algebraic]{projectionhelice}(t)
      {0}
      {Radius*sin(2*pi*t)}
      {Pas*t+dl-(Radius*cos(2*pi*t)-R_0)*tan(Alpha)}
\psSolid[object=courbe,r=0,
    range=0 20,
    linecolor=red,
    resolution=720,
    function=projectionhelice]%
\axesIIID(0,0,0)(5,2,16)
\rput(0,-1){$\alpha=0$}
\end{pspicture}
\end{document} 