Pensieve header: Making the ribbon and clasp singularities pictures. See also pensieve://Projects/Killam-2017/.

SetDirectory["C:\\drorbn\\AcademicPensieve\\2015-07\\PolyPoly"]

ribbon=Graphics3D[
{
Green, Tube[{{-1,0,0},{1,0,0}},0.05],
Red,
Tube[{{-3,1,0},{3,1,0}}, 0.1],Tube[{{3,-1,0},{-3,-1,0}}, 0.1],
Tube[{{-1,0,-2}, {-1,0,2}}, 0.1],  Tube[{{1,0,2}, {1,0,-2}}, 0.1],
Opacity[0.6],Blue,EdgeForm[None],
Polygon[{{-3,1,0},{3,1,0}, {3,-1,0},{-3,-1,0}}],
Polygon[{{-1,0,-2}, {-1,0,2},{1,0,2}, {1,0,-2}}]
},
Boxed -> False, ViewPoint->{-1.05544,-2.48236,2.04302},ViewVertical->{-0.355079,0.320399,1.36975}
]

MakeImage["RibbonSingularity", ribbon, ImageSize -> 720]

dt=π/32;
γ1[t_]:={2Cos[t]-3/2,Sin[t],0};
γ2[t_]:={3/2-2Cos[t],0,Sin[t]};
clasp=Graphics3D[
{
Green, Tube[{{-1/2,0,0}, {1/2,0,0}}, 0.05],
Red,
Tube[Table[γ1[t], {t, -π/2,π/2,dt}],0.1],
Tube[Table[γ2[t], {t, -π/2,π/2,dt}],0.1],
Opacity[0.6],Blue,EdgeForm[None],
Table[Polygon[{{-3/2,0,0},γ1[t],γ1[t+dt]}], {t,-π/2,π/2-dt,dt}],
Table[Polygon[{{3/2,0,0},γ2[t],γ2[t+dt]}], {t,-π/2,π/2-dt,dt}]
},
Boxed->False,ViewPoint->{0.530012,-2.81796,1.79672},ViewVertical->{0.0301724,-0.099258,1.45049}
]

MakeImage["ClaspSingularity", clasp, ImageSize -> 720]