Parametric Equation for A Wiggly Tube I need to form a shape where the side view in the $xz$-plane is parallel inverse sines, and the surface is a pipe with circular cross-sections. Is there a name for this shape?
I tried messing around with ParametricPlot3D in Mathematica, but couldn't figure it out. I tried messing around with the equation of circles for two slots and inverse sine for the other.
Fig. 1:

Fig. 2:


Since the cross section is a circle and the cross section from the side are parallel arc sine functions, we can form the shape as a continuous sequence of circles whose height changes as we go along the x-axis. With circles lying in the xz-plane and the arcsines in flat in the xz-plane we get this parametric function:
$x=t, y = r_0cos(\theta),z=r_0sin(\theta)-sin^{-1}(t)$ with $0 \leq \theta \leq 2\pi$  and $a \leq t \leq b$
So with $r_0 = 1, a = -10$, and $b = 10$ we have the graph:

