fred_dot_u fred_dot_u at yahoo.com
Tue Apr 10 13:43:53 EDT 2018

```At this point, I'm lacking the concentration to follow through on my
"discovery," but a preliminary drawing shows that the process of creating
the part can be made parametric. If it doesn't need to be parametric, it's
easier to make the drawing and pull the numbers off via the appropriate tool
for the drawing software.

I'm "building" this model by creating cylinders to be subtracted from the
monolithic base. For practical purposes, the cylinders can be considered
circles in this exercise.

Picture the smallest diameter for the collection of syringes. You want the
most support, but you don't want the C-shape of the cross section to impede
insertion. That makes the end result limited to the diameter of that
syringe. Any cross-section cut higher than the diameter becomes a "gripper"
of sorts and may be beneficial, but impedes this calculation. It can be
added later as a parameter sum of an arbitrary distance of percentage.

The centers of the circles are the parametric aspect that currently escapes
me. I know it's simple, but the pounding headache I have is preventing me
from proceeding.

What I have been able to determine is that the spacing of the center of the
second circle from the first circle is the diameter of the second circle
minus the distance of the chord of the second circle from its center, with
the chord of the second circle being the diameter of the first circle.

I've done math of this sort before and have found an abundance of formulae
to solve for this result. Because each circle references the preceding
circle, the primary formula should be iterative, allowing for as many circle
stacks as desired.

In the image above, I used syringe diameters based on arbitrarily taking the
capacity and making those numbers diameters, only to manage a relatively
proportional image.

I found a  web page containing the formula
<https://www.ck12.org/trigonometry/Length-of-a-Chord/lesson/Length-of-a-Chord-TRIG/>
I'd likely use to pursue this as an OpenSCAD project.

The "welded" version of the above diagram: