There might be better and easier ways to fix a laundry rack,
but what's the point in doing that if you own a 3D printer?

Btw, it's still working after two years of almost daily usage \o/

PROTIP:
Two of these clamps, combined with printing filament, can also
be used to span new wires between the existing ones...

Notes:

Do not print the provided STL file. It is only an example.
If you are not familiar with OpenSCAD, feel free to just
edit this file in Thingiverse's Customizer.

Basically, you only need to modify two variables, to create
your own, perfectly fitting Laundry Rack Repair Kit.

• the diameter of the frame, "lrDiaFrame"
• the diameter of the wire, "lrDiaWire"

Add ~0.5mm - 0.7mm to the measured values.

The example STL was created with

• lrDiaFrame = 14.7mm
• lrDiaWire = 3.3mm

For a finer control, I recommend editing the OpenSCAD file
directly. It is well documented (TM) and contains a special
"Edit Mode", in which you can examine the (otherwise not
visible) holes and cutouts.