Canon PowerShot SD1100 IS: Broken Gear
I have a broken point-and-shoot digital camera of circa-2008 vintage, and I think I've found the point of failure: a small red gear who is supposed to turn a lead screw but has cracked open.

Without its friction fit grip on the shaft, it now just spins loosely. An optical limit switch told the computer the actuator is no longer actuating, thus the error message on screen. And the crack affected tooth spacing, which means it would no longer smoothly mesh with an adjacent white gear, and thus explaining the mechanical noise.
The crack propagated through the weakest part of this gear, where a hole has been cut out of almost half of its depth. Why is this hole here? It looks too neat and deliberate to be an air bubble in the casting/molding process, and looks too deep to be any manufacturing process artifact I know about. (Injection molding ejector pin mark, injection sprue cutoff, etc.) I'm curious to its intended purpose, which I'm sure is not weakening the gear to fail under stress. But it is broken now, how might I fix it?
Cyanoacrylate Glue
First attempt was to glue it back together with cyanoacrylate. (CA, "Super Glue", "Crazy Glue", etc.) A set of calipers acted as small-scale vise to pinch the gear back together, and a dab of CA was dripped into the mystery hole of weakening. A tiny bit was applied to the back side of the crack as well.

After waiting 15 minutes to let the glue cure, I pushed this gear back on the lead screw.

It popped back open, and the cured blob of CA also popped free. I don't know what the plastic was used to make this little red gear, but the material is apparently not eager to bind to CA glue.
Melting Plastic
If chemical binding doesn't work, how about some mechanical binding? I thought I would install the finest tip I have for my soldering iron, and melt the plastic across this crack to weld the gear back together.

Of course, "fine" is a relative term. A 0.5mm soldering tip is pretty fine by normal standards, but in this context it is 1/6 of the diameter across this gear, turning it into a blunt heat applicator.

But I tried my best, mostly successfully avoided ruining the gear mesh surface or inner shaft mating surface. Then I repeated the process for the back side of the gear. After it had cooled, I pushed it back on the shaft.

That didn't work, either, as the gear opened back up again.
I opened this camera up with low expectation of repair. I thought it was more likely that I would find the point of failure, satisfied with "yep, there it is", and continue taking this apart into its individual pieces. Now that I have this tiny broken gear in front of me, a repair is tantalizing close and I'm not ready to give up yet. However, leaving the camera and all its components scattered on my workbench would keep me from switching to another project, and many of these components are one big sneeze away from disappearing into nooks and crannies never to be found again. To keep all parts together while I think of things to try, I will reassemble this camera before putting it away.