Opening the front of the K-3
Many K-3 troubles can be solved by removing the front of the camera and gently knocking on the gears.
Here's how to take off the front
Pry off the aluminum trim plate on the front. Some come off very easily, some require more persuasion. A single-edge razor blade (careful!) jammed under the trim and worked around will usually do the trick.
If you have a bayonette-mount K-3, you will first have to remove the three set-screws that hold on the mount.
Remove the four flat-head screws. Three will generally come out easily. The fourth, in the lower right corner, is generally gunked up with tar. Do not use that 99 cent screwdriver with the yellow handle you have laying around. Get a quality $7 screwdriver from Sears or even Home Depot. Otherwise, you run the risk of damaging the screwhead and then you've got problems.
It's best to hold the camera upside down when you remove the front so that the shutter release button will not fall out. There is a tiny spring surrounding the shutter release button. It only keeps the button from rattling around, and if you have trouble putting it back in, just leave it out.
The trigger release can be pushed in to run the camera, or pulled forward to expose a single frame.
Here's another view of the front. Those two wires are for the lightmeter sensor. They go into the side of the ground glass (directly above the mirror).