The Model 61 saw filer have 2 coil springs that provide a recoil to what Foley calls the cam shaft assembly. Apparently this helps maintain the rotary motion. The springs are number 50 on the parts list, and they fit over the vertical slide rods, parts 51 and 52.
These springs can break after 50 years, but replacement is easy. Remove the motor, motor bracket, and flywheel. Then take the wing frame off and place it on a workbench. Remove the set screws at the bottoms of the slide rods. Turn the wing frame upside down and carefully drive the slide rods out with a punch or other tool that won’t damage the rods. The tops of the slide rods are knurled for a force fit, and this prevents the rods from being driven through from the top.
The rods are 5/8” and off-the-shelf 7/8” O.D. x 4” springs were a good fit, but they have a couple fewer coils than the originals. I don’t know the original uncompressed length.
Fit the springs in position, wipe the rods clean, and slide them back in. Use a soft face hammer or center punch to drive the rods the last inch. When they are approximately flush at the top, install the set screws.
While you have the wing frame off, take a look at the slide block on the other side. It’s exactly square, so if it has visible wear it can be rotated a quarter turn to eliminate the free play. The slide block is attached with a reverse-thread shoulder screw. Mine took a little grinding with 400 grit paper to get it to fit. Put plenty of grease on it.
Speaking of grease, the flywheel is the only major bearing without an oil cup, so put grease on the shaft before reinstalling it.
After getting the filer back together, run it by hand enough times to be sure everything’s working correctly.