I worked on a Singer 360 tonight. It is one of five machines I picked up at a Goodwill a couple weeks back.
The motor was quite loose so I tightened up the bolt through the little hole in the plastic housing. It didn't help. The motor was still loose. Hmm. The difficulty in figuring out what was going on was that the plastic housing needed to be removed. It wasn't a terribly easy job but the halves came off without breakage (always a nice touch).
Ok, here's where Singer made their little slip-up back in 1975. The threaded hole into the casting was drilled off center of where it should have been, or the raised boss was machined wrong. It wasn't much but just enough that the bolt threads would catch on the motor bracket slot. Below is a photo of the offending hole and boss (center of the photo).
If you look closely at the above photo, the threaded hole is off to the left a little (toward the front of the machine). It isn't much but just enough to cause interference between the bolt and the motor bracket slot. Below is a photo of the bolt, with the threads worn from hitting the bracket, or maybe the assembler shaved down the threads to get the machine out the door.
I took a file to the motor bracket in the area where the bolt hit, to give a little relief to the bolt threads. It was just enough to get everything back together correctly. Getting the plastic housing back on was a bit more of a challenge than removing it, but again, no breakage. Now that the machine is all oiled up, it sews very nicely. I threw in some cams to test things out, then tried a buttonhole. Bottom to top they are: straight stitch, zigzag, multi zigzag (#2 cam) on long stitch length then short, blind hem (#3), domino (#6), crescent (#31) in short then very short (fine) stitch length, and finally the buttonhole on top. The machine didn't skip a beat, er, stitch.