The Singer 401 is a wonderful machine. One of Singer's finest. The needle bar does have a tendency to get stuck from dried oil and dirt. This will prevent the needle bar from swinging back and forth to accomplish the zig zag stictch and other variations.
It is very easy to fix. Heat and oil are your friends here. And you may need to move the needle bar back and forth manually many times. If you get tired, do it some more. A hair dryer works wonders at loosening the old dried oil. Be sure to apply new oil and use the good stuff; Tri Flow