The needle action you are describing is the needle feed part of the compound feed system that the 111W151 has. The other part is drop feed, which is accomplished with the feed dogs.
The term "walking foot" is a term to describe alternating presser foot, which is the correct term. Your machine has three shafts, one of which holds the needle and the other two shafts hold one part of the foot. When one of the foot shafts goes down, the other goes up, hence the name alternating presser foot.
You will have better luck with the web site www.singerco.com
, which has some instruction manuals available for free.