Kosher tzitzit: Is there such a thing as machine-tied tzitzit?

Our web store lists machine-spun tzitzit and hand-spun tzitzit as options on many of our tallit and tallit katan products. Some people mistakenly think this refers to the tying process. For example, we received this inquiry today:

Also your traditional Tallit Katan for 5.90$ says it has hand-spun tzitzit by a Ben Torah.  However when trying to place the order the free option says machine spun.  Are the hand-spun tzitzit hand or machine-spun? – Jay

I explained to Jay that a lot of people get confused over this. Spinning the tzitzit and tying the tzitzit are two very different things.
Actually almost all tzitzit are machine-spun. What’s called “machine-spun” are made on an advanced machine. Basically all a human does is push the button to start the machine. What’s referred to as “hand-spun tzitzit” are made on a very simple machine that is operated by real people. To understand the halachic significance of this difference, please refer to this post.
Once you have kosher tzitzit strings (whether machine-spun or hand-spun), the next step is getting them tied on. This is always done by a human. There is no such thing as a “tzitzit tying machine.” There is a question of who does the tying. Here are a few possibilities:
A non-Jew – This is completely non-kosher according to all opinions. It’s quite rare. I’ve heard stories of tallit katan makers having tzitzit tied on by Chinese workers. That’s considered a major scandal. If you buy a tallit made by a company under nonobservant ownership, in theory there could be problems. (Many of the modern hand-made and hand-woven tallit makers here in Israel are nonobservant.) For example, they might hire certain immigrants whose Jewish status is questionable according to halacha, to do the tzitzit tying.
A woman – This is kosher, but is somewhat frowned upon in some circles, and as noted in the Mishnah Berarah, some people avoid having women tie there tzitzit. Women tying tzitzit is not uncommon among the modern hand-made and hand-woven tallit makers.
A Jewish man under the age of 13 – This is not permitted according to all opinions. The only exception is if a boy under bar mitzvah age ties tzitzit for himself and then wears it himself after he is bar mitzvah. According to some opinions it would be allowed. In practice, the chances of a boy tying tzitzit for companies is very slim.
A Jewish man in jail – It’s not uncommon for tallit katan manufacturers to arrange to have prisoners tie tzitzit. Some people may be uncomfortable with the idea, but it’s certainly kosher, assuming there is proper rabbinical supervision (i.e. checking that they are Jewish, observant and tie properly).
A Jewish man who is not observant or somewhat observant – According to halacha, tzitzit must be tied with intent to fulfill the mitzvah of tzitzit (לשם מצוות ציצית). I have tried to get a solid opinion on how to properly define this. One rabbi told me someone who wears tzitzit can be relied upon to do the tying לשם מצוות ציצית.
ben Torah – If you have a ben Torah doing the tying, you can be fully confident none of the above issues come into play. For example, our in-house tzitzit tie-er is a kollel man who ties tzitzit at night. He has over 10 years’ professional experience (!) and is a second generation tzitzit professional (his father sells tzitzit).