Keilim, Chapter 21, Mishnah 1. This mishnah takes us into the weaver's workshop. To follow it, we first need to picture how cloth is produced, and then how a loom makes that work possible.
How cloth is woven
A weaver who wants a finished piece of cloth begins with a set of threads stretched parallel to one another. These are the warp threads, the ones running lengthwise. He then takes a single travelling thread, the weft, and passes it across them, going over one thread and under the next, thread by thread, all the way across. At the end of the row he turns it around and brings it back in the other direction. Row after row, this produces a criss-cross pattern which is then tightened, and the result is woven cloth. In short: some threads run vertically (the warp) and one thread keeps travelling back and forth horizontally (the weft).
A loom is what makes all of this practical. At the two opposite ends of a large frame there are two heavy rollers, and the warp threads are wound around them. Between the rollers sit the harnesses, each fitted with rings that hold the warp threads: one harness holds the odd numbered threads and the other holds the even numbered ones. By lifting one harness, the weaver raises every second warp thread at once, and the weft can be passed straight through. There are a number of other parts to the loom as well, and the mishnah will list them at length.
The question of the mishnah
The question the mishnah addresses is this: while a piece of cloth is still on the loom, are the various parts of the loom considered part of that cloth? The practical difference is tumah. If a given part counts as attached to the cloth, then when the cloth is tamei, the part is drawn into its tumah, and touching that part is like touching the cloth. If it does not count as attached, the part stays tahor even while the cloth is tamei, and tumah does not travel between them in either direction.
The parts that are not connected
The mishnah begins: "Hanogea bakoved ha'elyon uvakoved hatachton", one who touches the upper roller or the lower roller. The upper roller is the front one, onto which the finished cloth is wound as the work proceeds; the lower roller is the one at the back, holding the warp threads that have not yet been woven.
"Uvanirim", and the cords that lift the warp threads as the weaver works. "Uvakeros", the reed, the framed comb used to press the weft thread firmly into its place after each pass.
"Uvachut shehe'eviro al gabei ha'argaman", and a thread that the weaver laid across the purple wool. Purple wool was extremely costly, so when a weaver was working with it he would lay threads over it as a covering, to keep it from becoming soiled while he wove. These threads were not sewn or fastened into the purple wool; they were merely laid on top of it.
"Uva'ida she'einah atidah lehachaziro", and a piece of colored material that the weaver inserted between the warp threads but does not intend to leave in place. He wanted a touch of color while working, and the piece will be removed once it has served its purpose.
In all of these cases the ruling is tahor. None of these items is considered joined to the cloth being woven on the loom. They are all destined to be taken away from it. Therefore, even if the cloth itself is tamei, a person who touches any of them remains tahor. And the reverse is equally true: if the cloth is tahor and a person who is tamei touches one of these items, only the item he touched contracts tumah, while the cloth does not.
The parts that are connected
The mishnah now turns to the opposite list. "Benefesh hamasechet", one who touches the weft thread of the weave once it has already been passed through the warp threads. "Uvash'ti ha'omed", and the standing warp, the threads stretched between the rollers and ready to be woven into the cloth.
"Uvakaful shehe'eviro al gabei ha'argaman", and the doubled cloth spread over the purple wool. Here too the purpose is to protect that expensive wool, but the difference is decisive: this covering is not simply resting on top, it is sewn onto the wool.
"Uva'ida shehi atidah lehachazirah", and a piece of colored material that the weaver placed into the cloth and does intend to leave there permanently, so that it becomes part of the finished product.
All of these are considered connected to the cloth, and the ruling is tamei. If the woven cloth is tamei, one who touches any of these becomes tamei as well, because they are part and parcel of the cloth being made. And the reverse follows: if a person who is tamei touches one of these, the cloth itself becomes tamei together with them.
Wool on the distaff
The mishnah moves from weaving to spinning. A distaff is the implement that holds the unspun wool while the spinner works. "Hanogea batzemer she'al ha'ima", one who touches the wool that is on the ima, a rod-shaped implement with the unspun wool wound around it. "Uva'ashvaya", and the wool that is on the ashvaya, an implement shaped like a triangle, which likewise has wool wound around it.
The ruling is tahor. The wool is only wrapped around these implements, not fastened to them. It is therefore not regarded as joined to them for the laws of tumah, and touching the one does not carry tumah to the other.
The spindle and its weight
Finally the mishnah discusses the spindle, which we have already encountered earlier in the masechet. It consists of a rod together with a weight; the weight has a hole into which the rod is inserted, and the two are tied together. The question is whether the rod and the weight count as a single connected unit for tumah.
"Hanogea bapika", one who touches the weight attached to a spindle that is tamei. The mishnah rules: "Ad shelo pir'ah, tamei", so long as he has not undone the binding, one who touches the weight is tamei, since the two are tied together and treated as one object.
"Mishepir'ah, tahor." Once he has untied them, he is tahor. Even though the weight may still be sitting on the rod, it is no longer bound to it, and once the binding has been released we regard the two as detached and no longer a single entity. Consequently, even if the spindle is tamei, neither the weight nor the person who touches it contracts tumah.
The thread that runs through the entire mishnah is a single principle: what is destined to remain part of the finished product, or is genuinely fastened to it, shares its status for tumah, while what merely rests alongside the work and will be removed when the work is done stands on its own.