We are beginning siman 2, where the Chayei Adam gives the shiur necessary to be chayav for mechateich.
The Chayei Adam writes that one is chayav for mechateich if they cut off a piece of leather from a hide that is large enough to cover a kameiah (amulet). The Chayei Adam clarifies that, in addition to cutting a shiur’s worth of leather, one must cut it with intention to cut it to a specific size. If one cuts the leather without any specific intention for the size (ie, they will cut it and decide afterwards what to do with it), it would not fall under the chiyuv of mechateich.
We learned (s738) that the melacha of mechateich includes cutting an item to a general size within a valid range for the item, even if it is not cut to precise measurements. Another question is whether mechateich applies to other actions, such as whittling. While sometimes, the purpose of whittling is to finish the kli (tikkun kli), other times, the purpose is to create a certain shape, which could be argued is similar to cutting something to a certain size. There are poskim who therefore assume that mechateich would apply to those types of actions. Epxamples would include sharpening a pencil or cutting a piece of wood to make a toothpick. Regarding making a toothpick, the Rosh says the issur is tikkun kli, which the Rambam says the issur is mechateich, and, as we see, both aspects could be correct.
Rav Falk brings a fascinating example of mechateich: shaving down a cork in order to put it back into a bottle. In addition, according to the Rosh, it might fall under the issur of tikkun kli, so it may be assur from that angle as well.
Some scenarios of refuah on Shabbos also encounter the issur of mechateich. For example, if one is trying to cover a wound, and they need to cut surgical tape from the roll to hold down a bandage, if it is a sakanah, it is obviously muttar. If there is no sakanah, but the person is a choleh kol haguf, although issurei derabanan are lifted for this choleh, cutting the bandage to a specific size or cutting the medical tape would be issurei deoraysa and would be a problem.
Another application of mechateich is when the pages of a sefer are actually attached to each other (not just that they are compressed together, but when they are actually connected). There may be an issue of koreiah, but the Shmiras Shabbos Kehilchasa points out that it would also fall under the melacha of mechateich, because the goal is a specific size of paper.
Measuring a roll of table cover to cut it at an exact amount would be mesarteit (eg, the size of the table plus 4 includes on each side) and then cutting it is certainly mechateich. Additionally, eyeballing an approximate size and cutting it would be mechateich as well.
Summary
- The melacha of mechateich is the issur of cutting something to a specific size. The shiur given by the Chayei Adam is enough to cover a kameiah.
- The poskim assume that mechateich applies to cutting something to a specific shape, similar to cutting something to a specific size. Examples include whittling, sharpening a pencil, shaving a cork, or making a toothpick.
- Scenarios of refuah on Shabbos that will encounter mechateich include cutting a gauze to size or cutting medical tape.
- Other examples include pages of a sefer which are connected together, or cutting a specific or approximate amount of tablecloth from a tablecloth roll.