מסכת כלים

פרק יט משנה ב

The rope bed that comes out of the bed (this is extra rope that hangs from the bed after its surface was woven),

until five handbreadths

is tahor (as such a length is useless);

from five to ten

it is tamei (as such a length is useful)

from ten and outwards (i.e. that portion that is beyond ten handbeadths)

is tahor;

as with it (a rope of 5 - 10 handbreadths) they would tie the [lamb that would be the korban] pesachs

and they would lower the beds (such a rope would be used to lower the bed into a mikvah to purify it, or to the lower floor of a building).

פרק יט משנה ג

A mizran (a strap of cloth wrapped around the outside of the bed to help keep the boards and legs together)

that extends from the bed (this refers to an excess amount of the strap that is left dangling)

the smallest amount [is susceptible to tumah]

this is the opinion of Rabbi Meir (as he held that the bed's owner may at some point decide to reinforce the bed by using this excess amount to further wrap it);

Rabbi Yosi says

ten handbreadths (he sees it as the same as the rope in this regard, although he does not give it a minimum amount).

The remnants of a mizran (that are left after it had become too worn and/or torn for use with a bed)

[are susceptible to tumah if it is] seven handbreadths

such that it can be made into the strap for a donkey (this was used to either protect the donkey's load, or as a sort of blanket for the donkey).