a sling is what helps to support the extremity. A swath keeps it
from swinging.
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A swath is the width of cut made by a scythe. The phrase, "To
cut a swath" means then to cut a path, reap anything in your path
down, etc. It can even mean, to make a big impression.
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Splint injuries:
The sling and swath is used for all upper extremities. The sling supports the injured extremity and immobilizes the lower arm, while the swath functionally immobilizes the shoulder and keeps the arm from "chicken winging" outward.