The OED (Third Edition, 2006) suggests an influence from the word ancre1 that is probably unetymological. This lexeme may have the same origin as pollance.
s.
1ship.implementpulley for hoisting or hauling ropes (?):
(
1409-11
)
[...] .ij. yerdropes, .iij. petitz ropes febles, .ij. pendantz pour lez polankrez
iii 54
polankre (1409-11)