Epicycle: A little circle, whose center is in the circumference of a greater circle

From Ancient Greek ἐπίκυκλος (epikuklos), from ἐπί (epi), on, or upon and κύκλος (kuklos), a circle

In astronomy, an epicycle is a small circle with its center on the circumference of a larger circle.  This ides shows up in the old Ptolemaic model.  With Earth as the fixed central location, each of the seven planets revolved while fixed on a distant circumference.

In math an epicycle is a circle whose circumference rolls around that of another circle,

Confused?  English words from Greek words are pretty confusing.  Here is a diagram of a planetary epicycle.  Perhaps this will help.