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.