word-forming element, especially in scientific compounds, meaning "life, life and," or "biology, biology and," or "biological, of or pertaining to living organisms or their constituents," from Greek bios "one's life, course or way of living, lifetime" (as opposed to zoe "animal life, organic life"), from PIE root *gwei- "to live."
The correct usage is that in biography, but since c. 1800 in modern science it has been extended to mean "organic life," as zoo-, the better choice, is restricted in modern use to animal, as opposed to plant, life. Both are from the same PIE root. Compare biology.
late 14c., of a craft or skill, "pertaining to or involving mechanical labor" (a sense now usually with mechanical), also "having to do with tools," from Latin mechanicus "of or belonging to machines or mechanics; inventive," from Greek mēkhanikos "full of resources, inventive, ingenious," literally "mechanical, pertaining to machines," from mēkhanē "device, tool" (see machine (n.)). Meaning "of the nature of or pertaining to machines" is from 1620s.
in the names of sciences or disciplines (acoustics, aerobics, economics, etc.), a 16c. revival of the classical custom of using the neuter plural of adjectives with Greek -ikos "pertaining to" (see -ic) to mean "matters relevant to" and also as the titles of treatises about them. Subject matters that acquired their English names before c. 1500, however, tend to be singular in form (arithmetic, logic, magic, music, rhetoric). The grammatical number of words in -ics (mathematics is/mathematics are) is a confused question.
<a href="https://www.etymonline.com/word/biomechanics">Etymology of biomechanics by etymonline</a>
Harper, D. (n.d.). Etymology of biomechanics. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/biomechanics