Definition 1: A devioius scheme, an act of intrique.
[@more@]Usage 1: The [ch] in today's word tends to be pronounced with the Greek [k] in Britain but with the French [sh] in the US. The [k] is the older, more traditional pronunciation. "Machination" is the process noun from the verb "machinate." A person who plots and schemes is a machinator. The stem of all members of this family reflect the same dual pronunciation found in the stem of today's word.
Suggested usage: Even though the word contains "machine," machinations are not at all machine-like but are most human: "Major Miner manipulated his promotion by means of Byzantine machinations behind the scenes despite little combat experience." The capital of a country is usually the capital of machinations, since politics is probably impossible without intrigue and scheming.
Etymology: Latin machinatio "mechanism, contrivance" from the verb machinare "to design, contrive," a verb based on the noun machine "device" borrowed from Greek "makhana," dialectal variant of mekhane "machine." You are right to see an ancestor of our "mechanics" and "mechanism" in the Greek word. The original root also provided Russian moch' "can" (mogu "I can") and moshch' "power, might," plus Old English "magan," the forerunner of today's auxiliary verb "may" and both the auxiliary and noun "might."