loom, mechanism, machine, airplane, opportunity, potency, efficacy, occasion
機 centers on a structured device that transforms or enables action: a machine, mechanism, or loom. Its extended senses of opportunity, potency, and occasion grow from the idea of a mechanism that creates a favorable moment or effective result.
chance; opportunity
function; facility; faculty; feature
engine
chance; opportunity; occasion
machine; mechanism
crisis; critical situation; emergency; pinch
device; equipment; machinery; apparatus
airplane; aeroplane; plane; aircraft
model (of machine, device)
standing by; awaiting an opportunity; being on alert
fuselage; airframe
mechanism; machinery
maneuver (usu. of military force); manoeuvre
motive; incentive
humour; humor; temper; mood; spirits
organic
secrecy; highly classified information
machinery and materials; equipment
aircraft
electric fan
inside a plane; in-flight
vending machine
electrical machinery; appliances
captain (of an aircraft)
機 combines 木 (wood) with 幾, which likely contributes the sound and the idea of subtlety or small triggers. Historically, it referred to a wooden loom mechanism, later extending to machines and abstract triggers.
A wooden 木 frame with a complex mechanism 幾: picture an old wooden loom with many small moving parts. That loom is a machine, and every machine creates opportunities to get work done.
For キ, imagine a key turning in a machine: key -> キ, and the key starts the mechanism.