*ar(ə)-

The core idea of this root was:

fitting together

It’s the origin of a quite wide array of words that all in some way are about connecting parts or making parts fit.
Here’s a little (incomplete) overview:

• arm (bones joined together into a whole)
• arthritis (“related to joints”)
• arm (tool fitted together, then “weapon”)
• armor (again, stuff fitted together)
• alarm (originally: “to the weapons”)
• art, artificial, artist, artifact (“stuff fitted together”)
• article (“part of a whole”)
• articulate (“to say clearly, as separate parts”)
• order (“fitted together”)
• ordinary (originally “according to order”)
• subordinate (“ordered below”)
• harmony (“fitting tones”)

• rite
• ritual
• riddle
• read
• rhyme
• reason
• ratio
• …

The last group ties in with a branch that’s about “talking” which is also where German “reden” comes from.)