meshing

松本清張の短編小説 THE VOICE から引用します。
While these were all "facts," they didn't connect with each other. They were like cogs that had gone haywire and were no longer meshing. Each one of them was at cross-purposed with the others.
....
The handbag had been left after five, when the train had let up.
"For the first time two cogs are meshing. At five o'clock," the chief sad complacently.
日本語でいう歯車が噛み合うとか噛み合わないを英語でなんというのか知りませんでしたが、"mesh" を使うのですね。一応 "mesh" を英英辞書で見ます。
・Oxford English Dictionary: (of the teeth of a gearwheel) be engaged with another gearwheel.: one gear meshes with the input gear

・Collins Dictionary: If gear teeth mesh with other gear teeth, or are meshed with them, they fit together and start working together.: This gear meshes with another gear, which turns the pinion gear shaft.
・Cambridge English Dictionary: (of two or more things) to fit together or be suitable for each other: The teeth of the smaller and larger gears mesh with each other.

put out

"put out" は慣用句で「消す」意味となる事を大昔に習いましたが、松本清張の小説 THE VOICE（このVOICEは人の声を聴き分ける並外れた元電話のオペレータが偶然電話で耳にした殺人犯人の声を意味しています。）に出てきた次の "put out" は違う意味で使われています。
"Don't get impatient or you'll wind up losing. He'll be here before long." Kawai, with his tiny eyes and thin lips, was trying to be encouraging; but, in face, he was also getting irritated.
"What on earth could have happened?" Shigeo looked put out.
辞書を見ます。
・Macmillan Dictionary: annoyed, offended, or upset by something that someone has said or done: She was feeling extremely put out by his rudeness.

・Collins Dictionary: If you feel put out, you feel rather annoyed or upset.: I did not blame him for feeling put out.
・Wiktionary: Taking offense; indignant.: He was put out at the mere suggestion of misconduct.