Not entirely. For many years, the rating badge was worn on the right by bosun's mates (and cox'ns), gunner's mates, torpedomen, quartermasters, signalmen and maybe one or two other petty officers. It was worn on the left by all others, from yeomen to machinist's mates. Some time between the end of WWII and Korea, as I recall, all rating badges were tp be worn on the left sleeve. What lay behind this, I have no idea.
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