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602 Club patches large — Several patches on display in the 602 Club

Commodore Robert Wesley wears the "Starfleet Command" assignment patch

An assignment patch was a patch or badge on the uniform of Starfleet and MACO personal to denote the ship, station, or other post to which an individual is assigned to.

Histroy

In the early 22nd century, Starfleet personnel wore assignment patches on the sleeve of their left arm harkening back to the first days of space flight. The uniform would later be updated adding the Starfleet patch to the right arm.(ENT)

Several assignment patches, including ones from NASA missions, were on display in the 602 Club on Earth in the 2140s. (ENT: "First Flight")

While most of the patches seen were real NASA mission patches, one case contained fictional patches from the Star Trek universe, many of them seen for the first and only time in this episode.

Throughout the 23rd century, Starfleet continued the tradition of maintaining different assignment patch emblems for individual posts, now worn over the left breast. By 2278, however, this practice was abolished and Starfleet adopted the USS Enterprise's assignment patch as the standard emblem for all Starfleet personnel to commemorate the historic missions of that vessel. It was at this point that assignment patches fell into disuse in Starfleet, as they began using badges and combadges. (TOS, TNG: "Cause and Effect")

Starfleet Academy would bring the use of an assignment patch back with the introduction of the Red Squad unit in 2372. (DS9: "Homefront")

In the mirror universe, the 22nd century tradition was upheld. While the Empire uniforms had several variations from that of the normal universe, they still wore mission patches on their shoulders, even though a ship's patch would be different from that of their mirror counterpart. By the 23rd century though, the mission patch was already out of use in favor of the Imperial insignia. (ENT: "In a Mirror, Darkly", "In a Mirror, Darkly, Part II", TOS: "Mirror, Mirror")

Background

The Starfleet pins adopting the Enterprise emblem were first seen in Star Trek II: The Wrath of Khan; this badge was made into a combadge by 2344, the era of TNG: "Yesterday's Enterprise". Newer combadges were first seen in TNG: "Encounter at Farpoint".

The assignment patch for the USS Enterprise (NCC-1701) and the movie era Starfleet assignment badge are very similar to those used by US Space Command in the 20th century and early 21st century.

There are some stray elements which detract from the "one ship, one emblem" theory, however; some members of Kirk's academy class who cajoled Kirk in a lounge in TOS: "Court Martial" also wore the Enterprise patch. It would seem unlikely that Kirk's direct subordinates would take part in such a thing, classmate or no, so it least suggests they were assigned elsewhere, yet had the same patch.

Starfleet uniform styles

By era: