Assignment patch
An assignment patch, or mission patch, was a patch or badge seen on uniforms, most notably on Earth, where their use began in the 20th century. The United Earth Starfleet and MACO personnel continued to use assignment patches to denote the ship, station, or other post to which an individual was assigned, as did the later Federation Starfleet.

History 
In 20th and 21st century Earth, assignment patches were used on military uniforms and civilian uniforms alike. NASA patches from that era appeared in the Crash-n-Burn Bar in Bozeman, Montana, and at the 602 Club in San Francisco. (; )

Historical patches were a century later in the alternate reality in a similar fashion displayed behind the bar of the Riverside, Iowa Shipyard Bar. ()

In 1944 of an alternate timeline, Alicia Travers noted that the patch on Jonathan Archer's shirt said "" and surmised he was a sailor on the  aircraft carrier. She asked him how he wound up so far from the site of the ship's sinking, but he didn't elaborate. ()

In the early 22nd century, Starfleet personnel wore assignment patches on the sleeve of their left arm, in a similar style worn during the initial period of space flight on Earth. The uniform was later updated, adding the Starfleet patch to the right arm. () The assignment patch of Enterprise NX-01 was also used as a screensaver on monitors aboard the ship. ()

In the mirror universe, the Terran Empire used the traditional styling from the 22nd century. While the Empire's uniforms had several variations that distinguished them from those of the prime universe, they still wore mission patches on their shoulders. By the 23rd century, the mission patch had been replaced with the Imperial insignia. (; )

By 2233 assignment patches had seemingly been done away with, although a badge in the shape of the Starfleet insignia placed over the left breast was a part of the uniform, at least on the . ()

Some time before 2256, Starfleet adopted assignment patch-like variations in these badges, placing smaller symbols inside the Starfleet insignia, to indicate different branches or specialties. (, DIS) This also occurred in the alternate reality created by Nero's destruction of the Kelvin. (; ; )

Later in the mid-23rd century, Starfleet resumed the tradition of using unique patch emblems for different assignments, albeit placing them over the left breast. These patches usually but not always included the same symbols for the different divisions. The 's assignment patch was simply the Starfleet insignia. (TOS; )

By the 2280s, this styling ceased, and Starfleet once again adopted standardized badges in the shape of the Starfleet insignia for all personnel. () 

Assignment patches thus fell into disuse, and Starfleet eventually supplanted them with combadges in the shape of the Starfleet insignia. For example, such combadges were worn by the crew of the   in 2278 and the   in 2344. ()

20th and 21st century patches

22nd century patches

23rd century patches

24th century patches

Appendices

Background information 

According to the , the term "mission patch" was "not spoken in dialog, but was used in scene descriptions in '', where it described both ship and agency emblems. The classic Starfleet arrowhead emblem was created by costume designer William Ware Theiss."

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

The assignment patch for  was created by Wendy Drapanas, whereas the patch for the  was designed by Anthony Fredrickson. "When Wendy and I had our assignments on the pilot ['']," recalled Fredrickson, "one of hers was to design the NX-01 patch – which was a cherry assignment that I was very jealous she got! So when Mike [Okuda] gave me the Horizon patch, even though it was only for one show, I was very happy." ()

Michael Okuda has also designed two real world emblems; the STS-125 mission patch in 2009, and more recently, the emblem for Johnson Space Center's Flight Operations. 

A memo from Robert Justman dated 18 December 1967 discusses the Starfleet arrowhead emblem and individual crew patches. It states "all Starship personnel wear the Starship emblem that we have established for our Enterprise Crew Members to wear," meaning that the arrowhead was always meant to be the emblem for all of Starfleet. Further, the crew of the Antares was the "equivalent of the Merchant Marines or freighter personnel" and other emblems should be counted as production mistakes.

External link 
 
 

fr:Insigne de mission
ja:アサイメント・パッチ
Clothing accessories
Symbols