The Archimedes screw pump does not appear to have been known in either China or Japan until the early 17th century, and probably later in Korea.
Note: The Japanese medieval period is given as 1185 to the mid 16th century by the 'Cambridge History of Japan' but up to 1603 by Wikipedia. For China, the terms 'medieval' and 'middle ages' are not typically used: those who do have imposed various end dates.
The earliest mention of any kind of screw in Japan would appear to be 1544:
On another ship from China, arriving in 1544, was a Portuguese
blacksmith who taught Yaita how to apply a screw at the bottom end of
the barrel. With this screw in place, the risk of explosion was
For the Archimedes screw pump, the earliest mention and use I've found is 1618 where it was used in the Sado gold and silver mines to deal with flooding:
The Archimedes screw pump (suijorin...) was first introduced in 1618,
in an effort to tackle the perennial problem of flooding, and this
heralded Sado's most productive period.
The Archimedes screw was also widely used on Sado from the mid
Sado mining scrolls has a depiction of the Archimedes screw in it but, unfortunately, it does not appear to be available online. It is only mentioned in the text of this British Library article:
Where no running water was available a pit
was dug on the beach and filled with water. An Archimedes screw is shown drawing the water up out of the pit to
form a flow that could be used for sluicing.
(All quoted text below is from Archimedean Mechanical Knowledge in 17th Century China by Zhang Baichun and Tian Miao, in The Genius of Archimedes – 23 Centuries of Influence on Mathematics, Science and Engineering)
In 1612, Archimedean-screw was introduced by Sabbathinus de Ursis and
The above refers to the work Taixi Shuifa (Hydraulic Methods of the Great West, Hydraulic Methods). Sabatino de Ursis (1575–1620) was an Italian Jesuit who worked with the Chinese scholar Xu Guangqi to translate western texts into Chinese. This work "depicted some water-lifting devices such as Archimedean screw". In the book,
Xu Guangqi, the Chinese partner in translation of the book vividly
named it [water-screw] longwei che (vehicle with the shape as
The book also has an illustration of a water-screw. Then,
In 1623, Italian missionary Giulio Aleni (1582–1649), assisted by
Chinese scholar Yang Tingjun, compiled Zhifang Wai Ji (Areas Outside
the Concern of the Chinese Imperial Geographer, ZFWJ),...In which
Archimedes and his inventions were mentioned...
However, these tomes do not appear to have been widely available and the Archimedes water-screw mostly remained in books. However, there are a few examples of manufacture and practical usage:
There were some accounts of manufacturing and use of the waterscrew in
18th and 19th centuries. Xu Chaojun...had a good grasp of astronomy
and clockmaking. A book, which printed before 1911, told us that he
constructed a water-screw that could be driven by a child to irrigate
crop in 1809.
Qi Yanhuai (1774–1841), who first held office as a county magistrate
in Jinkui and afterwards as a prefect in Suzhou, also made a
water-screw and a pump
Mostly, though, it was found to be impractical and expensive:
For craftsmen and farmers, the construction and using of water-screw
also bring some inconvenience. Qian Yong told us a short story. A
waterscrew was made in Suzhou in 18th century. It may irrigate
cropland of thirty or forty mu (a traditional unit of area) every day.
However, its very expensive in construction. And if it was damaged, it
could not be repaired and be used again. A majority of farmers was so poor that they were not
able to make it...
...Archimedean mechanical knowledge exerted a limited influence on
China in 17th century. It had partly been studied and practiced by
Chinese by the mid-19th century.
References to Archimedes in Korea before the 20th century are few and far between.
The closest reference I've found is 1783 when the Joseon Dynasty King Jeongjo (ruled 1776 - 1800) was advised to use a
Yongmi-cha (Archimedean screw), a type of western waterwheel
though many Joseon scholars were fascinated by the enlightened ideas
of the West, none of the theoretical designs were actually used to
construct real waterwheels.
It is possible that some among the Korean elite were familiar with Chinese works which mentioned the Archimedes water-screw. The Korean scholar Choe Han-gi, in his 1867 book Seonggi unhwa, mentions several "contributions to physics" credited to Archimedes but not the water-screw.