From the Japan Science and Technology Agency, Kyoto University and the National Diet Library.
The tea-serving doll is the best-known karakuri of the Edo period. A doll in the National Museum of Nature and Science was made by the ninth Tamaya Shobei.
The doll is about 40 cm tall. It brings the tea with a clattering sound.
In the West, too, there were automata that walked or played music. But, as a historian of technology wrote for the Japan Science and Technology Agency, none is found that serves people directly, like this doll.
The mechanism of the tea-serving doll was the same as that of the wadokei, the Japanese clocks of the time. Wadokei were practical mechanical clocks, made only in Japan, that followed the length of day and night as it changed with the seasons.
Mechanical clocks were invented in the West around the 13th century and reached East Asia around the 17th century.
Most wadokei were made of iron, but the tea-serving doll is made of wood, which is much weaker. Its power came from whale baleen, and since baleen comes from an animal, its size was limited and it could not give much force. So the doll had to be light and delicate.
When a tea-serving doll made at the end of the Edo period was studied for repair, its wooden gears, glued together with the grain lined up, were found to have almost the same shape as modern involute gears.
In 1796, a book of designs for karakuri was published in Edo: Karakuri zui, in three volumes. It shows nine kinds of karakuri, including the tea-serving doll.
The author, Hosokawa Hanzo Yorinao (1741–1796), came from Tosa and was a scholar of the calendar. He worked as an assistant in the shogunate’s office of astronomy.
In the preface he wrote that to make clever machines, you should look at many things and keep them in your mind. When memory and experience build up, your mind works quickly on new things, and inventions are born.
There is no single right answer. Talking it over with someone at home is a good way to learn.