The Renaissance coincided with the development of the printing press and allowed more books on technology to be published. Leonardo da Vinci was one of the key figures of this period since his texts included many technical drawings many of which were ahead of his time. Later authors such as Besson, Ramelli, Agricola and Piccolpasso published books showing state of the art machinery. It does not appear that much work was put into tribology per se, but pictures of military and industrial equipment show signs of increasingly complex and well thought out bearing designs. Most likely tribological improvements were discovered by normal machinists, craftsmen, and designers instead of being developed by specially trained tribologists. I think it is only with the modern level of division of labor that people have been able to specialize in as specific a field as tribology.
Source: History of Tribology by Dowson