It follows an appeal launched in The Scotsman in May for memories and memorabilia to mark the 200th anniversary of the birth of the network.
Responses from readers increased the number of institutes on a newly-created database by more than half from 167 to 263.
Institutes were established across Scotland after the first was inaugurated in October 1821 as the Edinburgh School of Arts and led to the creation of Heriot-Watt University.
That led to over 9,000 institutes being formed worldwide over the following century which help train engineers in revolutionary developments in energy and transport.
The research project is being led by Sue Roaf, emeritus professor of architectural engineering at Heriot-Watt, who is compiling a Gazetteer of Scottish Mechanics’ Institutes with colleague Anne Ormston.
Prof Roaf said the photographic competition carried a £300 first prize, with £150 for second and £50 for third, for the best new or historic images of the elevation of institute buildings.
Entries should be submitted via the competition portal at https://www.hw.ac.uk/alumni/watt-club/mechanics-institutes-worldwide-2021.htm
Prof Roaf said: “Thanks to Scotsman readers, the Mechanics Institute Hunt – www.mechanicsinstitutes.org - has now reached an amazing 263 different buildings that were either called mechanics institutes or ran their courses.
"Many people have sent in really interesting histories and reminiscences from all over."
Prof Roaf said these included Jennifer Woods from Blairgowrie, who sent a large number of cuttings from different local histories of the town’s institute building on the High Street, which was built in 1870.
It had a library of more than 3,000 books, reading room and billiard and bagatelle rooms.
Mrs Woods said when she was a girl in the 1950s, it was still in use as a reading room, with an open fire tended by the librarian, and a large table by the window with all the daily papers, “where the old worthies would probably spend much of the day, warm and comfortable though silent, as talking was not encouraged”.
Prof Roaf said: “It is just such stories we are looking for, so please send them to [email protected]