DaasYochid: I always respect your knowledge but what you write is just not true. As said numerous times on this thread, there are thousands of Shabbos elevators throughout the world and thousands of jews use it. Escalators are certainly less “chomur’ and a poster mentioned the “shemiras Shabbos” who is “matter” it. It is pretty safe to say that he checked with R”Shlomo Zalman Auerbach on this.
As far as bicycles, although there is no specific issur, adults have refrained from using this due to “uvdo dechol” or “shemo jetaken”.
On umbrellas, it was a major machlokes in the 18th and 19th century. Check the Nodah bejehuda, SH”T Tenina, teshuvo 30. Although he ultimately forbids opening an umbrella, he ends by saying , that, if the umbrella is already open, there is a “tsad hetter”. As I wrote, there were towns and Hungary who had open umbrellas at the ready to avoid the problem of “ohel”. Obviously there has to be an eiruv in the town.
As far as trains or other public transport, both the “Shoiel Umeshiv” and the “Chelkas Yaakov” struggle to find any real issur and they both end up by saying, well, it is just not “shabbosdik”.
I have no problem with this but , clearly, therev is no real issur de’oiraisa or even miderabbonon in all of these examples.