When I arrived home,the door was found locked.当我到家时门是锁着的。（说明你说的时候锁已经打开了）Arriving home ,I found the door was locked 意思同上。（说明你说的时候锁还没有打开，你回家刚发现）

你的标题就是理论部分，一点错误也没有。但是你的例句就有问题了。 1. Arriving home ,the door was found locked. 是个错句 因为主语the door ，不能发出arrive-When I arrived home,the door was found locked. -Arriving home ,I found the door was locked 改写之后都是正确的。理论同上2. looking out of the window ,there are lots of people in the street. 这个也是错误的，理论同第一题-When you look out of the window,there are lots if people in the street. -Looking out of the window ,you can see there are lots of people in the street. 后面这2个都对。参考文献：个人观点