The earliest recorded (and perhaps the first) example of robotic mime can be seen as performed by Charlie Chaplin in 'Modern Times'.  Which. like all Chaplin films is as entertaining today as it was in at the beginning of the last century.  He is working on some kind of production line and imitating the movements of the machinery around him (You might want to check up on that as it's a long time since I watched it and you might not have anything better to do).

Many people have inaccurately attributed the invention to Michael Jackson. I've heard it credited to many different people, even myself.  Lots of things get attributed to Michael Jackson; he is responsible for neither the robot nor the moonwalk. Although he may be responsible for many other things, it's not for me to comment on. 

So it seems that Charlie's robot didn't exactly catch on.  Being before its time in 1936, it had to wait nearly fifty years before it really took off. 

There are some amusing videos on Youtube of robotic dancers from the eighties.  Tick and Tock wore dangly earrings!!!  Their mothers must have been so ashamed!  Charlie Chaplin saw what was coming and died three years previously.