Baseball rules question - base runner equipment

[Pivotonian]

Guys,

Sorry if wrong forum, I've had a poke around on Goolge but not got any loving, just wondering if anyone can help a non-American understand baseball a bit better.

What is the requirement of base runners with regard to the equipment they were wearing when batting? It seems runners often take off shin/elbow guards when they reach first, but hang onto gloves, and a couple of times in the post season I've seen runners ditch the helemt when they pass third.

Can anyone either clarify this for me or point me in the direction of the official rules or another source of this info?

Cheers.