What makes a mattress pedic?

Okay, I do know that there’s no regulating body out there that permits or disallows the use of -pedic as an impressive-sounding suffix.

But what does “-pedic” mean? I assume that mattresses (Tempur-Pedic, Posturepedic, Supple-Pedic, etc.) use it because it comes from “orthopedics,” and is therefore supposed to sound like it’s good for your skeleton.

The dictionaries I have access to break down “orthopedics” this way:

ortho-, from the Greek orthos, meaning “correct”
the Greek pais, meaning “child”

Child? Where does child come in to this? And does the suffix “-pedic” appear in any non-marketing-derived English words? If so, what does it mean?

http://www.amirmd.com/ortho-info/Ortho-history.html

“encyclopedic”?