There seems to be some semantic confusion in the participial discussion.  It's easy enough to resolve by going to phrase structure grammar in which the "participle" is a lexical item with certain formal characteristics (e.g., -ed or -ing ending) functioning as a part or all of a finite or nonfinite verb phrase.  The "participial phrase" is a nonfinite verb phrase with a participle as its head, always serving adjectivally.  The participial phrase is still a participial "phrase" even if it is only a bare participle (e.g., "dancing" bears).

Jeff Glauner
Park University