I was supposed to do my homework, but I went out clubbing instead.

On a literal interpretation, supposed to suggests that other people (or indeed, myself) might have supposed (thought, imagined, assumed) that I would do my homework. I could continue the synonyms (expected, demanded, required,...) but they're getting further and further away from the 'core' meaning of supposed.

So far as I know, the verb to suppose only has the 'duty'-related sense when used as a past participle in this way. Is this true, and if so, why?

And how come my Mum can't suppose me to do my homework? If she supposed I was doing it, that doesn't imply she instructed me to do it - just that (in the absence of evidence to the contrary) she thought that's what I was doing.

(Added later) I think all the above would remain valid and still be exactly the same question if I'd asked about meant instead of supposed.