About “Up” and its phrases

Normally, for a non-English speaker, “up” has the implication of “Upward” as opposed to “downward”. So, some verb+proposition phrases, which have evolved for so long that English learners might not be able to comprehend just from literal meanings, do frustrate them.. For example , “let up” “ round up” “set up”.Take “let up”. Up, in this sense, implicates stop doing something. This, I think, may derive from “ Time is up”. But why “UP’? why is it not “over”,or “out”? You see, Time is running out, The sands of time are running out. It dawns on me that It may be related to the ancient timing instrument.------the sandglass. When the sands have run out, you should put the sandglass upside down. Now the sands of time are up, that is “Time is up”. In this way, “UP” acquired the meaning of “over” ,”out”,or “end”, as in “die-up”, “end-up”.Am I right?But this cannot account for “round up”( to drive the cattle) ,”set up”( to frame), “UP” must have other meanings, can you help me?