Re: get hung up VS get tied up VS .....(a multiple choice question)       another quick stab at an explanation   
get caught up 
get hung up 
get held up 
get tied up   
all sort of have the feeling of the last 'get tied up'.  Someone or something has tied up your free time, interest, or you have litteraly become intertwined in something like a rope, meshing, machine or something.   
In this case, they weren't physically intertwined in the dumbwaiter mechanism (possible but not probable.)  Instead, they were trapped within or stuck and unable to move/get out.   
'got caught' would be possible, but 'got caught up' has the meaning as stated above.   
Does that make sense?         |