The man at one end weighs 150 lb.
The man [who is] at one end [of the lever] ...
The man supports the lever at one end.
* ... the lever [that is] at one end [of the lever]
Both examples fit the pattern:
< object> AT < location>
However, in the second case, attaching at one end to the noun phrase would be wrong. Additional semantics is needed.
Rule: an object may not be modified by a location on itself.