<<<<<I believe she measures the diameter of the cells with her front
legs.>>>>>
I read somewhere many years ago of experiments designed to check  this.
Removal of a portion  of one antenna left the queen completely
dis-orientated and she laid worker and drone eggs indiscriminately.
I suppose that using antennae would be more sensitive than using legs.
Perhaps  someone can come up with more positive evidence.               Sid
P.