I'm not sure what types of binding you want to make, do you want to bind all of them to <1>?

I think you are overlooking "tags", but there are a few ways to do it. The array method is ok, but you would be better off using a hash. There are many different ways to do it, depending on whether you need separate callbacks for each ball or not.

untested( but close to correct) :-)

# first way with tags, all outer balls will be bound
# to same callback
my $refitem = $zinc->add('arc',$centergroup2, [ [10,20], [20,30] ],
               -filled => 1,
               -fillcolor => $refgrad,              ##    $refgrad
               -linewidth => 0,
               -priority => 100
               -tags => ['outerring'],
               );

# make/clone 11/12 more of the above
for (1..11){
  my $relement = $zinc->clone($refitem);
  $zinc->rotate($relement,.53*$_);
}

$zinc->bind( 'outerring', '<1>',  \&ro6);
[download]

Now you can also do it to bind each outerring ball to a separate callback.

my %refitems;
my $refitem = $zinc->add('arc',$centergroup2, [ [10,20], [20,30] ],
               -filled => 1,
               -fillcolor => $refgrad,              ##    $refgrad
               -linewidth => 0,
               -priority => 100
              );

# make/clone 11/12 more of the above
for (1..11){
   $refitem{$_} = $zinc->clone($refitem);
   $zinc->rotate($refitem{$_},.53*$_);
   #here you bind each one separately, and/or
   #pass extra info to the callback 
   $zinc->bind( $refitem{$_}, '<1>',  [  \&ro6, $_  ]    ) ;  
}
[download]

As you can see, there are more than one way to do it. You can even assign the hash element as a tag, although it is a bit redundant; however it allows you to search for items thru the tag mechanism. I include it just to reinforce the idea that you can throw anything into the item's tags.

my $refitem = $zinc->add('arc',$centergroup2, [ [10,20], [20,30] ],
               -filled => 1,
               -fillcolor => $refgrad,              ##    $refgrad
               -linewidth => 0,
               -priority => 100
               -tags => ['outerring'],
               );

my %refitems;
# make/clone 11/12 more of the above
for (1..11){
   $refitem{$_} = $zinc->clone($refitem);
   $zinc->addtag($refitem{$_}, $refitem{$_});
   $zinc->rotate($refitem{$_},.53*$_);
   #here you bind each one separately, and/or
   #pass extra info to the callback 
   $zinc->bind( $refitem{$_}, '<1>',  [  \&ro6, $_  ]    ) ;  
}
[download]

Anyways, those are some ideas to explore. When you have more than 1 item, that you want to bind to the same callback, you can use tags, or pass an extra arg to the bind callback, to identify which ball called it.