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A Fire and Emergency New Zealand (Fenz) spokesman said the Balclutha brigade was called to Storer Rd at 9.15am after someone got one of their arms trapped in the machine.
St John communications adviser Gerard Campbell said the patient was flown by rescue helicopter to Dunedin Hospital in a moderate condition.
A packhouse spokesperson said the man was "ok" but declined to comment further.
WorkSafe have been notified of the incident and is making inquiries.