In this case the stamens are diagnostic. In The other species of Arthropodium, it is necessary to mention flower size in a comment, and to have photos of how the flowers are arranged on the flower stalk. For other plants, excellent photos that can be blown up are needed of leaves on a bit of stem and of the whole plant. Have a look at the photos in my free app (from Google Play Store and Apple) Plants of South Eastern New South Wales to see the sorts of photos showing diagnostic characters.