Projection apparatuses and associated methods are provided. As the cast moves through the passage, the cast outer surface and the passage inner surface define therebetween a reservoir for containing liquid glass or other molten material to prevent the external atmosphere from entering the melting chamber. The calculation definition tables and the calculation input definition tables are instantiated to produce a calculation graph model. Moreover, the linking apparatus includes: an operation mode control unit that shifts the linking apparatus to the second mode based on the shift command; and an access control unit that, after the shift to the second mode, prohibits the contact with the image forming apparatus, which is performed for the purpose of executing the specific operation.