I want to DIY build a machine (lathe) that would normally be made out of cast iron. I don't have the resources to pour and machine cast iron, so I was considering pouring the casting out of concrete instead. The problem is concrete shrinks as it sets/cures, which will end up throwing off the precise measurements that I need. I am looking for an alternative that is a reasonably economical non-shrinking (or expanding) substance that will harden like rock/iron. Any ideas?
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You could try making the pieces for concrete but set the precise portions such as the headstock into the concrete using epoxy.
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Concrete is a poor material for machine tools for a wide variety of reasons. My advice would be to forget building a lathe yourself and buy one of the imports for pretty cheap these days. Harbor Freight and Grizzly Tools carry them, among others. If you are determined to build a lathe, I'd suggest going to Lindsay's Technical Books http://www.lindsaybks.com/ and looking over Dave Gingery's series of books about building your own machine tools, step by step. There's also a lot there about machine design, if you are into that. And much more, it's a very cool place.
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Without addressing the suitability of using concrete, there is a shrinkage compensating concrete which uses type K cement. This is a proprietary product though that you will need to research if the local ready mix company can supply it.