Hello Sir ,
We are a group of developer including mechanical engineer , electronics engineer , product designer . We are working on this field for last 4 years . I am very interested on your project . infact we already developed this kind of functionality not exactly for this kind of project but with slimier functionality.
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Please check link first (design of our current project)
We already developing a restaurant delivery system .The project is completely different from your project but horizontal movement, vertical movement also included with the project . For horizontal movement we are using wheel over rail (I don't know is that ok for your system or not , we can use convair belt too ) and for vertical movement we are using four gear wheel like pully (we can use same for you) . We are using arduino with wifi shield(IOT) as micro controller.
Our primary prototype ready now we are working on control system . We are also going to manufacture that cart here at india , then we will ship to client's end (Austria) . We will also provide a technician for 6 month training , maintenance & installation at client's end . We can work with you similarly.
We should discuss more over your plan , i got your primary idea slimier like this
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we can chat over skype too . My id projjwalsen.
Regards
Projjwal