Manufactured by Astobe A.Stoeckle, Machines-Outils of Basle, Switzerland the Astoba name appears to have been contrived from that of the maker and the town - "ASTO + BA".  Research indicates that the original design was German, by Hans Luce, working in the 1930s at the Rheinmetall-Borsig company in Sömmerda. At the end of the Second World War, Luce went to the western part of Germany and later designed for Hommel the very similar UWG1 and UWG2 Universalwerkstättengerät (multi-purpose work machine or, in the vernacular a Eierlegende Wollmilchsäue). The Swiss-built Astoba appears identical to the original Luce design and one can only assume that Meyer & Burger had the facilities to copy it and, for some reason, were able to market it as a production of the Astobe A. Stoeckle Company.
Although the writer has a copy of the operator's manual for this fascinating machine - and a few photographs - he does not have any maker's publicity material. If, therefore, any reader can provide a set of high-resolution pictures of their machine, and copies of any catalogues, he would be delighted hear from you.