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 Universalwerkstättengerät (multi-purpose) UWG1 and UWG2 machines. 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 one photograph - he does not have any maker's publicity material. If, therefore, any reader can help in any way at all to fill in these gaps, he would be delighted hear from them.