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Based on Grass' results (1951), Muller (1955, 1959) developed a method of determining a wrapping curve for plane teeth. His mathematical equations could be applied to a few types of spatial drive only. The analytical and geometrical methods developed then are still used for investigating spatial teethed drives. It gradually became apparent to researchers dealing with theoretical problems of gear drives that application of the so-called kinematic method had the effect of simplifying research. Based on this method, Litvin and other outstanding representatives of the Soviet school dealing with theory of gear drives, for example Kolcsin (1949, 1968), Krivenko (1967), Litvin (1962, 1968, 1972), worked out suitable and efficient methods to determine equations and criteria for mating and contact conditions, for characteristics of curvature of contact surfaces and for the phenomena of interference.

As a consequence of the technology now being applied, the precision of the lead or the pitch is increasing with improvement in surface roughness. Owing to the limited precision in tool shape and the method of manufacture, manufacturing faults occur with continual use, the profile becoming deformed (the precision of tooth shape getting worse) and consequendy both the kinematic and loadcarrying capacities of the drive are reduced. The first method worthy of mention was worked out and patented by Niemann in Germany for circular profile worm gear drives (Olivier, 1842).

The author has applied his results achieved in the field of manufacturing geometry both at Miskolc University and at the DIGEP company. Now, at the beginning of the 21st century, it can be expected that CNC-controlled teething machines and 3D-controlled coordinatemeasuring devices will lead to the present tooth geometry and the techniques of tooth generation being changed drastically. 1 DEVELOPMENT OF MANUFACTURE OF CYLINDRICAL WORM GEAR DRIVES HAVING ARCHED PROFILE Previous investigations (Drobni, 1968; Dudas, 1973) unambiguously showed that the technical possibilities and characteristics of worm gear drives point to the cylindrical worm with arched profile (Dudas, 1976) as capable of development and manufacture, for example in wire-drawing machines.

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