The centerless superfinishing machines are widely used in the mass production of the critical parts in instrument and machine building. The basing and feeding of the workpieces on these machines are accomplished by roller systems. To date the roller systems have been designed with the use of the simple mathematical relations and generalization of the practical experience [1], although the theory of the shaping of the complex geometric surfaces has recently been quite thoroughly developed [2 and 3]. It is this situation that has led the present authors to propose a method for designing the rollers for machining the conical parts that is based on the modern theory of three-dimensional enveloping surfaces.
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