This paper presents models for defining the minimum circumscribed cylinder (MCC) of the cutter shank, the minimum circumscribed circular-arc-type revolving surface (MCCRS) and the minimum circumscribed corner arc revolving surface (MC-CARS) with a spiral groove. A systematic modeling procedure is presented for the assessment of the contour quality of the circular-arc end milling (CAEM) cutters with a cylindrical shank. The axis of the MCC of the cylindrical shank of a revolving cutter with a circular-arc generator curve and a corner radius is taken as the datum line. The profile tolerances and errors are estimated. The presented models are all illustrated and verified by example. This approach can be generalized to a cutter with more than two circular arcs in its shape profile. The paper provides a valuable reference for the evaluation of the actual contour quality of this type of revolving cutter.

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The toroid-shaped helical cutter with an involute generator is a precision tool used in the machining of involute helical gears. Taking the axis of the minimum circumscribed cylinder of the measured points on the cylinder shank as the datum axis, this paper provides models of the minimum circumscribed involute revolving surface and the minimum circumscribed toroid-shaped revolving surface. This paper also presents models for evaluating the contour quality of a toroid-shaped cutter with an involute generator. The validity and accuracy of these models are confirmed by worked examples.

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Outer cycloid gears are used widely in many instruments and machines. The outer cycloid slotting cutter is an important cutting tool used in the manufacturing of this type of gear. In the process of design, the ideal outer cycloid cutter is one where a cylindrical surface takes the tooth profile of the outer cycloid as the directrix. However, during the manufacturing process, it is used as a cutter and therefore a cutting edge is required. As a result, it will be seen that the processes of design and usage of the outer cycloid cutter are not the same. The range of the qualified length of tooth is deduced in this paper by using the mid-point and mid-line method. This paper also presents the associated outer cycloid slotting cutter design and manufacturing models so that the modelling accuracy and the necessary relief angles of the top cutting edge and side cutting edge can be ensured. This paper is intended as a reference to be used in the manufacture and application of this type of slotting cutter.