The ball-end cutter plays an important role in machining free-form surfaces due to its adaptability to a surface. It is widely used in aerospace, automobile, and die/mode industries. Thus, the demand for higher cutting performance and lower cost of the ball-end cutter has been increasingly focused. In this paper, based on normal helix cutting edge geometric model, the cone wheel, which was used to grind the rake and flank face of ball-end cutter, was designed. Then, we use homogenous coordinate transformation to derive for the ball-end cutter and establish the mathematical model for grinding this type cutter in terms of grinding parameters. Finally, the cutting angles of ball-end cutter were discussed.

A simple yet comprehensive method is proposed for the design of a Geneva indexing mechanism with curved slots. In the proposed approach, conjugate surface theory is employed to derive an analytical description of the profile of the curved slots with and without an offset feature. The use of an appropriate offset angle to eliminate the singular points and double-points on the profile of the curved slots is then demonstrated. Finally, a mock-up Geneva mechanism is constructed to demonstrate the feasibility of the proposed approach. The results confirm that the methodology presented in this study enables the integration of the design, analysis and machining tasks for a Geneva indexing mechanism, and therefore makes possible a flexible and automatic production process.

The pressure angle is one of the primary considerations in designing a cam mechanism since an inappropriate angle may cause excessive sliding loads on the follower. This paper presents a simple yet straightforward method for the design and analysis of a cam mechanism with a translating follower having double rollers. In the proposed approach, conjugate surface theory is employed to derive a kinematic model of the cam mechanism. Analytical expressions for the pressure angle is then derived. The validity of the analytical expressions is confirmed by machining a designed cam using a 3-axis CNC machine tool