Flank cutting can be effectively employed to machine ruled surfaces instead of traditional point cutting. In consideration of reducing discrepancies between designed and machined twisted ruled surfaces, an analytical model is established to account for undercutting incurred in flank milling by the use of cylindrical cutters. Based on the model, the twist angle, the ruling length, and the size of the used cutter relating to the magnitude of undercutting are observed. By flank milling twisted ruled blade surfaces of an impeller, an application example is given to show the developed 5-axis flank milling technique based on a type of a 5-axis machine tool.

The application of spline functions to the general synthesis of cam motion programs is presented. The approach provides a single, systematic, easily automated method of accommodating discrete constraints on follower displacements, velocities, and accelerations, even when the set of constraints becomes large. Yet, it is as easily applied in simple cases as are the more traditional methods of syntheses. It also allows the designer to refine the motion program by locally influencing characteristics of the motion while still satisfying the discrete constraints. A series of examples is presented to illustrate application of the method and to compare it to the more traditional techniques.

A systematic development for the theory of envelopes with proof is presented. It offers a simple and general procedure to determine the planar and spatial cam profiles. Based on the theory, a planar or spatial cam profile is defined as the envelope of its follower surfaces represented in a parametric form in different relative positions of the cam and the follower. The procedure is illustrated by determining the 2D and 3D cam profiles with analytical formulations. To demonstrate its accuracy and effectiveness, the results are then compared to those obtained by an earlier approach using the screw theory.

A procedure employing rational B-spline functions for the synthesis of cam-follower motion programs is presented. It differs from earlier techniques that employ spline functions by using rational B-spline basis functions to interpolate motion constraints. These rational B-splines permit greater flexibility in refining motion programs. Examples are provided to illustrate application of the approach.

A simple and useful procedure that can be used to determine profile surfaces of planar and spatial cams with cylindrical roller-followers is presented. Based on the rigid-body transformation between the cam and the roller-follower, the pitch (curve) surface which is the path of the point of the roller centre can be easily generated. Then the analytical profile surface of the cam can be represented by the offset surface of the pitch surface with a distance equal to the radius of the roller. T o illustrate the ease and effectiveness of the approach, analytical expressions of profile surfaces of a disc cam, two cylindrical cams and two globoidal cams are typically given. Furthermore, in order to show the validity of this method, the results are then compared to those derived by an earlier procedure based on the screw theory.