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In five-axis machining, the forward step (kinematics) error due to nonlinearity of the machine kinematics can significantly affect the quality of the machined surfaces. In a simple approach, kinematics error between two CC points can be reduced to within a prescribed tolerance by inserting enough points. However, this method is often inefficient, especially for high speed milling where a tool path containing a large number of points can slow down the milling process and is, therefore, undesirable. A technique of angle variation presented in Chap. 6 can also be used to minimize the kinematics error without inserting additional points. The error after minimization using this angle adjustment method can still, however, exceed the prescribed tolerance and more points or another minimization techniques are required. [ABSTRACT FROM AUTHOR]

Given the general optimization context given in the preceding chapters, we will now analyze a particular but important problem of sequencing the machine rotations. There exists a variety of research focused on the orientation of the cutting tool. The survey of which is given in Chap. 1. However, the accuracy is also affected by the way the orientations are being achieved. In other words, the kinematics error depends not only on the characteristics of the surface versus the tool orientation but on the previous rotations as well. The "history" of rotations becomes in particular important in the vicinity of the stationary points of the desired surface where the tool could make abrupt changes in the orientation. However, such analysis is not provided by commercial CAD/CAM systems such as Unigraphics, EdgeCam, Vericut, etc. Besides, only a few recent research papers deal with the subject. [ABSTRACT FROM AUTHOR]

Space-filling curves tool path generation technique presented in Chap. 4 has been designed for surfaces represented in such a way that the parametric coordinates are changing within a rectangular region. Once a minimal machining strip is evaluated, constructing a basic grid for the SFC generation in the rectangular region is trivial (see Sect. 4.3.1). However, such a grid is often inefficient since a small step between the tracks could be required only in certain areas. The rectangular grid is also inefficient in the case of a complex boundary of the so-called trimmed surfaces. These surfaces are characterized by the boundaries created by intersections with other surfaces. The complex boundaries also occur in the case of pocket milling when the parametric region includes internal boundaries around one or several pockets. From the viewpoint of computational mathematics the above are classic situations when a numerically generated adaptive curvilinear grid should be introduced. The grid may be easily converted to the zigzag tool path or replace the basic grid required at the first step of the SFC tool path generation method. [ABSTRACT FROM AUTHOR]

An N-dimensional space-filling curve (SFC) is a continuous, surjective1 (onto) function from the unit interval [0, 1] to the N-dimensional unit hypercube [0, 1]N. In particular, a 2-dimensional space-filling curve is a continuous curve that passes through every point of the unit square [0,1]2. [ABSTRACT FROM AUTHOR]

There are a number of issues involved in tool path planning for five-axis NC machining. Four fundamental issues are discussed in this chapter, namely, surface representation, machining strip width estimation, optimal tool orientation and forward step (kinematics) error. [ABSTRACT FROM AUTHOR]

Numerical control or numerically controlled (NC) machines are automatically operated by commands received by their processing units. The NC machines were first developed soon after World War II and made it possible for a precise and efficient production of large quantities of the desired components in a reliable repetitive manner. Early NC machines were often fed with instructions which were punched onto paper tape or punch cards. In the 1960s, NC machines largely gave way to computer numerical control (CNC) machines which refers specifically to a computer controller that reads G-code instructions (see Sect. 2.2) and drives the machine tool. [ABSTRACT FROM AUTHOR]

A variety of on-going research is focused on the development and analysis of methods to decrease the time required to progress from the computer modeling of the design surface to the machining while maintaining or improving the quality of the surface. One of the most important areas is tool path planning for numerical control (NC) machining. The main goal is obtaining the cutter location and orientation data that allow for an efficient surface milling within an allowed machining error. [ABSTRACT FROM AUTHOR]