## Kinematic Geometry of Surface MachiningThe principle of Occam’s razor loosely translates to “the simplest solution is often the best”. The author of Kinematic Geometry of Surface Machining utilizes this reductionist philosophy to provide a solution to the highly inefficient process of machining sculptured parts on multi-axis NC machines. He has developed a method to quickly calculate the necessary parameters, greatly reduce trial and error, and achieve efficient machining processes by using less input information, and in turn saving a great deal of time. This unique method will allow youto calculate optimal values for all major parameters of sculptured surface machining on multi-axis This one-of-a-kind resource guides you through this cutting-edge technique beginning with an analytical description of part surfaces, the basics of differential geometry for sculptured surfaces, and the principal elements of the multi-parametric motion on a rigid body in E3 space theory. The book reveals the analytical method for investigating cutting tool geometry and explains a set of described conditions required for proper part surface generation. Next, the author illustrates the selection of criterion for optimization and describes the synthesis of optimal machining operations. He includes examples of the Written by a leading expert in the field who holds over 150 patents, |

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### Contents

Geometry | 3 |

Chapter 2 Kinematics of Surface Generation | 27 |

Chapter 3 Applied Coordinate Systems and Linear Transformations | 63 |

Fundamentals | 87 |

Chapter 4 The Geometry of Contact of Two Smooth Regular Surfaces | 89 |

Chapter 5 Profiling of the FormCutting Tools of Optimal Design | 153 |

Chapter 6 The Geometry of the Active Part of a Cutting Tool | 217 |

Chapter 7 Conditions of Proper Part Surface Generation | 287 |

Application | 405 |

Chapter 9 Selection of the Criterion of Optimization | 407 |

Chapter 10 Synthesis of Optimal Surface Machining Operations | 427 |

Chapter 11 Examples of Implementation of the Differential GeometryKinematics DGKBased Method of Surface Generation | 459 |

Conclusion | 493 |

Notation | 495 |

501 | |

Back cover | 509 |