## Freedom in Machinery, Volumes 1-2Does a machine run well by virtue of its accuracies, or its freedoms? This work presents an exciting, diagrammatic display of the hidden geometry of freedom and constraint. It bolsters the imaginative design of robots, but applies across all fields of machinery. The figures and their captions comprise alone a self-standing story, and this connects effectively with the rigorously argued text. The seamless combination of the two volumes (1984, 1990) renders the internal cross-referencing (forward and backward within the volumes) easier to look up. The appearance of this paperback is a clear testament to the work's ongoing readership. The term screw theory occurs throughout. This relates (after Ball) to the book's philosophy; and one might equally mention kinetostatics (after Federhofer). An all-pervading, counter-intuitive fact accordingly presents itself: while, analogously, angular velocity relates to force, linear velocity relates to couple. A direct consequence of Freedom in Machinery is a more recent book by the same author. Specifically titled General Spatial Involute Gearing and published in Germany (2003), it exemplifies the many ways in which Freedom in Machinery clarifies the enigmatic field of spatial mechanism. That field continuously expands with the current, continuous thrust of ordinary engineering practice. |

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### Contents

VOLUME ONE Preface xii | 1 |

Mechanism and the mobility | 7 |

Overconstraint and the nature | 27 |

Some of the various lines in a moving | 45 |

Enumerative geometry and the powers | 61 |

Irregularity and the freedoms within | 77 |

The possibilities in reality for practical | 105 |

Some elementary aspects of two degrees | 131 |

Line systems and the dual vectors | 153 |

The linear complex of right lines in | 172 |

VOLUME TWO Preface xiii | 1 |

The vector polygons for spatial mechanism | 19 |

### Common terms and phrases

action dual algebra angle angular velocity available screws axes axodes Ball central axis centre chapter chosen collinear common perpendicular cone configuration congruence contact normals contact patch coplanar curve cylindrical cylindroid degrees of freedom direction directrices drawn dual vector ellipse equation example finite fixed frame friction gear set geometrical helices hinges hyperboloid infinite pitch instant instantaneous intersect kinematic chain kinematics linear complex linear velocity linkage loop machinery magnitude mechanism mentioned motion screws moving body n-lines namely nodal line overconstrained parallel pitch quadric planar pencil plane point Q points of contact principal screws prongs radius rate of twisting reciprocal Refer to figure regulus relative motion relevant respect right lines rigid body rotation ruled surface screw axes screw joint screw systems screw theory screws of zero seen shown single infinity space spatial special 3-system spherical surface theorem velocity polygon velocity vectors wheel wrench zero pitch