Does 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.

### Contents

Volume I: Preface; General introduction; 1. Mechanism and the mobility of mechanism; 2. Overconstraint and the nature of mechanical motion; 3. Some of the various lines in a moving body; 4. Enumerative geometry and the powers of infinity; 5. Rigidity and the instantaneous screw axis; 6. Irregularity and the freedoms within a joint; 7. The possibilities in reality for practical joints; 8. Some elementary aspects of two degrees of freedom; 9. The linear complex of right lines in a moving body; 10. Line systems and the dual vectors in mechanics; Volume II: Preface; 11. Geometrical properties of the linear line systems; 12. The vector polygons for spatial mechanism; 13. On the two theorems of three axes; 14. Some reciprocities across the middle number three; 15. The generality and the geometry of the cylindroid; 16. The discovery in a mechanism of a cylindroid; 17. Action, notion, clearances and backlash; 18. Singular events in the cycles of motion; 19. Fundamental relations and some algebraic methods; 20. The special geometry of some overconstrained loops; 21. The helitangent lines in a moving body; 22. The cylindroid in gear technology; 23. The general and the special screw systems; Bibliography; Index of proper names; Subject index.