"One way to deal with the matters... is to work with a set of numerical values. I can do this with the help of Ball's Cartesian equation for the hyperboloids of reguli of the 3-system (1900). This equation is quoted and proved by Hunt (1978)... I shall choose the three principle screws of a 3-system of motion... I have, (a) accorded with convention, (b) ensured that the pitch quadric will be real... Ball's equation... clearly represents a series of concentric quadric surfaces... This circumstance of there being none of the concentric hyperboloids coaxial with one of the principal axes is a characteristic of the 3-system. ...within a certain, central zone of the system, the intersections among the hyperboloids are complicated and not easy to understand. Outside that zone, however... the hyperboloids appear in relation to one another... Each successive hyperboloid is wholly 'outside' its predecessor (or wholly 'inside' as the case may be), and no intersections are apparent. ...outside a certain, central zone, only one real screw can be found to pass through a generall chosen point..."
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Sources
Jack Phillips, Freedom in Machinery (1984, 1990) Appendix 6C Notes on the quasi-general 3-system
https://en.wikiquote.org/wiki/Hyperboloid
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Hyperboloid
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