Classification of Screw Systems

1. Classification of Screw Systems Kenneth J. Waldron

2. Outline • Classification of Screw Systems [KJW, 20 mins] • Notation • Exhaustive list • Special screw systems

3. Forms of Screw System • In addition to the seven general forms, there are twenty-two special forms • Some forms are much more important in practice than others • Systems which are geometrically invariant under motion about any of their members are particularly important • Systems with large numbers of zero or infinite pitch members are particularly important

4. First Order Screw Systems

5. Second Order Screw Systems

6. Third Order Screw Systems

7. Third Order Screw Systems (continued)

8. Special Third Order System: Type 2 • System consists of zero pitch screws on all lines through a point • There are no members with other pitches • Screw system of spherical joint • Self-reciprocal

9. Fourth Order Screw Systems

10. Special Second Order System: Type 4 • System consists of plane of parallel, finite pitch screws plus one infinite pitch screw • Pitches of finite pitch members vary linearly with position in the array orthogonal to their direction

11. Fifth Order Screw Systems