Three prescribed positions of a rigid body
The whole of the design problem, before any mechanism exists. A body has to occupy these three positions — each one a place and an angle, three numbers — and what carries it between them is not yet decided. A forward analysis starts from link lengths and finds the motion. This starts from the motion, and the lengths are what has to be found. The marked points are the poles: any planar displacement is a rotation about one point, so each pair of poses has one, and the arcs show the turn each represents through the body's own origin. A pole is a property of the displacement and not a mechanism — nothing has been chosen yet. 1 of the 3 poles lies outside this frame and is not drawn; near-parallel displacements push their pole a long way off.
Where it is used
- The problem the other way round The problem backwards
- Three positions, and a circumcentre The problem backwards
- Exactly right, and unbuildable Drawn wrongly
- What the fourth position costs The problem backwards
- Four positions brought together The motion, not the mechanism
- Where a hinge pin can go Machines you have met
- What a synthesis assumes it knows The problem backwards
- Where a pin becomes a slide The problem backwards
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