Where the coupler is pivoting, at 70°
At any instant the coupler is turning about one point — not a pin, and usually not on the mechanism at all. Kennedy's theorem finds it: the crank and coupler share the pin at A, the coupler and rocker share B, so the coupler's centre relative to the frame must lie on both O₂A extended and O₄B extended, and it is where they cross. The dashed lines are that construction. The cross is a completely different route to the same point — the place where the coupler's solved velocity field is zero, computed from the Jacobian and knowing nothing about Kennedy. Across 119 positions the two agree to 2.7e-15. At this instant the centre lies outside the frame — the two construction lines are nearly parallel, the coupler is close to translating, and the pivot has run off rather than gone missing.
Derived from the motiondraggable: crank anglewide
Where it is used
- The mechanism drops out The motion, not the mechanism
- Rolling at one point only The shape is the unknown
- The other pole The motion, not the mechanism
- Where the coupler is turning The paths points trace
- Every motion is a screw Out of the plane
- A roll centre is not a point Machines you have met
- Six things a centre is not Drawn wrongly
- The road a wheel carries with it Wheels, and where they may not go
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