A spherical four-bar: 90°, 40°, 100°, 80°
Four revolute axes, all through one point, so the linkage lives on a sphere. Its link "lengths" are the angles between consecutive axes — 90°, 40°, 100°, 80° — and the arcs drawn between the axis directions measure 40.00°, 100.00°, 80.00°, 90.00°. The whole planar four-bar theory carries over with sines where lengths were, including Grashof's condition: sorted, the arcs give s + l = 140° against p + q = 170°, so the shortest arc does turn all the way round — and swept, the input reaches 36 of 36 positions over a driveable range of 360°. This is the mechanism a universal joint is a special case of, with two of the four arcs at 90°.
Screws and reciprocal systemsdraggable: input axiswide
Where it is used
- Every vertex is a spherical linkage Many of one thing
- The wrist is three joints and one point One path to the tool
- When the link lengths are angles Out of the plane
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