Hart's inversors

(Redirected from Hart's A-frame)

Hart's inversors are two planar mechanisms that provide a perfect straight line motion using only rotary joints.[1] They were invented and published by Harry Hart in 1874–5.[1][2]

Animation of Hart's antiparallelogram, or first inversor.
Link dimensions:
  Crank and fixed: a
  Rocker: b (anchored at midpoint)
  Coupler: c (joint at midpoint)

Hart's first inversor

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Hart's first inversor, also known as Hart's W-frame, is based on an antiparallelogram. The addition of fixed points and a driving arm make it a 6-bar linkage. It can be used to convert rotary motion to a perfect straight line by fixing a point on one short link and driving a point on another link in a circular arc.[1][3]

Rectilinear bar and quadruplanar inversors

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Animation to derive a Quadruplanar inversor from Hart's first inversor.

Hart's first inversor is demonstrated as a six-bar linkage with only a single point that travels in a straight line. This can be modified into an eight-bar linkage with a bar that travels in a rectilinear fashion, by taking the ground and input (shown as cyan in the animation), and appending it onto the original output.

A further generalization by James Joseph Sylvester and Alfred Kempe extends this such that the bars can instead be pairs of plates with similar dimensions.

Hart's second inversor

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Animation of Hart's A-frame, or second inversor.
Link dimensions:[Note 1]
  Double rocker: 3a + a (distance between anchors: 2b)
  Coupler: b
  Tip of the A: 2a

Hart's second inversor, also known as Hart's A-frame, is less flexible in its dimensions,[Note 1] but has the useful property that the motion perpendicularly bisects the fixed base points. It is shaped like a capital A – a stacked trapezium and triangle. It is also a 6-bar linkage.

Geometric construction of the A-frame inversor

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Example dimensions

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These are the example dimensions that you see in the animations on the right.

See also

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Notes

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  1. ^ a b The current documented relationship between the links' dimensions is still heavily incomplete. For a generalization, refer to the following GeoGebra Applet: [Open Applet]

References

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  1. ^ a b c "True straight-line linkages having a rectlinear translating bar" (PDF).
  2. ^ Ceccarelli, Marco (23 November 2007). International Symposium on History of Machines and Mechanisms. ISBN 9781402022043.
  3. ^ "Harts inversor (Has draggable animation)".
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