Hart's inversors

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.

Dimensions:
Cyan Links = a
Green Links = 0.5b + 0.5b and b
Yellow Links = 0.5c + 0.5c

c > b
0.5b + 0.5c > 2a
0.5c < 0.5b + 2a
Animation of Hart's A-frame, or second inversor.

Dimensions:
Cyan Links = 3a + a
Green Links = b
Yellow Links = 2a
Distance between anchors = 2b[Note 1]

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]

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.

Example dimensions

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

    • AB = Bg = 2
    • CE = FD = 6
    • CA = AE = 3
    • CD = EF = 12
    • Cp = pD = Eg = gF = 6
    • AB = AC = BD = 4
    • CE = ED = 2
    • Af = Bg = 3
    • fC = gD = 1
    • fg = 2

See also

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

References
  1. "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)".
  • bham.ac.uk – Hart's A-frame (draggable animation) 6-bar linkage


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