Hart's inversors
![](http://upload.wikimedia.org/wikipedia/commons/thumb/a/af/Harts_Inversor_1.gif/220px-Harts_Inversor_1.gif)
Link dimensions:
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]
Hart's first inversor
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
![](http://upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Quadruplanar_Inversor_Derivation_Alt.gif/220px-Quadruplanar_Inversor_Derivation_Alt.gif)
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
![](http://upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Harts_Inversor_2.gif/220px-Harts_Inversor_2.gif)
Link dimensions:[Note 1]
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
Example dimensions
These are the example dimensions that you see in the animations on the right.
-
- Hart's first inversor:
- AB = Bg = 2
- CE = FD = 6
- CA = AE = 3
- CD = EF = 12
- Cp = pD = Eg = gF = 6
-
- Hart's second inversor:
- AB = AC = BD = 4
- CE = ED = 2
- Af = Bg = 3
- fC = gD = 1
- fg = 2
See also
- Linkage (mechanical)
- Quadruplanar inversor, a generalization of Hart's first inversor
- Straight line mechanism
Notes
- ^ 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
External links
![](http://upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png)
- bham.ac.uk – Hart's A-frame (draggable animation) 6-bar linkage [dead link]