Physics:Hart's inversors
![](/wiki/images/thumb/a/af/Harts_Inversor_1.gif/250px-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
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
![](/wiki/images/thumb/e/ec/Harts_Inversor_2.gif/250px-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.
See also
- Linkage (mechanical)
- Quadruplanar inversor, a generalization of Hart's first inversor
- Straight line mechanism
Notes
- ↑ Jump up to: 1.0 1.1 The current documented relationship between the links' dimensions is still heavily incomplete. For a generalization, refer to the following GeoGebra Applet: [Open Applet]
References
- ↑ Jump up to: 1.0 1.1 1.2 "True straight-line linkages having a rectlinear translating bar". http://alexandria.tue.nl/repository/freearticles/603890.pdf.
- ↑ Ceccarelli, Marco (23 November 2007). International Symposium on History of Machines and Mechanisms. ISBN 9781402022043. https://books.google.com/books?id=UG0RlFBqwrgC&pg=PA307.
- ↑ "Harts inversor (Has draggable animation)". http://www.cut-the-knot.org/Curriculum/Geometry/HartInversor.shtml.
External links
- bham.ac.uk – Hart's A-frame (draggable animation) 6-bar linkage [|permanent dead link|dead link}}]
![]() | Original source: https://en.wikipedia.org/wiki/Hart's inversors.
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