Hart's inversors

"GENERAL" DIMENSIONS IN CAPTIONS NEED UPDATING.

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

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.

Rectilinear bar and quadruplanar inversors

Main article: Quadruplanar 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

Link dimensions: ]] Hart's second inversor, also known as Hart's A-frame, is less flexible in its dimensions, 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

A visual demo can be found here: https://www.geogebra.org/m/tdyw7ggf

Rough synopsis:

• Create two similar quadrilaterals, one which is mirrored vertically.
• Take the two bars on the right side and copy them to the left so it creates the shape of the A-frame.
• Scale down original quadrilateral as to match the width of the A-frame's base.
• Remove scaffolding. --

Example dimensions

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

Mecanismo de Hart (2).png| Mecanismo de Hart.png|

Notes

References

References

1. "True straight-line linkages having a rectlinear translating bar".
2. (23 November 2007). "International Symposium on History of Machines and Mechanisms".
3. The current documented relationship between the links' dimensions is still heavily incomplete. For a generalization, refer to the following [[GeoGebra]] Applet: [https://www.geogebra.org/classic/cNnq9YuN [Open Applet]]