Hart's inversors

[[File:Harts Inversor 1.gif|thumb|Animation of Hart's antiparallelogram, or first inversor. Link dimensions:

$$\begin{align} b &< c \\[4pt] 2a &< \tfrac{1}{2}b + \tfrac{1}{2}c \\[2pt] \tfrac{1}{2}c &< \tfrac{1}{2}b + 2a \end{align}$$ ]]

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


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
[[File:Harts Inversor 2.gif|thumb|Animation of Hart's A-frame, or 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.

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