Hart's inversors
Hart's inversors are two planar mechanisms that provide a perfect straight line motion using only rotary joints.
The addition of fixed points and a driving arm make it a 6-bar linkage.
[1][3] 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.
Link dimensions:
Crank and fixed:
a
Rocker:
b
(anchored at midpoint)
Coupler:
c
(joint at midpoint)
![{\displaystyle {\begin{aligned}b&<c\\[4pt]2a&<{\tfrac {1}{2}}b+{\tfrac {1}{2}}c\\[2pt]{\tfrac {1}{2}}c&<{\tfrac {1}{2}}b+2a\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/13d497f57a6f1006bd13a5acb4a7773e86490c7c)
Link dimensions: [ Note 1 ]
Double rocker:
3
a
+
a
(distance between anchors:
2
b
)
Coupler:
b
Tip of the A:
2
a