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Hart's inversors

Hart's inversors is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Hart's inversors rather than just read about it. In short: 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 inversors — main illustration
Hart's inversors — illustration

Key takeaways

  • Hart's inversors belongs to physics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Hart's inversors to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Hart's inversors from memory before moving on to harder problems.

Reference excerpt

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

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

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

References

External links

bham.ac.uk – Hart's A-frame (draggable animation) 6-bar linkage

Illustrations

Hart's inversors: Animation of Hart's antiparallelogram, or first inversor.Link dimensions: .mw-parser-output .legend{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .legend-color{display:inline-block;min-width:1.25em;height:1.25em;line-height:1.25;margin:1px 0;text-align:center;border:1px solid black;background-color:transparent;color:black}.mw-parser-output .legend-text{}  Crank and fixed: a   Rocker: b (anchored at midpoint)   Coupler: c (joint at midpoint) b < c 2 a < 1 2 b + 1 2 c 1 2 c < 1 2 b + 2 a {\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}}}
Animation of Hart's antiparallelogram, or first inversor.Link dimensions: .mw-parser-output .legend{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .legend-color{display:inline-block;min-width:1.25em;height:1.25em;line-height:1.25;margin:1px 0;text-align:center;border:1px solid black;background-color:transparent;color:black}.mw-parser-output .legend-text{}  Crank and fixed: a   Rocker: b (anchored at midpoint)   Coupler: c (joint at midpoint) b < c 2 a < 1 2 b + 1 2 c 1 2 c < 1 2 b + 2 a {\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}}}
Hart's inversors: Animation to derive a Quadruplanar inversor from Hart's first inversor.
Animation to derive a Quadruplanar inversor from Hart's first inversor.
Hart's inversors: Animation of Hart's A-frame, or second inversor. Link dimensions:[Note 1]   Double rocker: 3a + a (distance between anchors: 2b)   Coupler: b   Tip of the A: 2a
Animation of Hart's A-frame, or second inversor. Link dimensions:[Note 1]   Double rocker: 3a + a (distance between anchors: 2b)   Coupler: b   Tip of the A: 2a
Hart's inversors illustration
Hart's inversors illustration

Worked examples

Example 1 — a first encounter with Hart's inversors

Start with the simplest possible case. Write down what Hart's inversors claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Hart's inversors before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Hart's inversors ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Hart's inversors

In research
Hart's inversors appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Hart's inversors in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Hart's inversors is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1874 introductions, Linear motion, Linkages (mechanical), so understanding it makes those chapters shorter.
In everyday life
Look for Hart's inversors outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Hart's inversors in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Hart's inversors means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Hart's inversors out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Hart's inversors in simple terms?

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.

Why does Hart's inversors matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Hart's inversors?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Hart's inversors.

Tags

  • 1874 introductions
  • Linear motion
  • Linkages (mechanical)
  • Straight line mechanisms

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