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]
Animation of Hart's antiparallelogram, or first inversor. Link dimensions:
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]
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 inversoredit
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 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 inversoredit
Example dimensionsedit
These are the example dimensions that you see in the animations on the right.
^ ab The current documented relationship between the links' dimensions is still heavily incomplete. For a generalization, refer to the following GeoGebra Applet: [Open Applet]
Referencesedit
^ abc"True straight-line linkages having a rectlinear translating bar" (PDF).
^Ceccarelli, Marco (23 November 2007). International Symposium on History of Machines and Mechanisms. ISBN9781402022043.
hart, inversors, planar, mechanisms, that, provide, perfect, straight, line, motion, using, only, rotary, joints, they, were, invented, published, harry, hart, 1874, animation, hart, antiparallelogram, first, inversor, link, dimensions, crank, fixed, rocker, a. 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 Animation of Hart s antiparallelogram or first inversor Link dimensions Crank and fixed a Rocker b anchored at midpoint Coupler c joint at midpoint b lt c 2 a lt 1 2 b 1 2 c 1 2 c lt 1 2 b 2 a displaystyle begin aligned b amp lt c 4pt 2a amp lt tfrac 1 2 b tfrac 1 2 c 2pt tfrac 1 2 c amp lt tfrac 1 2 b 2a end aligned Contents 1 Hart s first inversor 1 1 Rectilinear bar and quadruplanar inversors 2 Hart s second inversor 2 1 Geometric construction of the A frame inversor 3 Example dimensions 4 See also 5 Notes 6 References 7 External linksHart s first inversor editHart 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 edit Main article Quadruplanar inversor nbsp Animation to derive a Quadruplanar inversor from Hart s first 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 edit nbsp 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 2aHart 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 editExample dimensions editThese are the example dimensions that you see in the animations on the right nbsp Hart s first inversor AB Bg 2CE FD 6CA AE 3CD EF 12Cp pD Eg gF 6 nbsp Hart s second inversor AB AC BD 4CE ED 2Af Bg 3fC gD 1fg 2See also editLinkage mechanical Quadruplanar inversor a generalization of Hart s first inversor Straight line mechanismNotes edit a b The current documented relationship between the links dimensions is still heavily incomplete For a generalization refer to the following GeoGebra Applet Open Applet References edit a b c True straight line linkages having a rectlinear translating bar PDF Ceccarelli Marco 23 November 2007 International Symposium on History of Machines and Mechanisms ISBN 9781402022043 Harts inversor Has draggable animation External links edit nbsp Wikimedia Commons has media related to Hart s inversor bham ac uk Hart s A frame draggable animation 6 bar linkage dead link nbsp This engineering related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Hart 27s inversors amp oldid 1180000564, wikipedia, wiki, book, books, library,
