{"product_id":"harts-a-frame-educational-model","title":"Hart's A-frame - Educational Model","description":"\u003ch2\u003eMy Educational Mechanical Examples Series\u003c\/h2\u003e\u003cp\u003eThis model is one of my educational mechanical mechanism examples on 80mm x 80mm base plates.\u003cbr\u003eYou can find all models of the series in this collection =\u0026gt; \u003ca target=\"_blank\" rel=\"noopener noreferrer ugc\" href=\"https:\/\/makerworld.com\/collections\/15048577-my-educational-mechanism-models\"\u003e[Mechanical Mechanism Examples]\u003c\/a\u003e\u003c\/p\u003e\u003cfigure class=\"image image_resized\" style=\"width: 61.78%\"\u003e\u003ca href=\"https:\/\/makerworld.com\/collections\/15048577-my-educational-mechanism-models\" target=\"_blank\" rel=\"noopener noreferrer ugc\"\u003e\u003cimg src=\"https:\/\/makerworld.bblmw.com\/makerworld\/model\/DSM00000002955283\/design\/2025-11-13_a0fbbb25e21458.png\"\u003e\u003c\/a\u003e\u003c\/figure\u003e\u003ch2\u003e \u003c\/h2\u003e\u003ch2\u003eThe present model\u003c\/h2\u003e\u003cp\u003eThis is an educational model of a Hart's A-frame, which is one of the \u003ci\u003eexact\u003c\/i\u003e straight-line linkages.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cfigure class=\"image\"\u003e\u003cimg src=\"https:\/\/makerworld.bblmw.com\/makerworld\/model\/DSM00000002955283\/design\/0e7345ccc68ca6a7.jpg\"\u003e\u003c\/figure\u003e\u003cfigure class=\"image\"\u003e\u003cimg src=\"https:\/\/makerworld.bblmw.com\/makerworld\/model\/DSM00000002955283\/design\/a20e6d89571580a2.gif\"\u003e\u003c\/figure\u003e\u003cfigure class=\"image\"\u003e\u003cimg src=\"https:\/\/makerworld.bblmw.com\/makerworld\/model\/DSM00000002955283\/design\/ccef97bf8ab46620.gif\"\u003e\u003c\/figure\u003e\u003cfigure class=\"media\"\u003e\u003coembed url=\"https:\/\/youtu.be\/QY2urTZ4ZTc\"\u003e\u003c\/oembed\u003e\u003c\/figure\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003ch2\u003eBrief Description\u003c\/h2\u003e\u003cp\u003eThe approximate straight-line mechanisms introduced so far — \u003ca target=\"_blank\" rel=\"noopener noreferrer ugc\" href=\"https:\/\/makerworld.com\/models\/2656748-approx-straight-line-linkages-educational-model\"\u003eWatt's linkage, the Chebyshev linkage, and the Grasshopper linkage\u003c\/a\u003e — are all based on four-bar linkages. The coupler point need not lie at a joint between two links; it may sit at the midpoint of a link or on its extension. Even so, these simple linkages confine the coupler point to a path that is only approximately straight — and they do so without any linear guide or prismatic pair. A four-bar linkage, however, cannot trace an exactly straight line.\u003cbr\u003e \u003c\/p\u003e\u003cp\u003eHart's A-frame achieves exact straight-line motion by raising the number of links to six. Five of them move; the sixth is the base plate itself, which serves as the hidden ground link. Laid out as the capital letter A, each slanted side is built from a long link and a short link half its length, joined end to end, and the two short links meet at the apex. The lower end of each long link is pinned to the base plate, and these two fixed pivots are spaced apart by twice the length of the crossbar. The crossbar — the horizontal stroke of the A — joins the two long links at the points that divide them in a 3:1 ratio, with the longer portion toward the fixed pivot. Only these two lower pivots are anchored; every other joint is free to move. Under this arrangement the apex of the A, which is the coupler point, is constrained to travel along a perfectly straight line: the vertical line engraved on the base plate, which is the perpendicular bisector of the two fixed pivots. Move the coupler point by hand and you can feel it being held to this line.\u003cbr\u003e \u003c\/p\u003e\u003cp\u003eAs you play with the model, though, you will find that this is not the only path open to the coupler point: the motion branches at the midpoint between the two pivots. There, the coupler point can leave the straight line for a second, skewed path that traces a distorted triangle, also engraved on the plate. Pushing on the coupler point alone will not carry it past the corners of that triangle; there you must also control how the links fold in order to pass through. To keep the motion well-behaved, confine the coupler point to either the upper or the lower half of the straight line, or guide it through the midpoint so that it does not slip onto the other branch.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003ch3\u003eReference\u003c\/h3\u003e\u003cul\u003e\u003cli\u003e\n\u003ca target=\"_blank\" rel=\"noopener noreferrer ugc\" href=\"https:\/\/en.wikipedia.org\/wiki\/Hart%27s_inversors\"\u003ehttps:\/\/en.wikipedia.org\/wiki\/Hart%27s_inversors\u003c\/a\u003e\u003cbr\u003e \u003c\/li\u003e\u003c\/ul\u003e\u003ch3\u003eRelated Models\u003c\/h3\u003e\u003cp\u003e\u003ca target=\"_blank\" rel=\"noopener noreferrer ugc\" href=\"https:\/\/makerworld.com\/models\/2078221-theo-jansen-mechanism-educational-model\"\u003e\u003cimg src=\"https:\/\/makerworld.bblmw.com\/makerworld\/model\/DSM00000002955283\/design\/471b6145345178f4.png\"\u003e \u003c\/a\u003e\u003ca target=\"_blank\" rel=\"noopener noreferrer ugc\" href=\"https:\/\/makerworld.com\/models\/2656748-approx-straight-line-linkages-educational-model\"\u003e\u003cimg src=\"https:\/\/makerworld.bblmw.com\/makerworld\/model\/DSM00000002955283\/design\/987a5737869ce86c.png\"\u003e\u003c\/a\u003e\u003ca target=\"_blank\" rel=\"noopener noreferrer ugc\" href=\"https:\/\/makerworld.com\/models\/2703379-peaucellier-lipkin-linkage-educational-model\"\u003e\u003cimg src=\"https:\/\/makerworld.bblmw.com\/makerworld\/model\/DSM00000002955283\/design\/d5843376abfbd16f.png\"\u003e\u003c\/a\u003e\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003ch2\u003eCase\u003c\/h2\u003e\u003cp\u003eThis model is compatible with the case included \u003ca target=\"_blank\" rel=\"noopener noreferrer ugc\" href=\"https:\/\/makerworld.com\/models\/1983088-educational-gear-examples-1\"\u003ein my first set\u003c\/a\u003e.\u003c\/p\u003e\u003cfigure class=\"image\"\u003e\u003cimg src=\"https:\/\/makerworld.bblmw.com\/makerworld\/model\/DSM00000002955283\/design\/2a97599f-d654-49e8-bff9-9a3803b32815.webp\"\u003e\u003c\/figure\u003e\u003ch2\u003ePrinting\u003c\/h2\u003e\u003cul\u003e\n\u003cli\u003eUse the models named \u003ci\u003e\u003cstrong\u003e???-printable.stl \u003c\/strong\u003efor printing\u003cstrong\u003e.\u003c\/strong\u003e\u003c\/i\u003e\u003cbr\u003eThe models named \u003ci\u003e\u003cstrong\u003e???-assembled.stl\u003c\/strong\u003e\u003c\/i\u003e are provided just to show how they should be assembled.\u003cbr\u003e \u003c\/li\u003e\n\u003cli\u003eUse \u003cstrong\u003ewell-dried PETG\u003c\/strong\u003e to have better dimensional accuracy.\u003c\/li\u003e\n\u003cli\u003eUse \u003cstrong\u003e0.1 mm or 0.08 mm layer height\u003c\/strong\u003e to have smoother surfaces.\u003c\/li\u003e\n\u003cli\u003eUse slow printing speed for overhangs.\u003c\/li\u003e\n\u003cli\u003eSelect \u003cstrong\u003e“Random” seam position\u003c\/strong\u003e to have smoother rotation.\u003cbr\u003eRandomly distributed seam should be easily worn out after some wearing.Printing\u003c\/li\u003e\n\u003c\/ul\u003e\u003ch2\u003eSanding and Filing\u003c\/h2\u003e\u003cp\u003eNote that, in this model, the rotation of the bases for bearings is intentionally made not too smooth.\u003c\/p\u003e\u003cp\u003eSometimes, the gears suffer from the stringing effect and\/or elephant foot effect, resulting in a too tight fit to the shafts (they are designed with a 0.15 mm radial clearance). \u003c\/p\u003e\u003cp\u003eIf you see rough surface on the shafts due to stringing, sand off the roughness with a small piece of sand paper.\u003c\/p\u003e\u003cp\u003e\u003cimg class=\"image_resized\" style=\"width: 32.08%\" src=\"https:\/\/makerworld.bblmw.com\/makerworld\/model\/DSM00000002955283\/design\/c42892e8-41c9-4bab-81fa-42275f5fad96.webp\"\u003e\u003cimg class=\"image_resized\" style=\"width: 31.94%\" src=\"https:\/\/makerworld.bblmw.com\/makerworld\/model\/DSM00000002955283\/design\/9d04dd53-7dc5-46b4-a9da-18068437968a.webp\"\u003e\u003cimg class=\"image_resized\" style=\"width: 31.92%\" src=\"https:\/\/makerworld.bblmw.com\/makerworld\/model\/DSM00000002955283\/design\/c8d8ef1c-9cc5-4f2b-a7c5-8d4b40f1ee3d.webp\"\u003e\u003c\/p\u003e\u003cp\u003eIf you feel the gears do not rotate smoothly due to an elephant effect, widen the hole slightly by using a thin round bar file.\u003c\/p\u003e\u003cfigure class=\"image image_resized\" style=\"width: 75%\"\u003e\u003cimg src=\"https:\/\/makerworld.bblmw.com\/makerworld\/model\/DSM00000002955283\/design\/c721d770-6619-492e-8792-c8696130b106.webp\"\u003e\u003c\/figure\u003e\u003cp\u003eWithout those issues, the parts should rotate very smoothly with minimal friction.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003ch2\u003eAssembly\u003c\/h2\u003e\u003cp\u003eSecure the links onto the shafts with the retaining rings.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cfigure class=\"image\"\u003e\u003cimg src=\"https:\/\/makerworld.bblmw.com\/makerworld\/model\/DSM00000002955283\/design\/c53ecacb74aafbb5.png\"\u003e\u003c\/figure\u003e\u003ch3\u003eOther examples\u003c\/h3\u003e\u003cp\u003eYou may also be interested in the models in my educational mechanical mechanism examples.\u003c\/p\u003e\u003cp\u003eFind them in this collection:\u003cbr\u003e\u003ca target=\"_blank\" rel=\"noopener noreferrer ugc\" href=\"https:\/\/makerworld.com\/collections\/15048577-my-educational-mechanism-models\"\u003ehttps:\/\/makerworld.com\/collections\/15048577-my-educational-mechanism-models\u003c\/a\u003e\u003c\/p\u003e\u003cfigure class=\"image image_resized\" style=\"width: 61.78%\"\u003e\u003ca href=\"https:\/\/makerworld.com\/collections\/15048577-my-educational-mechanism-models\" target=\"_blank\" rel=\"noopener noreferrer ugc\"\u003e\u003cimg src=\"https:\/\/makerworld.bblmw.com\/makerworld\/model\/DSM00000002955283\/design\/2025-11-13_a0fbbb25e21458.png\" width=\"964\"\u003e\u003c\/a\u003e\u003c\/figure\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eHappy printing!\u003c\/p\u003e\u003ch3\u003eAcknowledgement\u003c\/h3\u003e\u003cp\u003eI got into gears thanks to \u003cstrong\u003eK.$uzuki\u003c\/strong\u003e's amazing \u003ca target=\"_blank\" rel=\"noopener noreferrer ugc\" href=\"https:\/\/karakurist.jp\/\"\u003earticles\u003c\/a\u003e and \u003ca target=\"_blank\" rel=\"noopener noreferrer ugc\" href=\"https:\/\/www.youtube.com\/@karakurist\"\u003eYouTube videos\u003c\/a\u003e. Many of the mechanisms shown in this series came from the introductions on \u003ca target=\"_blank\" rel=\"noopener noreferrer ugc\" href=\"https:\/\/karakurist.jp\/\"\u003ehis website\u003c\/a\u003e. He also makes \u003ca target=\"_blank\" rel=\"noopener noreferrer ugc\" href=\"https:\/\/oishiiosushi.thebase.in\/\"\u003eexcellent gear models\u003c\/a\u003e himself. This series wouldn’t have existed without his inspiration.\u003c\/p\u003e\u003cp\u003eI learned a lot about technical detail of designing gear tooth profiles from \u003ca target=\"_blank\" rel=\"noopener noreferrer ugc\" href=\"https:\/\/involutegearsoft.hatenablog.com\/\"\u003eHaguruma-No-Hanashi website\u003c\/a\u003e. I’m truly grateful for that.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003ch2\u003eLicense\u003c\/h2\u003e\u003cul\u003e\n\u003cli\u003eThe 3D model(s) are licensed under \u003ca target=\"_blank\" rel=\"noopener noreferrer ugc\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\"\u003eCreative Commons Attribution 4.0 International\u003c\/a\u003e.\u003c\/li\u003e\n\u003cli\u003eHowever, the text and images on this page are copyright reserved.\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eDesign by osamutake on MakerWorld (license: BY).\u003c\/p\u003e","brand":"Mymadmanlab","offers":[{"title":"Default Title","offer_id":67398686015792,"sku":null,"price":5.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0987\/0809\/5280\/files\/0_be84b02d-f9b1-449f-84a2-76e0854a4b88.png?v=1784888023","url":"https:\/\/mymadmanlab.com\/products\/harts-a-frame-educational-model","provider":"Mymadmanlab.com","version":"1.0","type":"link"}