4-bar mechanism: Difference between revisions

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The world of articulated quadrilaterals is a vast one, and there's probably a solution that's closer to the ideal motion. The movement of connecting rods offers [https://mathcurve.com/courbes2d/troisbarres/troisbarre.shtml a wide variety of trajectories].</translate>  
The world of articulated quadrilaterals is a vast one, and there's probably a solution that's closer to the ideal motion. The movement of connecting rods offers [https://mathcurve.com/courbes2d/troisbarres/troisbarre.shtml a wide variety of trajectories].</translate>  


<translate>
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(Updated August 2026)
I discover the AI with Codex (gpt-5.6-sol) that served me at [https://github.com/99epep/dada-engine-4bar-optimizer start a python solver] in order to find an optimal geometry, the definition of the notation is still very arbitrary, but I have obtained interesting results.<br>


(Mise à jour août 2026)
<!--T:11-->
Je découvre l’IA avec Codex (gpt-5.6-sol) qui m’a servi à [https://github.com/99epep/dada-engine-4bar-optimizer commencer un solveur en python] dans le but de trouver une géométrie optimale, la définition de la notation est encore très arbitraire, mais j’ai obtenu des résultats intéressants.<br \>
For the dimensions of the mechanisms below, the points related to the frame of the crank and of the rocker are 100 distant.
 
Pour les dimensions des mécanismes ci-dessous, les points liés au bâti de la manivelle et du culbuteur sont distants de 100.
[[File:Animation E10.gif|frame|right]]
[[File:Animation E10.gif|frame|right]]
En cherchant sur le déplacement angulaire du culbuteur j’ai obtenu un résultat assez proche de celui présenté ci-dessus. La manivelle mesure 73, le coupleur 100, et le culbuteur 110,37. Le point de fixation du piston forme un angle de 27,9° avec le culbuteur.<br clear="all">
By looking on the angular displacement of the rocker I obtained a result quite close to that presented above. The crank measures 73, the coupler 100, and the rocker 110.37. The fixing point of the piston forms an angle of 27.9° with the rocker.
<br clear="all">


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[[File:Animation F65.gif|frame|right]]
[[File:Animation F65.gif|frame|right]]


Attacher le piston au coupleur semble permettre de plus grands rapports de compression. La recherche a été effectuée uniquement selon une projection sur l’axe de symétrie du mécanisme, il y a peut-être des mouvements plus proche de l’idéal à découvrir selon d’autres axes.<br \>
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Attaching the piston to the coupler seems to allow greater compression ratios. The research was carried out only according to a projection on the axis of symmetry of the mechanism, there are perhaps movements closer to the ideal to be discovered along other axes.<br \>


Sur le premier schéma la manivelle mesure 44,96, le coupleur 117,91, et le culbuteur 141,73. Dans le repaire local du coupleur avec la liaison à la manivelle comme centre, les coordonnées du point d’attache du piston sont (94,4 ; -88,65).<br clear="all">
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In the first diagram, the crank measures 44.96, the coupler 117.91, and the rocker 141.73. In the local reference frame of the coupler with the link to the crank as the center, the coordinates of the attachment point of the piston are (94.4 ; -88.65).<br clear="all">


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[[File:Animation F9.gif|frame|right]]
[[File:Animation F9.gif|frame|right]]
Sur ce deuxième schéma la manivelle mesure 65,64, le coupleur 105,99, et le culbuteur 115,26. Les coordonnées du point d’attache du piston sont (106,03 ; -35,19).
In this second diagram, the crank measures 65.64, the coupler 105.99, and the rocker 115.26. The coordinates of the attachment point of the piston are (106.03 ; -35.19).
<br clear="all">
<br clear="all">


Using a more complex could help approaching an ideal curve, and could introduce a way of varying piston stroke during adiabatic phases.
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Using a more complex could help approaching an ideal curve, and could introduce a way of varying piston stroke during adiabatic phases.</translate>

Latest revision as of 19:34, 24 August 2026

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The ideal movement can be approached by actuating the pistons using four-bar mechanisms, such as this one:

  • A crank connected to the motor shaft, length 100,
  • a connecting rod, length 183,
  • a rocker arm, length 200,
  • the points connected to the crank and rocker arm frames are 183 apart.

This mechanism is dimensioned in such a way as to give three very distinct phases to the movement of the rocker arm during a cycle:

  • at the first quarter-turn, it moves very little,
  • at the next quarter-turn, it covers its full travel,
  • during the remaining half-turn, it returns to its initial position.

By doubling this mechanism by symmetry, we can see that the movement of the rocker arms can be used to drive the pistons of our machine:

Motor cycle
Receiver cycle


The world of articulated quadrilaterals is a vast one, and there's probably a solution that's closer to the ideal motion. The movement of connecting rods offers a wide variety of trajectories.

(Updated August 2026) I discover the AI with Codex (gpt-5.6-sol) that served me at start a python solver in order to find an optimal geometry, the definition of the notation is still very arbitrary, but I have obtained interesting results.

For the dimensions of the mechanisms below, the points related to the frame of the crank and of the rocker are 100 distant.

By looking on the angular displacement of the rocker I obtained a result quite close to that presented above. The crank measures 73, the coupler 100, and the rocker 110.37. The fixing point of the piston forms an angle of 27.9° with the rocker.

Attaching the piston to the coupler seems to allow greater compression ratios. The research was carried out only according to a projection on the axis of symmetry of the mechanism, there are perhaps movements closer to the ideal to be discovered along other axes.

In the first diagram, the crank measures 44.96, the coupler 117.91, and the rocker 141.73. In the local reference frame of the coupler with the link to the crank as the center, the coordinates of the attachment point of the piston are (94.4 ; -88.65).

In this second diagram, the crank measures 65.64, the coupler 105.99, and the rocker 115.26. The coordinates of the attachment point of the piston are (106.03 ; -35.19).

Using a more complex could help approaching an ideal curve, and could introduce a way of varying piston stroke during adiabatic phases.

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