I want to correct the trajectory of the double pendulum model.

I create a double pendulum model using Simscape Multibody in MATLAB. Blocks are created mainly using Rigid Transform block, Revolute Joint Block, and Brick Solid Block etc. I was able to reproduce the double pendulum itself, but the trajectory is far from ideal.

Can you see the image? If you can see it, the left side is the ideal trajectory and the right side is the current trajectory. On the ideal trajectory, as the upper rigid body accelerates, the lower rigid body swings slightly delay due to inertia. The lower rigid body then catches up with the upper rigid body and straightens out.

But the current trajectory, the delayed angle of the lower rigid body is small. Also, the lower rigid body then overtakes the upper rigid body, and the angle of the upper rigid body becomes smaller.

Would changing the Revolite Joint Block or Brick Solid Block settings bring it closer to the ideal shape? Also, please tell me which specific items I should change.

Thank you in advance.

Answer 1

[Sam Chak]

Hi @KM,

I can see the image, but I'm unsure if I can visualize the swing motion that you described. Perhaps you can try comparing your model with the one shown in this Double Pendulum Example.

https://www.mathworks.com/help/sm/ug/double-pendulum-in-simulink-and-simscape-multibody.html

Answer 2

[Nathan Hardenberg]

How are you sure, that the left image is the correct/ideal trajectory? For me it seems that the right side is more accurate. You can try this online demo, to get a feeling for it. But note that in there (and also in the example mentioned by @Sam Chak) the center of masses are at the joints of the rods and not in the middle. This makes a difference, but for your case it is comparable.

To explain the phenomenon your question is about, you can try to imagine the following: As the lower body comes down it starts to rotate faster and "pulls" on the upper pendulum. That's why the upper pendulum decelerates and does not continue in an ideal swinging motion.

Please be reminded, that the trajectory of a double pendulum is not very intuitive. The potential energy of the system gets converted into and kinetic translational energy and back (and kinetic rotational energy in your brick-solid example). Plus the coupling between the pendulum is also moving.

To check you model, I also attached a model (most likly very similar to your), to try it out, if you want