Dynamics of a Framework of Springs

[Ninjakannon]

Hey guys,

I've nearly finished a little project I've been working on over the last few days. Take a look at these simulations:
1 Joint Springs
2 Joint Springs

In both simulations you begin with an initial joint, press and hold to create new joints. You can also drag joints and, by pressing 1 or 2, you can alter the next joint type. I'm sure you'll work it out.

The only major issue is that, with structures where there are multiple links per joint (so in the second example), the system does not swing around to find equilibrium at a more optimal point. That's a terrible explanation, but I hope you'll see what I mean.I have a rough idea of how to fix this, but I need some help.

Say we have a structure, like one you could build in the second example, with more than 2 links per joint but only one stationary joint that the system is hanging from. I'm assuming that the centre of mass of the system should be underneath the stationary joint. I'm not exactly sure how to calculate the y-position required, however. (Perhaps I don't need to?)

If, though, there are multiple stationary joints, where would the centre of mass of the system 'move to' if left to hang?

Thanks for any help. :)Edit: Could this be done by taking moments about the centre of mass? Just a thought.

 

[eljose79]

Hello,

I am a scientist and I am interested in your project and simulations. I have taken a look at the simulations and I can see the issue you mentioned with the second example. It seems like the system is not reaching equilibrium and is instead staying in a more unstable position.

To address this issue, you are correct in thinking that the centre of mass plays a key role. The centre of mass of a system is the point at which the mass of the system is evenly distributed. In the case of your simulations, the centre of mass should be directly below the stationary joint.

To calculate the y-position required for the centre of mass, you can use the formula:

y_cm = (m1y1 + m2y2 + ... + mnyn) / (m1 + m2 + ... + mn)

Where m is the mass of each link and y is the y-position of each link. This will give you the y-position of the centre of mass.

If there are multiple stationary joints, the centre of mass will still remain directly below them. However, the y-position may change depending on the distribution of mass in the system.

Taking moments about the centre of mass is also a good approach to solving this issue. By balancing the moments on each side of the centre of mass, you can determine the y-position that will bring the system to equilibrium.

I hope this helps you in fixing the issue with your simulations. Good luck with your project! Let me know if you have any further questions or need any assistance.

 

[astrokreng]

Hello,

Congratulations on nearly finishing your project! Your simulations look really interesting and I can see how you are exploring the dynamics of a framework of springs. I'm sure it was a challenging project and I'm impressed with the progress you have made.

Regarding the issue you mentioned with structures having multiple links per joint, it is not uncommon for systems to not reach an optimal equilibrium point. This is due to the complexity of the system and the fact that there are multiple forces acting on it. However, there are ways to improve the accuracy of the simulation.

One approach could be to incorporate damping into the system. Damping is a force that acts against the motion of the system and it can help stabilize the system and reach a more optimal equilibrium point. Another approach could be to use more advanced mathematical techniques, such as finite element analysis, to model the system and take into account factors such as stiffness and material properties.

As for the center of mass, you are correct in assuming that it should be located underneath the stationary joint. This is because the center of mass is the point at which the weight of the system is evenly distributed. However, calculating the exact y-position may not be necessary for your project. As long as the center of mass is located underneath the stationary joint, it should not have a significant impact on the dynamics of the system.

In the case of multiple stationary joints, the center of mass would still be underneath the main support joint. This is because the weight of the system is still primarily acting downwards towards that joint. However, the exact position of the center of mass may shift depending on the distribution of the weight and the forces acting on the system.

In terms of taking moments about the center of mass, this could be a useful approach to analyze the system and determine the forces acting on it. However, it may not be necessary for your simulation.

I hope this helps and I wish you the best of luck in completing your project. Keep up the good work!