Building an Augmented MBD solution in Julia

[cooperrc]

Augmented solution for one-bar linkage

In this video + notebook, we walk through the process of building an augmented MBD simulation using Julia. Main steps are:

1. create generalized coordinates, variables, and constants
2. Define Constraints, $C(q,~t)$ and its derivatives
3. apply external generalized forces, $Q_e\delta q$
4. solve the initial value problem for $q,~\dot{q}$
5. use solutions of $q~\dot{q}$ to determine constraint forces, $\lambda$ and visualize results

[cjdipietrantonio]

This was super helpful for completing Project 03. Thanks for uploading this!

[JimInput]

It's useful to add Baumgarte stabilization, but I also found that after working on project_03 one or two steps of Newton-Rhapson is quicker also helps to get those constraints stabilized.

By putting these two statements a couple times, it will really lock in the position for each time step.

Δq = Cq_mat \ Cval
q[1:6] .-= Δq

[AmeliaRattet]

This video was very helpful in creating project 3. I was able to use the concept of applying external generalized forces to assist in solving the initial value problem.

[ZakMatt0802]

While not directly commenting on the video content, when I had been looking through the project as well as this video I had noticed the order of all these terms can very easily be swapped and shifted around (ie: [x_1, y_1....] vs [y_1, x_1....]) assuming the order across these matrices is the same since if inconsistent the constraints and external forces will not be aligned and call incorrect system values. I wonder if for a manufacturing or control system application if this general order of going body by body for definition is used over an alternative system, like one that pairs the similar parameters instead of the parameters by body. For example listing terms like [x_1,x_2,x_3,y_1,y_2...] etc. I would be interested to here from anyone who may use systems like this on their insight.

[ZakMatt0802]

Also to mirror the comments of the others the video was helpful to reinforce what the team had already done for our project, and confirm our methodology made sense.

[jadongs]

Thank you, Dr. Cooper, for the video. It was extremely helpful to my group, and we were able to finish Project 3’s value problem because of it. It has been a pleasure taking this class with you and the rest of everyone in the course. Wishing everyone the best in their future endeavors.

[matlabkid]

Thought this video was a great check for the project, I will have to apply the force reaction animation to my work since we are doing similar work for duty cycles.

[alw14027]

I think it is interesting how much we have learned starting from the LaGrange equation to now especially with the most recent introduction of the baugerate stabilizer. I would like to understand when to use runge kutta vs. when we would choose another method?