# Simple Dynamics Help

## Main Question or Discussion Point

My model is similar to a piston: a rod is connected to a steel cylindrical mass within a pvc pipe. The other end of the mass is connected to a spring which is fixed at its other end. One pulls on the rod to create tension and a displacement of a few centimeters while their arm is connected to a device that measures voltage potentials. I then have to model the system in C++ and do the same voltage potential test with a haptic device to determine if the system is a good simulation.

My problem arises in that it has been a considerable amount of time since I have taken dynamics. I realize this is a relatively simple problem, but I have not used it since. Can anyone assist me with the characteristic equations for this system?

I need to be reminded how to model friction, intertia, displacement, etc. Pulling forces do not exceed 5 N. Probably shouldn't have sold that dynamics book after all :-/

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More information would be nice, like is the spring on the top of the system with gravity pulling down on the mass? so you pull down on the mass, decompress the spring, then let go and it oscillates to a stop? is there friction between the mass and the pvc sleeve, is the sleeve just there to keep it from bouncing all over the place? also the mass is solid right? and at the top of the pvc sleeve, there is adequate room for air to move in and out, making a more ideal free space model? We would also need to know the spring constant and length, to fulfill Hooke's law.

I would measure the spring length, then connect the mass. the mass is going to pull on the spring (if the spring is mounted at the top). (the restoring force of a spring is proportional to its total elongation)

If your system is similar to what i picture, you should be able to google a differential equation example of a stretched spring.

sorry if that didn't help, just bored answering post that have no replies.

More information would be nice, like is the spring on the top of the system with gravity pulling down on the mass? so you pull down on the mass, decompress the spring, then let go and it oscillates to a stop? is there friction between the mass and the pvc sleeve, is the sleeve just there to keep it from bouncing all over the place? also the mass is solid right? and at the top of the pvc sleeve, there is adequate room for air to move in and out, making a more ideal free space model? We would also need to know the spring constant and length, to fulfill Hooke's law.

I would measure the spring length, then connect the mass. the mass is going to pull on the spring (if the spring is mounted at the top). (the restoring force of a spring is proportional to its total elongation)

If your system is similar to what i picture, you should be able to google a differential equation example of a stretched spring.

sorry if that didn't help, just bored answering post that have no replies.
Sorry, I didn't make it clear enough. There is a good amount of friction from the fit so there is no oscillation, but the spring is strong enough to pull the mass back to or near enough to the starting position. The entire system is horizontal as well. The mass is made of 1040 steel so I'm having trouble finding the coefficient of friction between that and PVC since the two aren't commonly paired. The end of the "piston" is open so air pressure is negligible. The spring constant is around .5 lbf/in and about an inch long.

I am making some progress with the characteristic equation now but am having trouble with the coefficient of friction component (mu*N). Any idea on how to compute the normal force from an interference fit?

Hmm can I use Lame's equations for the interference stress then multiply by the surface area for the normal force?

That would just give me F(t) = mass·dv/dt + k·x + mu·N
Did I leave anything out?

So you are going to pull on this thing, and the spring is going to pull it back to the X not startin posistion? in this case i would imagine it would be moving really slow back to the start posisition? I think with that kind of friction I'm no longer sure how to approach the problem.

You are simulating this in C++, how? just mathematically?

So initially it is at rest (x=0) and I pull on it so that it translates a few cm's. I then pull less and less on it until it returns to x=0 at which point the amount of friction present disallows oscillation. The point of this is to measure the voltage potential in the forearm muscles during the linear action.

As far as the C++, yeah. The program's name I believe is Open Haptic and it needs mathematical constraints before simulation is possible.

Wait so are you acuatlly measuring EMG signals in your arm? Why don't you just hold some weights, a one pound weight, a two pound weight, etc. You don't need to move your arm nessesarily to get a voltage change, the force that your arm has to exert is proportional to the nerve signals sent from your brain.

The experiment is an analysis of the hypothesis that simple dynamic systems with < 3 degrees of freedom can be correctly simulated by haptic simulations. It's an opener to a catheter insertion simulation research project.

Yeah that is not in my area of knowledge. It seems like it is going to get pretty sophisticated to measure that small of a movement change. I know one person at our college is doing a project with a prosthetic arm, and went through a lot just to get it to move up and down with impulses from your brain to an EMG sensor on your forearm.

Q_Goest