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Determining position, velocity, acceleration equations symbolically

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rpatterson-2
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Determining position, velocity, acceleration equations symbolically

I've worked out, long hand, how to determine the desired equations for a cycloidal motion profile of cam I'm going to use as a discussion example.

I'd like to use Mathcad to integrate these equations for me, giving it boundary conditions and solving for the integration constants, but I keep running around in circles trying to figure out the syntax to do so.

I've included the worksheet I'm using, and would greatly appreciate insight into how to get Mathcad to do this symbolic integration for me.

The motion of this cam says there will be dwell at the beginning and end. The initial and ending velocity, acceleration, and position should be zero (these are my boundary conditions).

1 ACCEPTED SOLUTION

Accepted Solutions

Re: Determining position, velocity, acceleration equations symbolically

Something like the attached?

Alan

View solution in original post

6 REPLIES 6

Re: Determining position, velocity, acceleration equations symbolically

Something like the attached?

Alan

View solution in original post

Re: Determining position, velocity, acceleration equations symbolically

ryan patterson wrote:

I've worked out, long hand, how to determine the desired equations for a cycloidal motion profile of cam I'm going to use as a discussion example.

See too http://communities.ptc.com/videos/2077

Re: Determining position, velocity, acceleration equations symbolically

Alan,

Thank you very much, this is exactly what I'm looking for. Can you walk me through some things so I can understand what's going on?

- You've set up an equation, [ a(theta):=stuff ] but [ v(theta):= INT(0,theta) of a(rho)d*rho ] I don't really understand how this works. I've set up a new, simple equation below your work, on the second page, which uses the same technique, and seems to work too, but I'll be honest, I'm not sure why changing the independent variable allows me to symbolically evaluate this integral.

- You use the same dependent variable for integration in solving for s(theta). In my work below, I found that it didn't matter what we used as the independent variable for this symbolic integration, even the original independent variable, "theta" would work. So i'm wondering, why did you change from theta to rho?

I like the symbolic "Solve" function, I didn't know about this until now; the Mathcad help on it was very... helpful, and complete.

Now all I have to do is assign a machine period for theta, a period of rotation for the cam, beta, and a cam displacement, h, and my solution falls out nicely.

Thanks again for your help!

Re: Determining position, velocity, acceleration equations symbolically

ryan patterson wrote:

Alan,

Thank you very much, this is exactly what I'm looking for. Can you walk me through some things so I can understand what's going on?

- You've set up an equation, [ a(theta):=stuff ] but [ v(theta):= INT(0,theta) of a(rho)d*rho ] I don't really understand how this works. I've set up a new, simple equation below your work, on the second page, which uses the same technique, and seems to work too, but I'll be honest, I'm not sure why changing the independent variable allows me to symbolically evaluate this integral.

afn.PNG

I've set up a as a function of theta. The beta is in red because it hasn't yet been given a value. The red disappears if you define beta somewhere above the definition of a(theta) (actually, C would then turn red). Once C and beta have been defined you can calcuulate the value of a for any theta just by calling a with the desired value(s) of theta..

I've then created v as another function of theta, where theta is the upper limit of the integral. The variable of integration (which is phi by the way, not rho) is a dummy variable - it doesn't matter what you use. To avoid potential confusion it's good practice not to use the same variable name as that of the integral limit (though Mathcad will still work ok if you do).

... In my work below, ...

There is nothing "below" in your post!

Alan

Re: Determining position, velocity, acceleration equations symbolically

Hi Ryan, could you send me the attached file in .mcdx. I can't open it with my Mathcad prime 3.0.

Thanks

Jose

Re: Determining position, velocity, acceleration equations symbolically

BARTOLOME JOSE wrote:

Hi Ryan, could you send me the attached file in .mcdx. I can't open it with my Mathcad prime 3.0.

You should be able to download Mathcad 15 and use the XMCD Converter to create an mcdx file in Prime 3.0. I'd do the conversion for you,  but I've got Prime 3.1 and its mcdx files aren't readable in Prime 3.0.

Stuart

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