topic Re: Solve equations system for motion law in Mathcad

Solve equations system for motion law

gfraulini — Mon, 13 May 2024 22:52:56 GMT

Hi folks,
it has been passed some years from my last use of mathcad...
I want to solve a system of equation by using the Solve Blok to find the coefficients for the displacement and velocity of a m otion law with "pure" traphezoid shape of the acceleration.
I don't understand where I'm wrong.
n. equations = n. of variables

Re: Solve equations system for motion law

ppal — Tue, 14 May 2024 03:41:24 GMT

Re: Solve equations system for motion law

gfraulini — Tue, 14 May 2024 04:11:00 GMT

ra is the time the acceleration need to reach the max.

It is unknown and, by means of mu, it is inside every funzion of v or s.

Re: Solve equations system for motion law

Werner_E — Tue, 14 May 2024 11:44:11 GMT

Because you assume a symmetrical trpezoid, as I see it you only have three independent variables: a.max, r.a and TT !?

But basically you have only one equation: s(T)=s.max with T= 4*r.a+2*TT and s(t) being the integral of the integral of a(t) from 0 to t.

Because of symmetry we could also use s(T/2)=1/2*s.max

So we should expect an infinite number of solutions (as Prime also says) and the 14 variables which you introduce would be highly dependable on each other, I guess.

Re: Solve equations system for motion law

Werner_E — Tue, 14 May 2024 12:37:38 GMT

I created function d for displacement with the three parameters r.a, TT and a.max.

You can choose any (reasonable) value for two of them and can derive the value of the third one so the max displacement is a given value (1 meter in the examples below):

Prime 10 worksheet attached

Re: Solve equations system for motion law

anursingh — Mon, 27 May 2024 21:24:48 GMT

Hi @gfraulini,

I wanted to follow up with you on your post to see if your question has been answered.
If so, please mark the appropriate reply as the Accepted Solution.
Of course, if you have more to share on your issue, please let the Community know so that we can continue to help you.

Thanks,
Anurag