Sinusoidal vs Trapezoidal Acceleration 3

[fritzl65]

Hello All,
why would one choose one over the other?
I know that a sinusoidal has less "jerk" than a trapezoidal, but what other factors are there?
Thank you

 

[fritzl65]

Hello all,
PNachtwey,
Thank you for those equations.
Please tell me wht the
p(t) term is.
I believe that v(t) is velocity with respect to time and that a(t) is acceleration with respect to time.
Is this correct?
Fritz
P.S. I am so very gratefule to all for their posts and willingness to share.

 

[Skogsgurra]

"p" is probably position. A more common variable name would be "s".

Gunnar Englund

http://www.gke.org

--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...

 

[fritzl65]

I was under the impression that X or D are position/ displacement, after looking at the equation I do thinkit to be displacement/ position

 

[PNachtwey]

"p" is probably position. A more common variable name would be "s".

You are right but I never use s for position because it messes up my Laplace transforms that I use for simulation. I usually use x or y. I used p in the example above because I thought is would be obvious that it is positon.

Here is something relavant to the original question. I saw in my ftp site that I did a while back.
ftp://ftp.deltacompsys.com/public/PDF/Mathcad%20-%20SineMove%20SI.pdf

fritzl65, do you understand that the velocity and acceleration parameters are just limits to keep the controller from asking the machine to do what it can't? The mechanical engineers and the one who select the drives and motors are the one that determine what the acceleration and velocity parameters should be.

 

[fritzl65]

PNachtwey,
I do understand that these parameters are to limit the physical system.
I am interested on how to calculate the 3 separate oves.
Thankk you again... especially fro the 2 pages.

 

[PNachtwey]

If you want to generate the formulas then it is just a matter of solving a set of simultaneous equations

p1=p0+v0*t01+(a0/2)*t01^2+(j/6)*t01^3
v1=v0+a0*t01+(j/2)*t01^2
a1=a0+j*t01
p2=p1+v1*t12+(a/2)*t12^2+(j/6)*t12^3
v2=v1+a*t12+(j/2)*t12^2
a2=a+j*t12
etc until you get to point 7.
a1=a2=a is the max acceleration and j is the max jerk
I think there are 17 or 19 instead of the obvious 21 simultaneous equations to solve because not all segments have a non zero jerk and acceleration. You can do it by hand using substitution.
t01 is the time it takes to go from point 0 to point 1.

Solving for the simultaneous equations is easy. The problem is that there are so many cases. For instance the motion profile may not reach the max acceleration or deceleration. It may not even reach the maximum velocity in the case of short moves. Then what. What happens when you issue a new command while ramping up or ramping down or the position is now in the opposite direction from the current one.

After all the positions, velocities, accelerations and times are work out you can build a state machine with a switch or case statement where each state has the position, velocity and acceleration formulas for each segment.