Jerked motion calculations

Hello everyone,

I'm currently working on a system where motion is involved. The thing I want to do is make calculations for a motion system where there is also a jerk.

Is there anyone who knows how to calculate the following questions:

• The distance as a function of time for given distance, velocity, acceleration, deceleration and jerk.
• The time as a function of position for given distance, velocity, acceleration, deceleration and jerk.
• The velocity required for a motion path with given distance, acceleration, deceleration and jerk in a given time.

I think i have got the distance as a function of time. I managed to calculate the maximum velocity the axis is going to travel at in order for it to move a certain distance. The formula's are quite difficult and I would like to calculate the time as well when the distance is known and also the velocity when I want the axis to move the given distance in the given time.

I need to take into account that the given profile might not reach the desired velocity since then it would overshoot the distance but also that it might not reach the commanded velocity since then it might overshoot the acceleration and/or deceleration.

Anyone here who can help me out?

Kind regards,


Bob

You should check out this recent thread. I have verified the calculations with some of my test cases. The solutions are excellent.

http://www.plctalk.net/qanda/showthread.php?t=119883


calculating the time as a function of distance requires calculating cubed roots.


Check out
https://deltamotion.com/peter/Maxima/Seg1234567.html

This is a simple example. It gets far more complicated.

Hi,

Thank you for your reply! The site is not so intuitive to me but a nice idea! I can calculate the distance as a function of time and for all the segments I can calculate the time as a function of distance except for segment 3 and 5. I would appreciare some help with that. So I almost solved it except for the 2 segments and the issue described below.

Another issue I have is that given the limits of the motion profile I have the time allowed to travel this distance. And it should be exactly that time. How can I calculate the velocity when the distance, acceleration, deceleration, jerk and time are the known variables?

Thanks for the help.

SSJVegetto said:

Hi,

Thank you for your reply! The site is not so intuitive to me but a nice idea!

Click to expand...

Cheeco's site is very intuitive. How else would you do it? Think about that. Look at my example. They are similar.

I can calculate the distance as a function of time and for all the segments I can calculate the time as a function of distance except for segment 3 and 5.

Click to expand...

You didn't look at my wxMaxima example.

I would appreciare some help with that. So I almost solved it except for the 2 segments and the issue described below.

Click to expand...

Yes, a lot of people would. It isn't easy but I provided an example.

Another issue I have is that given the limits of the motion profile I have the time allowed to travel this distance. And it should be exactly that time.

Click to expand...

Yes, that happens. Limits limit speed, acceleration, deceleration, and jerk. The limits may keep the target from getting the the destination at the desired time.


If you solve the problem the way I did it you need to have N equations to solve for N unknowns.

How can I calculate the velocity when the distance, acceleration, deceleration, jerk and time are the known variables?

Click to expand...

Are you talking about the peak velocity or the velocity as a function of time? The calculation for the peak velocity can sometimes be a long equation and very long equation.


Cheeco has worked it out. I don't know how he did it. I solve for N unknowns using N equations as shown in my wxMaxima example. I suspect cheeco may solve the problem iteratively but we get the same answer to 6 digital on the travel time. I only use 6 digits. Cheeco used 7.

My apologies, the site didn't seem to work on my mobile device. I just tried it on my laptop. Seems to be giving good results and I'll compare them with my own results tomorrow. It works wonderfull. Even the starting values can be entered.

The wxMaxima example, it works only for a seven segment motion profile and to me it seems like this one solves distance as a function of time if I'm correct? This one I have already figured out. I don't mind posting my solution to this though but I will verify my answers with the OJET Trajectory generator. The formula I need is to calculate the time given a distance. I might miss something here, if so, my apologies.

What I meant with my last issue was that when a distance, acceleration, deceleration, jerk and duration is given. For what velocity will the motion profile finish the motion in the given time and the given distance. From initial values 0 to final values the distance and velocity = 0, acceleration = 0 and jerk = 0. Hope this made the question more clear.

Thank you for your replies.

SSJVegetto said:

The wxMaxima example, it works only for a seven segment motion profile

Click to expand...

Yes, this is a simple example. There are about 50 different combinations of segments that make sense. I posted a picture of all the combinations of segments I try on cheeco's thread.

and to me it seems like this one solves distance as a function of time if I'm correct?

Click to expand...

position, velocity and acceleration as function of time.

This one I have already figured out. I don't mind posting my solution to this though but I will verify my answers with the OJET Trajectory generator. The formula I need is to calculate the time given a distance. I might miss something here, if so, my apologies.
What I meant with my last issue was that when a distance, acceleration, deceleration, jerk and duration is given. For what velocity will the motion profile finish the motion in the given time and the given distance. From initial values 0 to final values the distance and velocity = 0, acceleration = 0 and jerk = 0. Hope this made the question more clear.

Thank you for your replies.

Click to expand...

I understand but you need to solve for many unknowns at the same time. There will be many cases depending on the distances, accelerations and jerks. if the jerk is low segments 2 and 6 will not exist. Read cheeco's thread.

I understand but you need to solve for many unknowns at the same time. There will be many cases depending on the distances, accelerations and jerks. if the jerk is low segments 2 and 6 will not exist. Read cheeco's thread.

Click to expand...

I verified my solution with the OJET trajectory generator and my solution seems to work. Besides, it works for any possible case. The problem I was having with the calculations is that I needed to work it out with complex numbers when having the time as a function of the distance.

The only problem remaining is to calculate the velocity with a given distance, acceleration, deceleration, jerk and duration. Do you maybe have some tips on how to solve this issue?

Kind regards,


Bob

SSJVegetto said:

Besides, it works for any possible case.

Click to expand...

How do you know? You can't test all the cases manually. I wrote a program that tests my target generator thorough. I let it run for days. It ran over 200 trillion tests. I found errors testing combinations that I doubt a human would try.

The problem I was having with the calculations is that I needed to work it out with complex numbers when having the time as a function of the distance.

Click to expand...

You shouldn't have complex numbers unless you are trying take cube roots.

The only problem remaining is to calculate the velocity with a given distance, acceleration, deceleration, jerk and duration. Do you maybe have some tips on how to solve this issue?

Click to expand...

I used multiple equations to find multiple unknowns. The formula is long if all the begging and ending positions, velocities and accelerations are non-zero.

I am curious how cheeco solved this. Did cheeco use the same technique?

The most difficult solutions are ones where the command velocity and accelerations are never reached.

I attached .png file showing initial position, velocity and acceleration at 0, 3, and -50 and moving to a P,V,A of 1,0,0
I didn't post this on cheeco's thread. Cheeco's solution was the same as mine. This one is difficult. You can see the velocity doesn't reach the command velocity of 10. The accelerations do not reach the command acceleration and decelerations of 100. This is one of the first test I will try.

OT I have NEVER liked the way images are uploaded on this site. I don't know if there will be a link or a real picture.





It is a real picture this time.