Beyond velocity and acceleration: jerk, snap and higher derivatives (2016)

I have two questions:

1) does this hold for all 3 of jerk, snap and crackle, like OP suggested?

2) In applications where no humans are involved (robot actuators etc.), would it make sense to minimize jerk, snap and crackle too?

>1) does this hold for all 3 of jerk, snap and crackle, like OP suggested?

They aren't the fundamental quantities you would look at, typically the output of a multi body system are displacement/velocity/acceleration, but of course if you look at a plot of acceleration you can just see these quantities (at least the first and second derivative are quite easy to see) or calculate them. And of course the ride comfort is related to the smoothness of the forces you experience, which is the same as wanting to minimize the derivatives of force. But I would suggest that these quantities are quite hard to analyze quantitatively as they are, naturally, subject to far more noise.

Where these quantities definitely are considered is when you look at vibrations.

>2) In applications where no humans are involved (robot actuators etc.), would it make sense to minimize jerk, snap and crackle too?

Yes, if you care about durability. Parts can break for different reasons, intuitively you easily understand that exceeding certain loads breaks them. Another, far more insidious, failure case is a cyclic load, which never exceeds a particular threshold. Again, vibrations play an important role there.

In response to #2, consider that every material is fundamentally "springy"[1], and many engineering materials deflect a human-noticable amount when enough force to move them is applied. Thus, you can model every connection between an actuator and an object as a spring. When the actuator starts accelerating, it applies a force through that spring, which causes the spring to extend, and the force actually applied to the object is provided only by the extension of the spring. It's only once the spring is applying the same force as the actuator is that the two objects are moving at the same speed. However, at that point, the actuator and object are moving at different speeds, so the spring is still extending. As a result, you end up with an oscillation in the velocity of the object, which is almost never desirable. For a start, if one of the parts is metal, this causes fatigue, which will cause the part to fail much sooner. Secondly, you generally want the object being moved to follow a precise path, and that oscillation will show up as ringing[2]

[1] Yes, this is a vast oversimplification, but the model I'll build using it is reasonably accurate.

[2] Most 3d printing enthusiasts are familiar with this issue; e.g. https://www.simplify3d.com/resources/print-quality-troublesh... . However, most of the advice you see amounts to "make everything stiffer", which helps, but the real solution is to be less jerky.

Modern cars are designed on GUI simulation software like MATLAB, they model head accelerations few inches ahead of the most important headrest and run optimizer on variables. If it can be made into equations, they can cancel it.

btw, minimizing higher orders of derivatives improve passenger comfort only so much if the driver isn't so good at look-ahead path planning, you can't make coffee cup rides not sickening by software.

>Modern cars are designed on GUI simulation software like MATLAB

MATLAB is the programming language. You are talking about Simulink. But there are also dedicated software packages for car multi body dynamics.

>you can't make coffee cup rides not sickening by software.

Plainly false.

> >you can't make coffee cup rides not sickening by software.

> Plainly false.

I'm not sure how this is false, but I'm also not sure what the person you're replying to is getting at. coffee cup rides have no driver and therefore no look ahead path planning at all.

The entire appeal of these rides is that they exaggerate perception of third and higher derivatives by deliberately creating a chaotic field of view for their occupants, combined with constantly changing both the rate and direction of the acceleration of their squishy bodies in the rigid capsules to which they are loosely secured.

Smoothing this out with software would be possible, sure, but then the result would no longer be a coffee cup ride. I feel like this is a poorly formed example.

I was thinking what would be the most steady and disorienting activity with higher integrals of lateral accelerations, and couldn't come up with a better example than a cup ride. I admit it wasn't a good one.