<p>The units for jerk should be meters per second cubed or m/s<sup>3</sup>. </p>

<p>Meters are the basic unit for <em>distance</em>. The first derivative is speed, or <em>velocity</em>, m/s. The second derivative is <em>acceleration</em>, m/s<sup>2</sup>. The third derivative is <em>jerk</em>, m/s<sup>3</sup>.</p>

<p>It is rate of change in acceleration. </p>

<p>While seldom used, I've only heard it once concerning the Hubble Space telescope, there is a fourth derivative call <em>jounce</em>, m/s<sup>4</sup>. </p>

CC BY-SA 4.0
2019-06-25T21:40:36.637Z
While this expands on the physics definitions in the original question, it does not address what jerk means in 3D printing or why the units are different.
Davo
CC BY-SA 4.0
2019-06-25T20:30:04.607Z
2019-06-26T12:10:11.660Z
2019-06-26T12:10:11.660Z
Jim
<p>In step based motion control, the time between two steps is calculated directly from velocity. If that time is not constant then you are accelerating or decelerating based on a specified acceleration. The next time between steps is calculated from the current velocity based on the desired acceleration. However when moving 2 or 3 axes at once, this can result in very poor and slow performance when moving through complex curves composed of many small moves, because by the math one axis always needs to slow down too much if no jerk is involved. When doing motion calculations for step based systems, actual jerk m/s³ directly translates into how much velocity 'error' is acceptable in calculation of the next velocity (m/s) to allow turning lo angle corners more quickly, but without missing steps or stalling motors. This velocity error comes directly from the actual jerk between two steps and it does have physical meaning, (and the proper units). Also, low power microprocessors can do the math fast enough, which is not the case if square and cube roots get involved.</p>

CC BY-SA 4.0
2021-04-26T11:40:26.493Z
2021-04-26T11:49:50.393Z
2021-04-26T11:49:50.393Z
user28067
<p>The jerk setting in 3D printing G-code and firmware represents a concept similar to, but distinct from, the physical definition of jerk. Rather, it's a [limit on] instantaneous change of speed.</p>
<p>Mathematically, one way to make sense of this is to think that, rather than being the second derivative of speed with respect to time, this &quot;jerk&quot; is the entire remainder of the first-order expansion of speed with respect to time - it corresponds to the second-order term <em>and all higher order terms</em>. Such terms cannot be combined just as coefficients, since they all have different units corresponding to different powers of time; rather, they can be combined only <em>with their corresponding powers of time</em>, in which case the resulting unit is mm/s.</p>

CC BY-SA 4.0
2019-06-25T14:34:59.247Z
Confused me for a sec - I always look at the Nth derivative of position, not speed.  Just noting this in case anyone else is as poor at reading as I was.
Carl Witthoft
CC BY-SA 4.0
2019-06-25T14:36:57.120Z
@CarlWitthoft: *Of position*. I specifically said *of speed*.
R.. GitHub STOP HELPING ICE
CC BY-SA 4.0
2019-06-27T11:00:33.480Z
@CarlWitthoft Speed (v) is the derivate of positon (s) over time. because of that the physical jerk = v'' = s'''
Trish
CC BY-SA 4.0
2019-06-24T19:06:41.793Z
2021-04-26T12:20:32.817Z
2021-04-26T12:20:32.817Z
R.. GitHub STOP HELPING ICE
<p>In 3D printing firmware and slicers, jerk settings are expressed in units if mm/s. This is contrary the physical definition of jerk, which is in units of mm/s³, being the second derivative of speed with respect to time (or the third derivative of position). What is the reason for this discrepancy and how does one interpret jerk in this contect?</p>

CC BY-SA 4.0
2019-06-24T19:07:18.270Z
I'm not sure what other tags would be appropriate for this question; please suggest or edit them in if you have good ideas.
R.. GitHub STOP HELPING ICE
<firmware>
Why does jerk have units of mm/s rather than mm/s³?
R.. GitHub STOP HELPING ICE
# Why does jerk have units of mm/s rather than mm/s³?

(Asked by: username_0 on 2019-06-24)

In 3D printing firmware and slicers, jerk settings are expressed in units if mm/s. This is contrary the physical definition of jerk, which is in units of mm/s³, being the second derivative of speed with respect to time (or the third derivative of position). What is the reason for this discrepancy and how does one interpret jerk in this contect?

**Tags:** firmware

> **Comments:**
> **username_0**: I'm not sure what other tags would be appropriate for this question; please suggest or edit them in if you have good ideas.  

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## 3 answers

### Answer by username_0 on 2019-06-24. Score: 9 | Accepted answer

The jerk setting in 3D printing G-code and firmware represents a concept similar to, but distinct from, the physical definition of jerk. Rather, it's a [limit on] instantaneous change of speed.

Mathematically, one way to make sense of this is to think that, rather than being the second derivative of speed with respect to time, this "jerk" is the entire remainder of the first-order expansion of speed with respect to time - it corresponds to the second-order term *and all higher order terms*. Such terms cannot be combined just as coefficients, since they all have different units corresponding to different powers of time; rather, they can be combined only *with their corresponding powers of time*, in which case the resulting unit is mm/s.

> **Comments:**
> **username_4**: Confused me for a sec - I always look at the Nth derivative of position, not speed.  Just noting this in case anyone else is as poor at reading as I was.  
> **username_0**: @username_4: *Of position*. I specifically said *of speed*.  
> **username_5**: @username_4 Speed (v) is the derivate of positon (s) over time. because of that the physical jerk = v'' = s'''  

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### Answer by username_1 on 2019-06-25. Score: 1

The units for jerk should be meters per second cubed or m/s3.

Meters are the basic unit for *distance*. The first derivative is speed, or *velocity*, m/s. The second derivative is *acceleration*, m/s2. The third derivative is *jerk*, m/s3.

It is rate of change in acceleration.

While seldom used, I've only heard it once concerning the Hubble Space telescope, there is a fourth derivative call *jounce*, m/s4.

> **Comments:**
> **username_2**: While this expands on the physics definitions in the original question, it does not address what jerk means in 3D printing or why the units are different.  

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### Answer by username_3 on 2021-04-26. Score: 1

In step based motion control, the time between two steps is calculated directly from velocity. If that time is not constant then you are accelerating or decelerating based on a specified acceleration. The next time between steps is calculated from the current velocity based on the desired acceleration. However when moving 2 or 3 axes at once, this can result in very poor and slow performance when moving through complex curves composed of many small moves, because by the math one axis always needs to slow down too much if no jerk is involved. When doing motion calculations for step based systems, actual jerk m/s³ directly translates into how much velocity 'error' is acceptable in calculation of the next velocity (m/s) to allow turning lo angle corners more quickly, but without missing steps or stalling motors. This velocity error comes directly from the actual jerk between two steps and it does have physical meaning, (and the proper units). Also, low power microprocessors can do the math fast enough, which is not the case if square and cube roots get involved.


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