Editing Jerk (physics) (section)

== In motion control ==
In [[motion control]], the design focus is on straight, linear motion, with the need to move a system from one steady position to another (point-to-point motion). The design concern from a jerk perspective is vertical jerk; the jerk from tangential acceleration is effectively zero since linear motion is non-rotational.

Motion control applications include passenger [[elevator]]s and machining tools. Limiting vertical jerk is considered essential for elevator riding convenience.<ref>{{cite web|url=http://www.schindler.com/content/ie/internet/en/mobility-solutions/products/elevators/schindler-5300/_jcr_content/rightPar/downloadlist/downloadList/3_1340031711862.download.asset.3_1340031711862/05SML9039_Inform_Sheet_EN.pdf|title=Archived copy|url-status=dead|archive-url=https://web.archive.org/web/20140826120525/http://www.schindler.com/content/ie/internet/en/mobility-solutions/products/elevators/schindler-5300/_jcr_content/rightPar/downloadlist/downloadList/3_1340031711862.download.asset.3_1340031711862/05SML9039_Inform_Sheet_EN.pdf|archive-date=2014-08-26|access-date=2014-08-22}}</ref> [[List of ISO standards|ISO 8100-34]]<ref>{{cite web|url=https://www.iso.org/standard/73086.html|title=Lifts for the transport of persons and goods -- Part 34: Measurement of lift ride quality|last1=ISO 8100-34:2021|publisher=International Organization for Standardization|access-date=31 December 2014|archive-date=26 September 2022|archive-url=https://web.archive.org/web/20220926033856/https://www.iso.org/standard/73086.html|url-status=live}}</ref> specifies measurement methods for elevator ride quality with respect to jerk, acceleration, vibration, and noise; however, the standard does not specify levels for acceptable or unacceptable ride quality. It is reported<ref>{{cite web|url=http://www.lift-report.de/index.php/news/176/368/Elevator-Ride-Quality|title=Elevator Ride Quality - The Human Ride Experience|last1=Howkins|first1=Roger E.|publisher=VFZ-Verlag für Zielgruppeninformationen GmbH & Co. KG|url-status=dead|archive-url=https://web.archive.org/web/20150314224900/http://www.lift-report.de/index.php/news/176/368/Elevator-Ride-Quality|archive-date=14 March 2015|access-date=31 December 2014}}</ref> that most passengers rate a vertical jerk of 2&nbsp;m/s<sup>3</sup> as acceptable and 6&nbsp;m/s<sup>3</sup> as intolerable. For hospitals, 0.7&nbsp;m/s<sup>3</sup> is the recommended limit.

A primary design goal for motion control is to minimize the transition time without exceeding speed, acceleration, or jerk limits. Consider a third-order motion-control profile with quadratic ramping and deramping phases in velocity (see figure).

[[File:Schematic diagram of Jerk, Acceleration, and Speed.svg|center|This picture shows a schematic diagram of jerk, acceleration, and speed, assuming all three are limited in their magnitude, when linearly going from one point to another, which are sufficiently far apart to reach the respective maxima.]]

This motion profile consists of the following seven segments:

# Acceleration build up — positive jerk limit; linear increase in acceleration to the positive acceleration limit; quadratic increase in velocity
# Upper acceleration limit — zero jerk; linear increase in velocity
# Acceleration ramp down — negative jerk limit; linear decrease in acceleration; (negative) quadratic increase in velocity, approaching the desired velocity limit
# Velocity limit — zero jerk; zero acceleration
# Deceleration build up — negative jerk limit; linear decrease in acceleration to the negative acceleration limit; (negative) quadratic decrease in velocity
# Lower deceleration limit — zero jerk; linear decrease in velocity
# Deceleration ramp down — positive jerk limit; linear increase in acceleration to zero; quadratic decrease in velocity; approaching the desired position at zero speed and zero acceleration

Segment four's time period (constant velocity) varies with distance between the two positions. If this distance is so small that omitting segment four would not suffice, then segments two and six (constant acceleration) could be equally reduced, and the constant velocity limit would not be reached. If this modification does not sufficiently reduce the crossed distance, then segments one, three, five, and seven could be shortened by an equal amount, and the constant acceleration limits would not be reached.

Other motion profile strategies are used, such as minimizing the square of jerk for a given transition time<ref>{{cite journal |last1=Hogan|first1=Neville|date=1984|title=An organizing principle for a class of voluntary movements|journal=J. Neurosci. |volume=4|issue=11|pages=2745–2754|doi=10.1523/JNEUROSCI.04-11-02745.1984|pmid=6502203|pmc=6564718|doi-access=free}}</ref> and, as discussed above, sinusoidal-shaped acceleration profiles. Motion profiles are tailored for specific applications including machines, people movers, chain hoists, automobiles, and robotics.

=== In manufacturing ===
Jerk is an important consideration in [[manufacturing]] processes. Rapid changes in acceleration of a cutting tool can lead to premature tool wear and result in uneven cuts; consequently, modern [[motion control]]lers include jerk limitation features. In mechanical engineering, jerk, in addition to velocity and acceleration, is considered in the development of cam profiles because of [[tribology|tribological]] implications and the ability of the actuated body to follow the cam profile without [[Machining vibrations|chatter]].<ref>Blair, G., "Making the Cam", ''Race Engine Technology '' 10, September–October 2005</ref>
Jerk is often considered when vibration is a concern. A device that measures jerk is called a "jerkmeter".