*Categorisation of Jerk Applications*

The 21 jerk categories chosen with their respective references were:

1. Jerk in advanced manufacturing [27–90];


The next section presents brief summaries of the papers in the different categories.

#### **3. Results and Discussion**

#### *3.1. Jerk in Advanced Manufacturing*

Jerk in advanced manufacturing can be categorised into jerk in industrial robots [27–63], machining [64–78], motors [79–83], and 3D printers [84–90].

### 3.1.1. Jerk in Industrial Robots

Jerk is mainly used to generate smooth trajectories in industrial robots (also referred to as manipulators) [27–63]. It is outside the scope and purpose of this paper to explain the jerk-controller. Details (author, source, SJR ranking and the title) of the Q1 articles are tabulated in Table 1.

As mentioned above, all of the cited reference used jerk as a limit for generating or controlling a smooth motion.

#### 3.1.2. Jerk in 3D Printers

In recent years, jerk has been used in 3D printers [84–90]. One important consideration in 3D printing is that the term jerk, in the majority of 3D firmware, is defined in terms of the maximum "instantaneous" velocity change without consideration of the time required [84,90].

Inconsistent terminology causes confusion and needs to be addressed in the future. Notwithstanding, in an article on 3D printing by Hernandez [86], the actual jerk was considered (see Table 2).

#### 3.1.3. Jerk in Machining

Jerk is recently used in generating smooth trajectories in machining [64–78]. Details of Q1 articles are tabulated in Table 3.


**Table 1.** Jerk in industrial robots.



**Table 2.** Jerk in 3D printers.

#### 3.1.4. Jerk in Motors

Jerk is also used in motors mostly a as a measure to control/generate smooth trajectories [79–83] (Table 4).

#### *3.2. Jerk in Amusement Rides*

Jerk is rarely mentioned in textbooks but is quite an important physical parameter, as we quite often experience it in daily life. One important aspect of jerk is that jerk is an element in the comfort and safety of amusement rides, as well as reducing the need for equipment maintenance (Table 5).

#### *3.3. Jerk in Cosmology and Space Technology*

Jerk is used in cosmology as well as space technology. Details of articles which were eligible based on the inclusion criteria of the current work are given in Table 6.

#### *3.4. Jerk in Criteria for Discomfort*

Ride comfort is an important parameter in amusement rides [1,4,5], sea-keeping [9,10,122,126] and traditional land-based vehicles [12,25,45,95,98–106,108,109,111–113,115,118–121,123–125,127–131]. There are still discussions ongoing regarding the significance of jerk regarding ride comfort for vehicles, and jerk is probably a better measure for driving comfort than acceleration, as pointed out by van Santen [128] and confirmed, e.g., in the study by Grant and Haycock [107]. Jerk monitoring also offers insurance companies a way to follow up the behaviour of drivers, as a basis for car insurance pricing [195].

The Dutch institutes TNO and MARIN have initiated a joint project to study the impact of jerk on the comfort of passengers in a master thesis conducted by Werkman [10]. Details of this work are given in Section 3.4.2 of this paper.

Förstberg [104] investigated ride comfort and motion sickness in trains. The results indicated that "it is motion dose from horizontal jerk or horizontal acceleration as well as roll acceleration or roll velocity that is the primary causes of provocation." Unfortunately, Förstberg passed away shortly after presenting his thesis.

Svensson and Ericsson [123] referred to concrete jerk values from American Association of State Highway and Transportation Official Standards (AASHTO; 2001) [206] in their master thesis. A value of lateral jerk ranging from 0.03 to 0.09 g/s has been used for highway design. Jia [25] claims that the jerk should be below 0.2 g/s in trains for passenger comfort. Martin and Litwhiler [118] investigated acceleration and jerk profiles in the metro-rail system in Washington DC and found jerk peaks of around 1.3 g/s.

Minimising the discomfort experienced during a journey between two points with the fixed travel time was studied by Anderson et al. [96]. They proposed jerk as a discomfort criteria. Their work was then revisited by Antonelli and Klotz [97] and Lemos [116] one and three years later, respectively. The jerk is proposed as a discomfort criteria. Antonelli and Klotz (2017) [97] and Lemos (2019) [116], commented on this work and mentioned that the integral of the square of acceleration and the integral of square of jerk should be considered as criteria for discomfort.

#### 3.4.1. Jerk in Ride Comfort: Amusement Rides

Jerk is used as a ride comfort measure in amusement rides [1,4,5]. Details of studies mentioning jerk as a ride comfort parameter in amusement rides are given in Section 3.2, Table 5.

#### 3.4.2. Jerk in Ride Comfort: Sea-Keeping

Jerk is used a ride comfort measure in sea-keeping [9,10,122,126]. Details of these studies are given in below Table 7.


**Author**

Masoudi

(2016) [82]



A controller

minimum

 jerk model

 for

 based

 on a

**Comments**


**Table 5.** Jerk in amusement rides.







## 3.4.3. Jerk in Ride Comfort: Vehicles

Jerk has been used as a measure of ride comfort in vehicle engineering [9,10,122,126] and vehicle land-based traditional [12,25,45,95,98–106,108,109,111–113,115,118–121,123–125,127–131]. Details of studies in Q1–Q4 journals are given in Table 8.

## *3.5. Jerk in Equation of Motion (EOM)*

Jerk is proposed to be used in the EOM, and details of studies explored this can be found in Table 9. The idea has been discussed earlier but, to date, no concrete examples where someone claims that adding higher-order derivatives might explain the discrepancies between theory and observations, have been seen.
