Subhash Divyaksh

Aurélie Chander

Maria Pia Tomezzoli

Mathieu Cavatorta

Stéphane Gréau

Charles Marie

Pontonnier

Divyaksh Subhash Chander

Aurélie Tomezzoli

Maria Pia Cavatorta

Mathieu Gréau

Stéphane Marie

Charles Pontonnier
email: charles.pontonnier@inria.fr

Biomechanical requirements of meat cutting tasks: a pilot study quantifying tasks

Keywords: wrist, occupational musculoskeletal disorders, muscle strength, range of motion, articular, biomechanical specifications

de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Work-related Musculoskeletal Disorders (MSDs) are a major public health issue [START_REF] De Kok | Work-related musculoskeletal disorders : Prevalence, costs and demographics in the EU | Safety and health at work EU-OSHA. European Agency for Safety and Health at Work (EU-OSHA)[END_REF].

The meat processing industry is one of the most affected industrial sectors, as MSDs prevalence is 10 to 15 times higher than in the general population [START_REF] Lemerle | Observatoire des troubles musculo-squelettiques des actifs agricoles : Bilan national 2012-2016 (N o 12030)[END_REF]. [START_REF] Nordander | Risk of musculoskeletal disorders among females and males in repetitive/constrained work[END_REF] reported high prevalence of hand, wrist, and elbow MSDs among male meat cutters. Furthermore, [START_REF] Moore | Upper extremity disorders in a pork processing plant : Relationships between job risk factors and morbidity[END_REF] reported that hand and wrist MSDs prevailed (77%) over elbow MSDs (23%) among distal MSDs (n=104), in a pork processing facility employing 1100 individuals. Consequently, attempts to mitigate the risk of MSDs are suitable, especially at the distal upper limb.

Several risk factors for MSDs have been identified in the workplace, such as physical workload (e.g., high forces, repetition, awkward postures), organizational (e.g. task and job duration, recovery time), environmental (e.g., inappropriate lighting, low temperatures, noise), psychosocial (e.g., job demands, job content) and individual (e.g., individual skills, health problems) factors [START_REF] Karasek | Job decision latitude, job demands, and cardiovascular disease : A prospective study of Swedish men[END_REF]NF ISO 11228-3, 2007). Similarly, in the meat processing industry, several epidemiologic studies have found statistical links between the physical workload and MSDs incidence or prevalence [START_REF] Frost | Occurrence of carpal tunnel syndrome among slaughterhouse workers[END_REF][START_REF] Moore | Upper extremity disorders in a pork processing plant : Relationships between job risk factors and morbidity[END_REF][START_REF] Nordander | Risk of musculoskeletal disorders among females and males in repetitive/constrained work[END_REF]. Detailed ergonomics and biomechanical description of work organization and meat cutting tasks have been provided [START_REF] Arvidsson | Rationalization in meat cutting-Consequences on physical workload[END_REF][START_REF] Silvin | Sollicitations biomécaniques des opérateurs dans les ateliers de découpe de viande[END_REF]. Several studies attempted to understand the effect of work organization or knife sharpening in the meat cutting industry MSD issues [START_REF] Karltun | Maintaining knife sharpness in industrial meat cutting: A matter of knife or meat cutter ability[END_REF][START_REF] Savescu | Objective assessment of knife sharpness over a working day cutting meat[END_REF]. A number of studies focused on the effect of various additional parameters influencing risk factors e.g., the use of a hand tool like a knife [START_REF] Claudon | Analyse de la tenue en main des couteaux lors d'opérations de désossement dans différents secteurs de la filière viande[END_REF][START_REF] Gorsche | Prevalence and incidence of stenosing flexor tenosynovitis (trigger finger) in a meat-packing plant[END_REF], the characteristics of the knife [START_REF] Marsot | Assessment of knife sharpness by means of a cutting force measuring system[END_REF][START_REF] Tirloni | Exertion Perception When Performing Cutting Tasks in Poultry Slaughterhouses : Risk Assessment of Developing Musculoskeletal Disorders[END_REF], or the effect of the workbench height [START_REF] Pontonnier | Cutting Force and EMG Recordings for Ergonomics Assessment of Meat Cutting Tasks : Influence of the Workbench Height and the Cutting Direction on Muscle Activation Levels[END_REF]. A recent study proposed in situ evaluation of physical risk factors [START_REF] Villalobos | Prediction of slaughterhouse workers' RULA scores and knife edge using low-cost inertial measurement sensor units and machine learning algorithms[END_REF]. Attempts have been made to mitigate those risk factors: improved ergonomics of workstations (R. W. [START_REF] Mcgorry | The effect of workstation and task variables on forces applied during simulated meat cutting[END_REF][START_REF] Pontonnier | Strengths and limitations of a musculoskeletal model for an analysis of simulated meat cutting tasks[END_REF], automation [START_REF] Arvidsson | Rationalization in meat cutting-Consequences on physical workload[END_REF][START_REF] Tappin | The role of contextual factors for musculoskeletal disorders in the New Zealand meat processing industry[END_REF]. These attempts are still struggling to significantly enhance the work conditions, especially due to the industrial constraints that are still prevalent. To further reduce physical stress in meat cutting industry, exoskeletons or cobots [START_REF] Maithani | Exoscarne : Assistive strategies for an industrial meat cutting system based on physical human-robot interaction[END_REF] delivering an assistive force to the user during the task execution can also be considered [START_REF] Chander | Biomechanical requirements of meat cutting tasks : An overview[END_REF][START_REF] Tomezzoli | Effect of mass addition on upper limb joint torques during meat cutting tasks : A parametric study[END_REF]. However, such systems raise numerous issues, such as their control, the adaptability to the user, possible undesired effects [START_REF] Pontonnier | Evaluating the action detection of an active exoskeleton : A muscle-control synchronicity approach for meat cutting assistance[END_REF][START_REF] Tomezzoli | Effect of mass addition on upper limb joint torques during meat cutting tasks : A parametric study[END_REF]. Moreover, such systems may have to be designed with regard to the biomechanical requirements related to the task [START_REF] Chander | Biomechanical requirements of meat cutting tasks : An overview[END_REF]. According to [START_REF] Tirloni | Cutting force measurement: Hand tool instrumentation used in slaughterhouses -a systematic review[END_REF], the most recent measures of meat cutting forces using an instrumented knife are almost one decade old.

The use of a single aggregated indicator that globally reflects the biomechanical risk factors influencing the appearance of MSDs is interesting to assess the sustainability of a task and to forecast the effect of ergonomic interventions or assistive devices. Although analysis of specific risk factors like joint angles and torques are mandatory to understand in depth the biomechanical demand for a task, an aggregated indicator is also useful to specify the assistance requirements of an exoskeleton. The OCRA index [START_REF] Occhipinti | Updating reference values and predictive models of the OCRA method in the risk assessment of work-related musculoskeletal disorders of the upper limbs[END_REF], the Strain Index [START_REF] Moore | The Strain Index : A proposed method to analyze jobs for risk of distal upper extremity disorders[END_REF] and the TLV (ACGIH, 2016) are prominent methods to summarize the risk of MSDs for the upper limbs in repetitive tasks through one single indicator (NF ISO 11228-3, 2007) . The current version of the TLV (ACGIH, 2016) relies on the maximal acceptable effort (MAE) model described by [START_REF] Potvin | Predicting maximum acceptable efforts for repetitive tasks : An equation based on duty cycle[END_REF], after refitting the model to enable higher maximal efforts for repetitive tasks occupying more than 50% of the work cycle [START_REF] Abdel-Malek | Exploring Localized Muscle Fatigue Responses at Current Upper-Extremity Ergonomics Threshold Limit Values[END_REF]. The MAE is the maximal effort sustainable for tasks performed for 8 hours per day, determined experimentally through psychophysical studies. As the MAE method targeted fatigue phenomena at the distal upper limb, which is a frequent MSDs location in butchers [START_REF] Nordander | Risk of musculoskeletal disorders among females and males in repetitive/constrained work[END_REF], this method is a good candidate to assess meat cutting tasks in terms of physical demand in this population. A mathematical relationship between the MAE and the duty cycle (DC), defined as the ratio of the task duration within a cycle to the work cycle time (𝐶𝑇), was proposed.

Based on this relationship, the assistive torque required to reduce the effort to the level of MAE and the rest required (𝑅𝑅) after a given task can be computed. For a work cycle consisting of multiple tasks, the cumulative rest required can also be computed by summing up the 𝑅𝑅 for each task [START_REF] Gibson | Calculating the Maximum Acceptable Effort for an Isolated Subtask While Still Accounting for the Demands of all Other Subtasks[END_REF]. To the best of our knowledge, the MAE method has not been used in application to meat cutting tasks before. The current study is an exploratory study aimed at evaluating the biomechanical requirements of meat cutting tasks at professional butchers' dominant wrist, by the cutting force, joint angles, joint torques, along with an estimation of the overall sustainability of the task and, when needed, theoretical assistive torque required to reach sustainability using the MAE model.

METHODS 2.1 Experiments

Six professional butchers, free from any musculoskeletal pain or discomfort in the last 6 months and fully operational in the plant, participated in the experiments in a motion analysis laboratory. Three pork pieces and one beef piece cutting tasks (Table 1) were selected by the partner meat processing plant (COOPERL, France) regarding activities with frequent sick-leave disrupting the company. In this work, only the pork trials were investigated due to limited beef trials, which had only two repetitions each for two subjects. The study was approved by a national ethics committee (Comité Opérationnel d'Evaluation des Risques Légaux et Ethiques, COERLE, n° 2021-07). Subjects signed an informed consent form prior to participating in the experiment.

Equipment

Motion capture data was recorded at 200Hz using an optoelectronic system with 32 cameras (Qualisys Track Manager (QTM) 2021). 40 reflective markers were placed on the subject and 4 on the knife (Figure 1). Cutting force and moments were measured with a wireless instrumented knife (6 degrees of freedom (dof) force sensor, ATI Mini45-E Transducer, mounted between the handle and the replaceable blade, 500Hz). The partner meat processing plant supplied two blades with different lengths of 11cm (shown in Figure 1; the figure shows the distance between the blade tip and the sensor reference frame and not the blade length) and 19.2cm that are typically used in the selected tasks. The subjects preferred the shorter blade for all pork trials and the longer blade for beef trials.

Forces and moment applied to the worktable, ground reaction forces and EMG signals of several upper limb muscles were recorded (not used in this study). All signals were synchronized with the motion capture system through the Transistor-Transistor logic (TTL) synchronization signal of the motion capture system. The joint strength at the wrist was measured using a Con-Trex MJ® isokinetic dynamometer (CMV AG, Dübendorf, Switzerland), following the constructor recommendation for isometric wrist strength assessment. . Additionally, markers located on the knife and table (one marker on the table was on the opposite and is not visible in the photo). The coordinate system on the knife shows the force sensor origin. (b) a subject in action during a pork belly cutting trial (left), and a maximal isometric wrist radial deviation strength test (right).

Protocol

After being briefed, the height and weight of the subject were recorded. Next, isometric maximal joint strength in wrist flexion (WF), wrist extension (WE), ulnar deviation (UD), and radial deviation (RD) of the dominant arm were measured with the dynamometer, in the posture recommended by the ergometer manufacturer (seated on the chair, strapped to fix shoulder, arm and trunk, shoulder at rest, elbow flexed at 90°, forearm pronated at 0° or 90° depending on the degree of freedom assessed, wrist at rest), for five seconds with verbal encouragements. The subject was then equipped with motion capture markers and EMG electrodes. They wore protective equipment (chainmail apron and sleeve for the non-dominant arm), markers located on the sternum, pelvis front left and right, nondominant wrist and hand were placed on top of the protective equipment.

Next, a range-of-motion (ROM) trial was performed for geometrical calibration of the biomechanical model of the subject. The piece to be cut was placed on the table and weighed by the force sensor.

Then, the meat cutting trials were performed. To facilitate data processing, the subject marked the beginning and end of the cutting task by tapping the knife on the table. The knife was sharpened as and when deemed necessary by the subjects. Five repetitions were planned for each subject.

However, one repetition each from Subject 1 and Subject 2 could not be used due to technical issues during the recording of the motion capture data, with no data saved.

Data analysis

Inverse kinematics and dynamics analysis

Marker trajectories were processed in QTM and low pass filtered (4 th order Butterworth with no phase shift at 10Hz). All force data was resampled to the mocap frequency. All trials were cropped to isolate the cutting task using the start and end taps in the cutting force. A biomechanical model of the upper limb (3 segments, 7 degrees of freedom), available in the motion analysis library CusToM [START_REF] Muller | CusToM : A Matlab toolbox for musculoskeletal simulation[END_REF], was used in this work. The model of the subject was scaled according to the height of the subject and the weight including the equipment (5.5 kg). The ROM trial was used for geometrical calibration of the model [START_REF] Puchaud | Accuracy and kinematics consistency of marker-based scaling approaches on a lower limb model : A comparative study with imagery data[END_REF]. The knife force was applied to the hand of the subject after transformation into the global reference frame through the markers located on the knife. Wrist joint angles and joint torques were computed using CusToM. Further, the percentage durations of joint angles and joint torques between WF and WE, and UD and RD during the cycle were also computed. The grip of the knife was observed from the video recording of the trial.

Sustainability analysis

To perform the sustainability analysis, it was required to normalize the joint torques obtained from the inverse dynamics analysis to make them comparable to the MAE model. The normalized effort required by the subject for meat cutting was computed as the ratio of the joint torque required at the wrist to the joint (maximal) strength of the subject in the corresponding direction. The changes in the joint strength due to changes in joint angle and velocity were modeled by the torque-angle-velocity (TAV) envelopes for the wrist [START_REF] Xia | Wrist joint torque-angle-velocity performance capacity envelope evaluation and modelling[END_REF]. The envelopes were scaled by the ratio of the subject's isometric strength in the neutral posture to the strength from the TAV envelope at zero angle and velocity to obtain one 𝑇𝐴𝑉(𝑞, 𝑞̇) envelope per exertion type (WF, WE, RD and UD respectively), depending on the joint position 𝑞 and velocity 𝑞̇.

The cycle time (𝐶𝑇) for the trial performed by the subjects was computed as the duration between the starting and ending tap recorded by the subject. The largest 𝐶𝑇 from the repetitions performed by a subject was considered as the 𝐶𝑇 for the task. However, if the second largest 𝐶𝑇 was less than 75% of the largest 𝐶𝑇, the repetition with the largest 𝐶𝑇 was excluded from the sustainability analysis as an outlier to possibly account for an unfamiliar laboratory environment and measuring equipment for the subjects. This affected one repetition each from Subject 1 and Subject 3. All individual cutting events (also called as exertions) in a given trial were defined by blocks of time with cutting force continuously greater than 5N. Duty Cycle (𝐷𝐶 𝑖 (%)) of an exertion 𝑖 was computed as the ratio of the Time of Exertion 𝑇𝐸 𝑖 to 𝐶𝑇.

Since the peak effort lasted for a fraction of the duration of an exertion, often consisting of several cutting strokes, an equivalent effort (𝐸𝑞𝐸𝑓𝑓 𝑖 ) was computed as the peak of a bell curve of equivalent area under the curve (equal impulse) as that of the effort in the exertion 𝑖, during the same 𝑇𝐸 𝑖 . The joint torques issued from the inverse dynamics were processed the same way, resulting in equivalent joint torque per exertion (𝐸𝑞𝐽𝑇 𝑖 ).

The 𝑀𝐴𝐸 𝑖 (%) for an exertion 𝑖 was computed using the equation:

𝑀𝐴𝐸 𝑖 = 1 -[𝐷𝐶 𝑖 -1/28800] 0.24 (1)
28800 is the number of seconds in a standard 8-hour workday and implied that MAE = 100% for DC ≤ 1s/workday as defined in Potvin 2012.

The sustainability of each exertion was checked in isolation, for the four exertion directions at the wrist. If the 𝐸𝑞𝐸𝑓𝑓 𝑖 exceeded the 𝑀𝐴𝐸 𝑖 for a given exertion, the exertion and work cycle were considered unsustainable. The assistive torque 𝑇𝑎𝑠𝑠1 𝑖 needed to make the exertion 𝑖 sustainable is denoted as Tass1 and was computed as the difference in percentage of 𝐸𝑞𝐸𝑓𝑓 𝑖 between 𝐸𝑞𝐸𝑓𝑓 𝑖 and 𝑀𝐴𝐸 𝑖 , multiplied by the equivalent joint torque of exertion 𝑖 𝐸𝑞𝐽𝑇 𝑖 .

𝑇𝑎𝑠𝑠1 𝑖 = {0, 𝑖𝑓 𝐸𝑞𝐸𝑓𝑓 𝑖 ≤ 𝑀𝐴𝐸 𝑖 (𝐸𝑞𝐸𝑓𝑓 𝑖 -𝑀𝐴𝐸 𝑖 )/𝐸𝑞𝐸𝑓𝑓 𝑖 * 𝐸𝑞𝐽𝑇 𝑖 , 𝑖𝑓 𝐸𝑞𝐸𝑓𝑓 𝑖 > 𝑀𝐴𝐸 𝑖 (2)
The rest required per exertion 𝑅𝑅 𝑖 was computed based on the 𝑇𝐸 𝑖 with the following equation [START_REF] Gibson | An equation to calculate the recommended cumulative rest allowance across multiple subtasks[END_REF]:

𝑅𝑅 𝑖 = 𝑇𝐸 𝑖 [1 -𝐸𝑞𝐸𝑓𝑓 𝑖 ]
Naturally, a work cycle with at least an exertion with 𝐸𝑞𝐸𝑓𝑓 𝑖 greater than 𝑀𝐴𝐸 𝑖 was unsustainable as 𝑅𝑅 𝑐 would exceed the 𝑅𝐴 𝑐 . In such cases, computation of δ and 𝑇𝑎𝑠𝑠2 𝑖 did not include 𝑇𝑎𝑠𝑠1 𝑖 .

In the results, the average of the maximum values of 𝑇𝑎𝑠𝑠1 𝑖 and 𝑇𝑎𝑠𝑠2 𝑖 considering all the exertions in the work cycle are presented for each subject. The above calculations for sustainability, i.e., 𝑅𝑅 𝑐 , 𝑇𝑎𝑠𝑠1, and 𝑇𝑎𝑠𝑠2 were computed independently for each exertion direction at the wrist.

RESULTS

There were differences in the laboratory 𝐶𝑇 for subjects performing the same task. However, the exertion frequencies were comparable for the subject pairs except for Subjects 3 (38.4 exertions per minute) and 4 (24.8 exertions per minute) (See Supplementary Material). The type of measurements, and subsequently of assistance are discussed. Wrist flexion angle exceeded the safety threshold of 45° (NF ISO 11228-3, 2007) for one subject, wrist extension for 5 subjects, ulnar deviation for 5 subjects and radial deviation for 3 subjects. Most of the work cycle was spent with the wrist flexed in ulnar deviation for cutting pork belly side (2 subjects), with wrist extended in radial deviation for cutting pork shoulder (2 subjects); both patterns were encountered for cutting pork spare rib (1 subject each) (Table 2). Peak resultant cutting force varied between 58 ± 7N and 105 ± 11N. Flexion joint torque was over-represented across time for every subject except Subject 4, irrespective of the flexion-extension joint angle. Conversely, radio-ulnar deviation and torque directions seemed cross-coupled e.g., predominant radial torque being associated with predominant ulnar deviation (Table 2). Histograms of joint torques and efforts as functions of joint angles displayed various profiles depending on tasks, subjects and joint angles (see Figure 2C to F and Figure 3C to F for Subject 1; see supplementary material for the other subjects).

Subjects 1 and 2 used a forward knife grip while Subjects 5 and 6 used predominantly the edge-in reverse knife grip. Subjects 3 and 4 used both grips during the trial, with Subject 3 starting with the forward knife grip and switching to the edge-in reverse knife grip midway through the trial. Instead, Subject 4 started with the edge-out reverse knife grip, switched to forward knife grip, and finished with edge-in reverse knife grip (Figure 4). Based on the sustainability analysis used in this study, the work cycle of only Subject 4 was sustainable in all exertion directions, as 𝑅𝑅 𝑐 was less than 𝑅𝐴 𝑐 . For the remaining five subjects, 𝑅𝑅 𝑐 exceeded 𝑅𝐴 𝑐 in two exertion directions (Table 3). Wrist extension was the only direction for which 𝑅𝑅 𝑐 never exceeded 𝑅𝐴 𝑐 . Subjects 1, 2 and 3 had 𝑅𝑅 𝑐 exceeding in radial deviation, while Subjects 5 and 6 had 𝑅𝑅 𝑐 exceeding in ulnar deviation. 𝑇𝑎𝑠𝑠1 indicates if any exertion in the work cycle had 𝐸𝑞𝐸𝑓𝑓 𝑖 that exceeded the 𝑀𝐴𝐸 𝑖 for its corresponding 𝐷𝐶 𝑖 (Table 3). For three subjects (Subjects 3, 5 and 6), there was at least one and maximum three exertions where the 𝐸𝑞𝐸𝑓𝑓 𝑖 that exceeded the 𝑀𝐴𝐸 𝑖 , on a total of 27 exertions per cycle on average (See Supplementary Material). The mean of the peak assistive torque required to reduce the 𝐸𝑞𝐸𝑓𝑓 𝑖 to 𝑀𝐴𝐸 𝑖 across the repetitions of the subjects was at most 1.6Nm. Naturally, subjects requiring 𝑇𝑎𝑠𝑠1 required 𝑇𝑎𝑠𝑠2 as well to make the work cycle sustainable in the corresponding exertion directions. 50% (1.1Nm) reduction in wrist flexion effort (torque) was needed for Subject 5. While 56% (5.6Nm) reduction in ulnar and radial deviation effort (torque) was needed for Subject 5 and 3, respectively.

The work cycle can be unsustainable even if individual exertions are sustainable as seen in the case of Subjects 1 and 2 performing PB. They do not require 𝑇𝑎𝑠𝑠1 but require up to 60% (5.8Nm) reduction in wrist flexion effort (torque) and up to 40% (2.2Nm) reduction in radial deviation effort (torque) to make the work cycle sustainable. Subjects 3 and 6 also required 𝑇𝑎𝑠𝑠2 in wrist flexion while not requiring 𝑇𝑎𝑠𝑠1. In wrist extension, Subject 6 required Tass2 in only one repetition, resulting in mean 𝑅𝑅 𝑐 lower than 𝑅𝐴 𝑐 . Likewise, in ulnar deviation Subjects 2 and 3 required Tass2 in one and two repetitions, respectively, resulting in mean 𝑅𝑅 𝑐 lower than 𝑅𝐴 𝑐 .

T1 T2 T1 T2 T1 T2 T1 T2 (s) (s) (N m) (N m) (% ) (s) (N m) (N m) (% ) (s) (N m) (N m) (% ) (s) (N m) (N m) (%

DISCUSSION

The aim of this exploratory study was to propose an extensive biomechanical characterization of meat cutting tasks performed by a reduced set of professional butchers, to estimate the need for assistance and, when required, to provide data on the direction and level of assistance needed at the wrist. The global assessment of the tasks showed that every professional butcher but one exceeded the biomechanical sustainability threshold described by [START_REF] Potvin | Predicting maximum acceptable efforts for repetitive tasks : An equation based on duty cycle[END_REF] and [START_REF] Gibson | An equation to calculate the recommended cumulative rest allowance across multiple subtasks[END_REF].

Comprehensive kinematic and kinetic data with professional butchers performing real meat cutting tasks were collected for this study. Joint angle values often exceeded recommendations (NF ISO 11228-3, 2007), especially in wrist extension (45°) and ulnar deviation (20°). Capturing the kinematics of the knife was also critical to understand the difference in knife grips and its consequences for the joint torques required at the wrist. For example, this study showed that for PSR, Subject 4 had a sustainable work cycle while Subject 3 had an unsustainable work cycle. This can be due to the specific strategy of Subject 4. Subject 4 used three different knife grips enabling him to obtain a fairly even split in duration of exertion between the exertion directions, unlike Subject 3, who used two knife grips. Moreover, the additional change in knife grip for Subject 4 resulted in greater 𝐶𝑇 and 𝑅𝐴 𝑐 compared to Subject 3, leading to a lower frequency of exertions in the work cycle. These factors favorably affected the sustainability analysis for Subject 4. Given the limited subjects in this study, a future study with more subjects should investigate in detail if switching knife grips could be a viable strategy to reduce the risk of MSDs.

Raw value of forces also exceeded recommendations stated in the RULA ergonomics tool assessment [START_REF] Mcatamney | RULA : A survey method for the investigation of workrelated upper limb disorders[END_REF], as peak and average forces always exceeded the first threshold of 20N for repeated loads and for Subject 2, the peak force exceeded the second threshold (100N). This is consistent with epidemiological studies that display correlations between physical load and MSDs incidence or prevalence in the meat cutting industry [START_REF] Frost | Occurrence of carpal tunnel syndrome among slaughterhouse workers[END_REF][START_REF] Gorsche | Prevalence and incidence of stenosing flexor tenosynovitis (trigger finger) in a meat-packing plant[END_REF][START_REF] Moore | Upper extremity disorders in a pork processing plant : Relationships between job risk factors and morbidity[END_REF][START_REF] Nordander | Risk of musculoskeletal disorders among females and males in repetitive/constrained work[END_REF]. In addition, peak and average cutting moments of 16.2Nm and 4.0Nm, respectively, have been reported for pork shoulder deboning tasks (Dempsey & McGorry, 2004). The cutting moments at the handle core approximately translated into peak and average cutting force of 75N and 19N, respectively, considering blade length of 15cm and half handle length of 6.5cm (Dempsey & McGorry, 2004;[START_REF] Mcgorry | A system for the measurement of grip forces and applied moments during hand tool use[END_REF]. These values compare well with the values reported in the current study. The consistency of epidemiological and biomechanical literature with our study legitimates the use of assistance to reduce the physical workload, though the number of tasks and subjects investigated was low in our study. Thus, the direction, then the level of assistance that could be proposed based on our results will be discussed consecutively.

Directions to be assisted

In our study, wrist flexion torques were excessive compared to subject individual capabilities for almost every subject, ulnar deviation or radial deviation torques were excessive depending on subjects, and extension torques were considered sustainable for every subject. The differences in torque and assistance requirement between radio-ulnar deviation can be associated with changes in cutting strategy or knife grip for different tasks. PB, performed by Subjects 1 and 2 with the forward knife grip, were over-represented in radial deviation while PS, performed by Subjects 5 and 6 with predominantly the edge-in reverse knife grip, were over-represented in ulnar deviation. Thus, our results suggest that assistive devices must be able to adjust to task and/or subject specific requirements to be efficient. In addition, high inter-subject (or inter-task) variability was found for every parameter measured or computed in our study, which was expected in meat cutting tasks [START_REF] Chander | Biomechanical requirements of meat cutting tasks : An overview[END_REF]Dempsey & McGorry, 2004;[START_REF] Silvin | Sollicitations biomécaniques des opérateurs dans les ateliers de découpe de viande[END_REF]. Moreover, only three tasks were investigated in the study, while a range of different tasks is usually performed in a meat processing plant, and each task was performed by two subjects specialized in this specific task. To further evaluate the results of the study, the consistency of our data with the MSDs encountered in the meat cutting industry are discussed.

The epidemiologic literature highlights carpal tunnel syndrome, trigger finger syndromes [START_REF] Frost | Occurrence of carpal tunnel syndrome among slaughterhouse workers[END_REF][START_REF] Gorsche | Prevalence and incidence of stenosing flexor tenosynovitis (trigger finger) in a meat-packing plant[END_REF] and non-specific hand/wrist pain [START_REF] Moore | Upper extremity disorders in a pork processing plant : Relationships between job risk factors and morbidity[END_REF] as the most prevalent distal upper limb MSDs in the meat cutting industry. Forceful exertions, especially when combined with repetitive movement or awkward posture of hand or fingers, are considered a risk factor for carpal tunnel syndrome [START_REF] Keir | Relationships and Mechanisms Between Occupational Risk Factors and Distal Upper Extremity Disorders[END_REF]. Trigger finger syndromes are due to finger flexor tendons tenosynovitis [START_REF] Durand | Trigger digits][END_REF], finger flexors being involved both in fingers and wrist flexion [START_REF] Marieb | Anatomie et physiologie humaines[END_REF]. Consequently, the excessive wrist flexion exertions highlighted in our study seem consistent with the high prevalence of carpal tunnel and trigger finger syndromes in butchers, although such results should be confirmed on a larger cohort of subjects. Also, the sustainable exertions in wrist extension highlighted in our study seems consistent with the epidemiologic literature, as e.g. finger extensors MSDs are not highlighted in epidemiologic studies performed in the meat processing industry [START_REF] Frost | Occurrence of carpal tunnel syndrome among slaughterhouse workers[END_REF][START_REF] Gorsche | Prevalence and incidence of stenosing flexor tenosynovitis (trigger finger) in a meat-packing plant[END_REF][START_REF] Moore | Upper extremity disorders in a pork processing plant : Relationships between job risk factors and morbidity[END_REF]. Elbow

tendonitis are common among butchers [START_REF] Moore | Upper extremity disorders in a pork processing plant : Relationships between job risk factors and morbidity[END_REF], but no details about the medial versus radial elbow tendonitis were found in the literature. Additionally, radial and ulnar deviations are both controlled by several muscles, inserted on both lateral and medial epicondylitis, like finger extensors and flexor carpi radialis for radial deviation and flexor and extensor carpi ulnaris for ulnar deviation.

Thus, literature does not give indication regarding the relative importance of a radial or ulnar deviation torque assistance and cannot help prioritizing between assistance for radial or ulnar deviation.

Consequently, wrist flexion and possibly radio-ulnar deviation seem the more relevant directions to be assisted during meat cutting tasks. As overrepresentation across time of wrist flexion was always associated with overrepresented ulnar deviation, and wrist extension with radial deviation, a coupled functional motion can be suspected. This coupled motion, known as a "dart-throwing motion" of the wrist, has been demonstrated to be the most common wrist motion in activities of daily living [START_REF] Moritomo | IFSSH Committee Report of Wrist Biomechanics Committee : Biomechanics of the So-Called Dart-Throwing Motion of the Wrist[END_REF]. This raises the question of the need to assist the wrist proportionally in coupled degrees of freedom. In addition, maximal torques were developed in different wrist positions, depending on the subject (see Figure 2A and Figure 3A for Subject 1). Consequently, assistance should be provided on the largest possible articular amplitude in flexion/extension.

Level of assistance

Assistive torque requirements were computed in two ways. 𝑇𝑎𝑠𝑠1 (Table 3) identified exertions that were highly stressful due to large effort requirement for the 𝐷𝐶 𝑖 of the exertion. 𝑅𝑅 𝑐 and 𝑇𝑎𝑠𝑠2

(Table 3) served to understand the overall sustainability of the work cycle. Meat cutting is a highly dynamic activity with cutting exertions often consisting of several cutting strokes, resulting in peaks and dips in the computed effort. The sustainability analysis showed more instances of 𝑇𝑎𝑠𝑠2 requirement than 𝑇𝑎𝑠𝑠1 requirement, indicating that the fast-paced and repetitive nature of meat cutting tasks is a problem that affected subjects more than isolated exertions with large force/torque requirements. There can be several ways to address the problem. With 𝑇𝑎𝑠𝑠2, we adapted a strategy of uniform reduction in the effort required in the work cycle to achieve sustainability while maintaining the same cycle time. With 𝑇𝑎𝑠𝑠1, we targeted specific exertions and made them sustainable in isolation, without considering the sustainability of the overall cycle, which explains why 𝑇𝑎𝑠𝑠1 is much lower than 𝑇𝑎𝑠𝑠2. 𝑇𝑎𝑠𝑠1 and 𝑇𝑎𝑠𝑠2 can potentially be used to determine the specifications of an assistive device, however the data must be extended with more subjects. While Subjects 1 and 2, performing PB, showed similar reduction in effort in the corresponding exertion directions, subject pairs for PSR and PS showed some inconsistencies in the level of assistance required.

𝑇𝐴𝑉 envelopes [START_REF] Xia | Wrist joint torque-angle-velocity performance capacity envelope evaluation and modelling[END_REF] were implemented in the 𝑀𝐴𝐸 models, defining the joint strengths.

The 𝑀𝐴𝐸 model accounted more or less for torques, repetitiveness, joint angles, and velocity in a single indicator, the three first factors being major factors of MSDs (NF ISO 11228-3, 2007). The choice in this study was to measure isometric joint strengths, making 𝑇𝐴𝑉 envelopes specific instead of using some of the literature. It was indeed expected that butchers will be stronger in wrist strength compared to literature data. This was true for all but Subjects 5 and 6 in radial deviation strength [START_REF] Chander | Biomechanical requirements of meat cutting tasks : An overview[END_REF][START_REF] Xia | Wrist joint torque-angle-velocity performance capacity envelope evaluation and modelling[END_REF]. Thus, the results in this study must be carefully considered when applying to new butchers, whose wrist strength may not still be conditioned by their work. [START_REF] Mcgorry | Experimental appraisal of a manual task evaluator[END_REF] found that experienced butchers spent less time applying torque than less experienced butchers and suggested that using more power and less time allowed experienced butchers a greater recovery period or conditioning at job allowed them to sustain higher exertion levels than less experienced butchers. Based on the 𝑀𝐴𝐸 model, sustainability can be achieved by reducing effort or increasing recovery period, or a combination of both. It is also certain that an increase in joint strength of experienced butchers due to job conditioning will reduce the effort exerted in all the exertions and, consequently, result in a reduction in RR for the task. Moreover, as seen in this study, change of knife grip during meat cutting tasks might also be a strategy that could be employed to improve the sustainability of the task. The 𝑀𝐴𝐸 model, with subject specific joint strength, can indeed be used to investigate the strategies used by experienced butchers in a future study.

However, joint strength implemented in 𝑀𝐴𝐸 models are only estimations, as many factors are known to modify them [START_REF] Nuzzo | CORP : Measurement of upper and lower limb muscle strength and voluntary activation[END_REF]. For example, neither the influence of interactions between the different degrees of freedom on wrist joint strength (La [START_REF] Delfa | A musculoskeletal model to estimate the relative changes in wrist strength due to interacting wrist and forearm postures[END_REF], nor the influence of remote joint angles like elbow and shoulder [START_REF] Delp | Maximum isometric moments generated by the wrist muscles in flexion-extension and radial-ulnar deviation[END_REF][START_REF] Xia | Wrist joint torque-angle-velocity performance capacity envelope evaluation and modelling[END_REF], Haering et al. 2017) could be estimated by available models. Both issues are encountered in the tasks, as flexion-extension and radio-ulnar deviations are performed during meat cutting, i.e. with or without shoulder abduction.

Additionally, joint torques estimated are net joint torques. Thus, muscle co-contraction is not accounted for during the tasks, even if co-contraction is necessary to ensure a given level of performance during the execution of the task. This is an approximation [START_REF] Latash | Muscle coactivation : Definitions, mechanisms, and functions[END_REF], which can underestimate the assessment of MSDs risk. On the opposite, we also assumed that the muscles were activated to provide an exertion torque in a given direction. However, the same joint torque can be provided by different muscles over time, with adaptive changes in muscle recruitment patterns in case of fatigue [START_REF] Blangsted | Voluntary low-force contraction elicits prolonged low-frequency fatigue and changes in surface electromyography and mechanomyography[END_REF] in real working conditions. Thus, 𝑅𝑅 𝑐 might be overestimated in our study. These two conflicting issues may ask for further analyses at the muscle level e.g. by EMG, to gain an in-depth understanding of the motor adaptations associated with performing meat cutting tasks over a long period of time and better assess their sustainability.

Limitations

Limitations due to the low number of subjects involved in the study and assistive torque computation have been previously discussed. Nevertheless, we can emphasize that the individual differences associated with this small cohort may have a significant effect on the results, particularly as a result of the healthy worker effect [START_REF] Li | A review of the healthy worker effect in occupational epidemiology[END_REF]. Limitations due to the conditions of measurement also exist. The study was performed in a laboratory, where working conditions substantially differ from those encountered in industry. For example, butchers usually work in a cold, noisy environment at a sustained pace [START_REF] Silvin | Sollicitations biomécaniques des opérateurs dans les ateliers de découpe de viande[END_REF], all these factors being identified as risk factors for MSDs (NF ISO 11228-3, 2007). Conversely, specific constraints exist in a laboratory, like extra equipment and procedures for data collection. Furthermore, our study focused on exertions at the wrist, as distal MSDs are the most common [START_REF] Nordander | Risk of musculoskeletal disorders among females and males in repetitive/constrained work[END_REF], but assessment of other exertions could also be of interest.

For example, using a hand tool like a knife involves finger flexors exertion [START_REF] Marieb | Anatomie et physiologie humaines[END_REF] and is a known risk factor for MSDs in butchers [START_REF] Claudon | Analyse de la tenue en main des couteaux lors d'opérations de désossement dans différents secteurs de la filière viande[END_REF][START_REF] Gorsche | Prevalence and incidence of stenosing flexor tenosynovitis (trigger finger) in a meat-packing plant[END_REF].

Measurements related to the gripping force [START_REF] Gorsche | Prevalence and incidence of stenosing flexor tenosynovitis (trigger finger) in a meat-packing plant[END_REF]) might be of interest, though technical possibilities of assisting gripping do not seem easy to implement [START_REF] Mayer | Effects of an active hand exoskeleton on forearm muscle activity in industrial assembly grips[END_REF], due to the changes in knife gripping type in a single meat cutting task [START_REF] Claudon | Analyse de la tenue en main des couteaux lors d'opérations de désossement dans différents secteurs de la filière viande[END_REF]. The physical workload at the shoulder should also be assessed while evaluating an assisting device, as MSDs are also common at shoulder [START_REF] Nordander | Risk of musculoskeletal disorders among females and males in repetitive/constrained work[END_REF]. More generally, MSDs are multifactorial diseases [START_REF] Bernard | Musculoskeletal disorders and workplace factors : A critical review of epidemiologic evidence for work-related musculoskeletal disorders of the neck, upper extremity, and low back[END_REF]Gouvernement du Canada, 2022;NF ISO 11228-3, 2007). In consequence, the assistance of joint torques must be mixed with other factors to be acceptable as an ergonomic approach.

Finally, sustainability thresholds should be considered with caution. It has to be noticed that the 𝑀𝐴𝐸 method, specifically developed to characterize the onset of upper limb fatigue [START_REF] Potvin | Predicting maximum acceptable efforts for repetitive tasks : An equation based on duty cycle[END_REF], is only one of the various methods for globally assessing the physical risks of MSDs appearance. The choice among these methods has been proven to influence the risk level estimation in some situations [START_REF] Antonucci | Comparative analysis of three methods of risk assessment for repetitive movements of the upper limbs : OCRA index, ACGIH(TLV), and strain index[END_REF]. This choice is still in discussion within the scientific community (ACGIH, 2016; [START_REF] Moore | The Strain Index : A proposed method to analyze jobs for risk of distal upper extremity disorders[END_REF][START_REF] Occhipinti | Updating reference values and predictive models of the OCRA method in the risk assessment of work-related musculoskeletal disorders of the upper limbs[END_REF]. However, in a recent study challenging different criteria for rest requirement assessment, this model was found to require shorter duty cycle times and lighter loads to be sustainable [START_REF] Neumann | A comparison of work-rest models using a "breakpoint" analysis raises questions[END_REF].

CONCLUSION

This work proposed an extensive characterization of biomechanical requirements for a reduced set of professional butchers, and computed the sustainability and assistive torque requirements in case of the potential use of an exoskeleton at the wrist. Five of six subjects in this study exerted predominantly in wrist flexion, resulting in an unsustainable workload. The exertions in radio-ulnar deviations depended on the task and possibly on knife grip used by the subjects. Peak assistive torque values were around 5.6 -5.8Nm in wrist flexion, ulnar deviation, and radial deviation. However, an ideal exoskeleton design should enable adjustable assistance to suit the requirements of different tasks, even if practical issues may enforce the design to be focused on the most unsustainable subtasks to be efficient on the largest population. The sustainability analysis showed that the fast pace of the meat cutting tasks affected subjects more than isolated stressful exertions. Future work should extend the sustainability analysis to more subjects and tasks, potentially also investigating subject-specific strategies for the same task. In addition, the other degrees of freedom of the upper limb recorded during this experimentation should be investigated in a similar manner to give a more complete view of the biomechanical requirements of meat cutting.

SUPPLEMENTARY MATERIAL

The data presented in the following pages correspond the descriptive representation of the biomechanical quantities investigated during the task for each subject individually. For sake of concision, only subject 1 was presented in the article. The first table summarizes general information about the cutting task for each subject.

Figure 1 :

 1 Figure 1: (a) Marker placement on the subject (markers on the right side are shown in orange, while those on the left side and centre are shown in blue).Additionally, markers located on the knife and table (one marker on the table was on the opposite and is not visible in the photo). The coordinate system on the knife shows the force sensor origin. (b) a subject in action during a pork belly cutting trial (left), and a maximal isometric wrist radial deviation strength test (right).

Figure 2 .

 2 Figure 2. Wrist flexion-extension for Subject 1: distribution of joint angles frequencies, and distribution of cutting force, wrist flexion and extension torque and effort depending on wrist flexion and extension angles

Figure 4 .

 4 Figure 4. Knife grips used during the experiments: a.) forward knife grip; b.) edge-in reverse knife grip (cutting edge inwards) ; c.) edge-out reverse knife grip (cutting edge outwards).

Figure 1 .

 1 Figure 1. Wrist flexion-extension for Subject2: distribution of joint angles frequencies, and distribution of cutting force, wrist flexion and extension torque and effort depending on wrist flexion and extension angles

Table 1 . Subject demographics and cutting trials performed. Se x Height 1 (cm) Age (years ) Weight 1 (kg) Dominan t Hand Experienc e (years) Piece cut Repetition s

 1

	S	M	172	50	82.2	Right	27 Pork belly side 1 (PB_	5
	1							1)
	S	M	180	50	76.0	Right	21	Pork belly side 2	5
	2							(PB_2)
	S	M	178.5	47	86.1	Right	27	Pork spare rib (PSR)	5
	3
	S	M	176	40	78.4	Right	11	Pork spare rib (PSR)	5
	4
	S	M	172.5	48	53.6	Right	32	Pork Shoulder (PS)	5xPS then
	5							and	2xBC 2
								Beef collar (BC) 2
	S	M	179.5	21	60.4	Right	5	Beef collar (BC) 2 and	2xBC²
	6							Pork Shoulder (PS)	then 5xPS
	1 Height and weight is with shoes. 2 Not included in this study

  A work cycle was considered unsustainable if 𝑅𝑅 𝑐 (rest required per cycle, computed as the sum of the 𝑅𝑅 𝑖 ) exceeded 𝑅𝐴 𝑐 . If the work cycle was unsustainable, the 𝐸𝑞𝐸𝑓𝑓 of all the exertions were reduced by a constant percentage 𝛿 of their current value such that 𝑅𝑅 𝑐 was equal to 𝑅𝐴 𝑐 . This percentage reduction was converted to assistive torque for each exertion 𝑖, denoted as 𝑇𝑎𝑠𝑠2 𝑖 , by multiplying 𝛿 b 𝐸𝑞𝐽𝑇 𝑖 .

			𝑅𝐴 𝐶 = 𝐶𝑇 -∑ 𝑛	𝑇𝐸 𝑖		(4)
			𝑖=1
	𝑇𝑎𝑠𝑠2 𝑖 = {0,	𝑖𝑓	𝑅𝑅 𝐶 ≤ 𝑅𝐴 𝐶 𝛿 * 𝐸𝑞𝐽𝑡 𝑖 ,	𝑖𝑓	𝑅𝑅 𝐶 > 𝑅𝐴 𝐶
			4.167 + 1/28800	-𝑇𝐸 𝑖	(3)
	Despite each exertion being sustainable in isolation, a work cycle can be unsustainable due to a lack
	of adequate recovery period. The rest available in the work cycle, RAC (s), is computed as the difference

between the CT and sum of the duration of all the 𝑛 exertions of the cycle:

Table 2

 2

	Subjec
	t		Joint Angle		Joint Torque
		Flexion Extension UD	RD	Flexion Extension	UD	RD
			Peak value (°)		Peak value (Nm)
				35			4.2	-6.2
	S1	45 (2)	-27 (3)	(1) -9 (0) 7.9 (1.1) -1.7 (0.7)	(3.1)	(0.8)
				41			3.4	-6.5
	S2	42 (3)	-45 (8)	(1) -5 (2) 9.9 (1.2) -1.2 (0.4)	(1.1)	(1.3)
				27			6.8	-8.5
	S3	41 (4)	-51 (2)	(3) -8 (1) 8.0 (0.6) -1.4 (0.3)	(0.6)	(0.9)
				26	-30		5.5	-4.1
	S4	13 (11)	-57 (2)	(3)	(1) 5.8 (1.4) -3.0 (0.5)	(0.4)	(1.1)
				25	-18		9.7	-1.3
	S5	39 (7)	-59 (2)	(2)	(2) 9.6 (1.3) -1.6 (1.2)	(0.7)	(1.0)
				20	-21		8.4	-4.1
	S6	44 (7)	-64 (3)	(1)	(1) 8.3 (1.2) -5.1 (0.6)	(0.7)	(1.0)
			Average value (°)		Average value (Nm)
				22			0.8	-1.7
	S1	22 (1)	-10 (2)	(1) -6 (1) 2.8 (0.4) -0.3 (0.1)	(0.2)	(0.2)
				23			0.8	-1.7
	S2	13 (2)	-10 (1)	(2) -2 (1) 2.4 (0.2) -0.3 (0.1)	(0.3)	(0.2)
				14			2.4	-3.2
	S3	23 (3)	-31 (3)	(1) -3 (1) 2.7 (0.1) -0.4 (0.1)	(0.1)	(0.1)
				15	-17		1.9	-1.4
	S4	7 (7)	-30 (2)	(1)	(1) 1.7 (0.3) -0.7 (0.1)	(0.3)	(0.3)

. Wrist postures and exertion: mean (+/-SD) of peak and average joint angle and joint torque values, and percentage of the work cycle that the subjects spent between different wrist postures and exertion directions

Yellow cells: joint angles > ergonomic thresholds, respectively

45°, 45°, 20° and 15° for flexion, extension, ulnar and radial deviation (NF ISO 11228-3, 2007)

. UD: ulnar deviation. RD: radial deviation

Table 3 Table 3 .

 33 Rest available in the work cycle RAC , rest required RRC, assistive torques τ required computed 275

	276	in Tass1 (T1) and Tass2 (T2) (Nm), decrease δ in current effort value required computed in Tass2 (%):
	277	individual results, mean μ and standard deviation (SD)
	278
		Flexion	Extension	Ulnar Deviation	Radial Deviation

Table 1 :

 1 Cutting task summary parameters: Cycle time, number of exertions, frequency of exertions, average and peak cutting force and moment. Mean (+/-SD)

				Frequency	Cutting Force (N)	Cutting Moment (Nm)
	Subject CT (s)	Number of exertions	of exertions (/min)	Average	Peak	Average	Peak
	S1	53 (-)	28 (1)	31.4 (0.7)	24.2 (3.2) 79.9 (10.8)	1.2 (0.1)	5.0 (1.4)
	S2	71 (-)	42 (3)	35.2 (2.9)	21.0 (2.1) 104.7 (11.0) 1.0 (0.0)	4.2 (0.6)
	S3	21 (-)	14 (3)	38.4 (8.2)	23.7 (0.8)	58.1 (5.4)	1.4 (0.1)	5.1 (0.4)
	S4	31 (-)	13 (3)	24.8 (5.0)	20.5 (3.8)	57.7 (7.0)	1.4 (0.2)	4.5 (0.5)
	S5	52 (-)	28 (4)	31.6 (4.1)	29.9 (1.5)	90.8 (3.2)	1.8 (0.1)	5.1 (0.4)
	S6	75 (-)	40 (8)	32.2 (6.6)	21.5 (2.5)	67.8 (9.3)	1.6 (0.1)	5.9 (0.4)

ACKNOWLEDGMENTS

This study has been funded by the Région Bretagne, within the frame of the EXOSCARNE 2.0 project, and supported by French government funding managed by the National Research Agency under the Investments for the Future program (PIA) with the grant ANR-21-ESRE-0030 (CONTINUUM project).

The authors thank COOPERL company workers for their participation, and the LAB4i company for their support during the experimentation.


Claire Dumas
email: claire.dumas@irccyn.ec-nantes.fr

Stéphane Caro

Mehdi Chérif

Sébastien Garnier

Benoît Furet

M Cherif

A methodology for joint stiffness identification of serial robots

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

I. INTRODUCTION

Serial robots are mainly used in industry to realize tasks requiring a good repeatability, but not necessarily a good global pose accuracy (position + orientation as defined in ISO9283 [START_REF]Robots manipulateurs industriels -Critères de performance et méthodes d'essai correspondantes[END_REF]) of the robot end-effector (REE). Nevertheless, they start to be used to realize machining operations such as trimming, deflashing, degating, sanding and sawing of composites parts that require high precision and high stiffness. Therefore, robots need good kinematic and elastostatic performances to realize such operations. It is then relevant to pay attention to the robot performances in order to optimize their use for machining operations. In this vein, some research works deal with: (i) the tool path optimization considering both kinematic and dynamic robot performance [START_REF] Kim | Toolpath Generation along directions of Maximum Kinematic Performance; a first cut at Machine-Optimal Paths[END_REF], [START_REF] Matsuako | High-Speed End Milling of an Articulated Robot and its Characteristics[END_REF]; (ii) the determination of optimal cutting parameters to avoid tool chattering [START_REF] Matsuako | High-Speed End Milling of an Articulated Robot and its Characteristics[END_REF], [START_REF] Pan | Chatter Analysis of Robotic Machining Process[END_REF]; (iii) the robot stiffness analysis [START_REF] Nagata | CAD/CAM-based Position/Force Controller for a Mold Polishing Robot[END_REF]; (iv) the determination of robots performance indices [START_REF] Zhang | Machining with Flexible Manipulator: Toward Improving Robotic Machining Performance[END_REF], [START_REF] Nawratil | New Performance Indices for 6R Robots[END_REF], [START_REF] Kucuk | Comparative Study of Performance Indices for Fundamental Robot Manipulators[END_REF]. It is apparent that the robot stiffness is a relevant performance index in robot machining [START_REF] Lecerf-Dumas | La Robotique au service de l'Entreprise: Nécessité de maîtriser le comportement des robots[END_REF]. Accordingly, this paper deals with the stiffness modelling of serial robots as well as the identification of their stiffness parameters. A model based on the conservative congruence transformation (CCT), introduced in [START_REF] Chen | The 6x6 Stiffness Formulation and Transformation of Serial Manipulators via the CCT Theory[END_REF], was used in [START_REF] Alici | Enhanced Stiffness Modeling, Identification and Characterization for Robot Manipulators[END_REF] to identify the stiffness values of the first three actuated revolute joints of a 6R robot. This model was used instead of the classical formula developed in [START_REF] Chen | Conservative Congruence Transformation for Joint and Cartesian Stiffness Matrices of Robotics Hands and Fingers[END_REF], which is only valid for unloaded manipulators. Two methods are presented in [START_REF] Abele | Modeling and Identification of an Industrial Robot for Machining Applications[END_REF] to obtain the Cartesian stiffness matrix (CaSM) of a 5R robot. The best results are obtained with the second method in which both the joint and link stiffnesses are considered. Indeed, when a load is applied mehdi.cherif@u-bordeaux1.fr to the REE, all deformations are considered including those due to the links deformations and/or radial joint stiffness values. Pham et al. [START_REF] Pham | Identification of Joint Stiffness with Bandpass Filtering[END_REF] proposed a method for the identification of joint stiffness with bandpass filtering and based on the robot's dynamic model. This method requires a closed-loop control in addition to real-time actuator currents. In this paper, a method is introduced for the identification of the joint stiffness values of any industrial 6-DOF serial robot. This method aims at evaluating all the joint stiffness values of any 6R serial robot using the model based on the conservative congruence transformation [START_REF] Chen | The 6x6 Stiffness Formulation and Transformation of Serial Manipulators via the CCT Theory[END_REF]. The developed procedure is easy to use and not time-consuming as it does not require any closed-loop control, nor actuator currents and uses few experiments. Besides, the robustness of the method and the sensitivity of the results to measurement errors and to the number of experimental tests are analyzed. The Kuka KR240-2 robot1 [START_REF] Kuka | Dossier de spécification[END_REF] is used as an illustrative example throughout the paper. Section II deals with its kinematic and stiffness modelling. The new method proposed for the identification of the joint stiffness values is presented in Section III. The experimental setup is illustrated in Section IV. Finally, the robustness of the method is analyzed in Section V.

II. KINEMATIC AND STIFFNESS MODELLING

This section deals with the robot kinematic and stiffness models used to develop the proposed methodology for joint stiffness identification.

A. Parameterization and Kinematic Modelling

The 6 × 6 kinematic Jacobian matrix J of the robot is obtained by means of its DHm parameters and the SYMORO+ software [START_REF] Symoro+ | The software package SYMORO+[END_REF] developed in IRCCyN. It relates the instantaneous joint motions to the instant Cartesian motions of the REE, namely,

t = ṗ ṙ = J θ (1)
t is the end-effector twist expressed in the base frame F 0 and composed of its translational velocity vector ṗ and its angular velocity vector ṙ. Moreover,

θ = θ1 θ2 θ3 θ4 θ5 θ6 T (2)
θi being the ith actuated revolute joint rate. The kinematic performances of the robot are analyzed in Section III based on matrix J.

B. Stiffness Modelling

In the scope of this paper the robotic-system response to an applied external load -force and moment, i.e., wrench -under static equilibrium is analyzed through the CaSM of the robot. By means of this matrix, it is possible to determine the linear and angular deflections of the REE when subjected to an applied wrench. The robot deflection is due to both its link and joint flexibilities. However, as mentioned in [START_REF] Zhang | Machining with Flexible Manipulator: Toward Improving Robotic Machining Performance[END_REF], [START_REF] Alici | Enhanced Stiffness Modeling, Identification and Characterization for Robot Manipulators[END_REF], the latter are mainly responsible for the flexibility of serial robots. Accordingly, in order to come up with a simple stiffness model, also called elastostatic model, of the robot, it is assumed that its links are rigid and its joints are linear elastic torsional springs. As a matter of fact, the simpler the elastostatic model of the robot, the easier the identification of its stiffness parameters. The damping is also supposed to be negligible for a matter of model simplicity. As explained in [START_REF] Lecerf-Dumas | Joints Stiffness Identification of Serial Robots Dedicated to Machining Operations[END_REF], this elastostatic model of the robot can be written as follows,

ω = K X δd (3)
with

K X = J -T (K θ -K C ) J -1 (4)
ω is the 6 × 1 wrench vector composed of the forces and torques exerted on the REE and expressed in F 0 . K X is the 6 × 6 CaSM of the robot. δd is the 6 × 1 vector composed of the translational and rotational displacements of the REE expressed in F 0 . J is the kinematic Jacobian matrix of the robot defined in [START_REF]Robots manipulateurs industriels -Critères de performance et méthodes d'essai correspondantes[END_REF]. K θ is the diagonal joint stiffness matrix:

K θ =         k θ1 0 0 0 0 0 0 k θ2 0 0 0 0 0 0 k θ3 0 0 0 0 0 0 k θ4 0 0 0 0 0 0 k θ5 0 0 0 0 0 0 k θ6         (5)
k θi , i = 1, . . . , 6, being the ith joint stiffness value. K C is the complementary stiffness matrix (CoSM) defined in [START_REF] Chen | The 6x6 Stiffness Formulation and Transformation of Serial Manipulators via the CCT Theory[END_REF] and takes the form:

K C = ∂J T ∂θ 1 ω ∂J T ∂θ 2 ω ∂J T ∂θ 3 ω ∂J T ∂θ 4 ω ∂J T ∂θ 5 ω ∂J T ∂θ 6 ω (6)
It is apparent that K C is not null and modifies matrix K X when a wrench is applied to the REE.

III. METHOD FOR THE JOINT STIFFNESS IDENTIFICATION

The method proposed for the joint stiffness identification is illustrated in Fig. 1. First the zones of the robot workspace and joint space in which the robot has a good dexterity are identified. It appears that a good dexterity is required for a good convergence of the procedure. Then, the areas in which K C is negligible with respect to K θ are identified as the stiffness model of the robot can be simplified in those areas. Once good robot configurations are obtained, some of them can be selected in order to perform some tests. For each test, a wrench (force + moment) is exerted on the REE while its displacement (translational and rotational) is measured by means of an external measurement system (Laser tracker).

Identification of the Z ic (i = 1, 2, 3) zones of the joint space, in which the robot has a good dexterity (Subsection III.A)

Identification of the areas of Z ic , where K C is negligible

Z ∈ {θ 2 , θ 3 , θ 4 , θ 5 } / Z = Z ic ∩ Z νp ∩ Z νr (

A. Optimal robot configurations according to kinematic performance

From (4), it makes sense that the numerical determination of the joint stiffness values is highly sensitive to the conditioning number of J. As a consequence, the conditioning number of J is used as a criterion to select appropriate robot configurations for the tests. In the literature, several kinematics performance criteria have been proposed [START_REF] Merlet | Jacobian, Manipulability, Condition Number, and Accuracy of Parallel Robots[END_REF], [START_REF] Caro | Sensitivity Analysis of 3-RPR Planar Parallel Manipulators[END_REF]. Amongst them, the condition number of the Jacobian matrix is widely used to measure the robot dexterity [START_REF] Angeles | Fundamentals of Robotic Mechanical Systems Theory, Methods, and Algorithms[END_REF]. The condition number κ F (M) of a m × n matrix M, with m ≤ n, based on the Frobenius norm is defined as follows:

κ F (M) = 1 m tr(M T M)tr [(M T M) -1 ] (7)
The condition number of matrix J is meaningless, due to the fact that all its terms are not homogeneous; they do not have same units. Therefore, as shown in [START_REF] Li | Geometrical Consideration of Robot Kinematics[END_REF] and [START_REF] Paden | Optimal Kinematic Design of 6R Manipulator[END_REF], the Jacobian matrix can be normalized by means of a normalizing length. Let J N be the normalized Jacobian matrix of the Kuka KR240-2 robot expressed as follows:

J N = 1 L I 3×3 0 3×3 0 3×3 I 3×3 J ( 8
)
I 3×3 is the 3 × 3 identity matrix, 0 3×3 is the 3 × 3 zero matrix and L is the characteristic length of the robot. It is noteworthy here that the condition number is computed only to identify the zones (on θ 2 and θ 3 ranges) where the robot has a good dexterity. It appears that the condition number of J N depends on the characteristic length L, but not the location of the zones.

As the second and third revolute joints are the most influential joints on the translation motions of the end-effector and that the first revolute joint does not affect the robot dexterity, let θ 1 be null and the wrist angles θ 4 , θ 5 and θ 6 be set to 45 • so that the corresponding wrist configuration is far from singularities. Figure 2(a) depicts the isocontours of the inverse condition number of J N based on the Frobenius norm, i.e., κ F (J N ) -1 , throughout the robot Cartesian workspace. The higher κ F (J N ) -1 , the better the dexterity. Likewise, Fig. 2(b) shows the isocontours of κ F (J N ) -1 throughout the robot joint space. The oblique black line characterizes the configurations in which the wrist center is located on the first joint axis. The horizontal black line in Fig. 2 [START_REF] Alici | Enhanced Stiffness Modeling, Identification and Characterization for Robot Manipulators[END_REF] by means of (4) and a nonlinear least square optimization problem. Nevertheless, this method is not robust as it is very sensitive to the starting point of the optimization algorithm. This is why it is relevant to analyze the sensitivity of K X to K C . From (4), K X depends on both K θ and K C . It makes sense that the joint stiffness identification is easier when K C is negligible with respect to K θ . As a matter of fact, (4) is

θ 3 Z 1c 0 • to 110 • -245 • to -170 • Z 2c 0 • to 25 • 0 • to 29 • Z 3c 100 • to 146 • 0 • to 29 •
reduced to the following equation when K C is negligible with respect to K θ :

K X ≈ J -T K θ J -1 (9)
Consequently, the influence of K C on K X is analyzed based on the robot translational and rotational displacements. For that matter, two indices were defined in [START_REF] Lecerf-Dumas | Joints Stiffness Identification of Serial Robots Dedicated to Machining Operations[END_REF] to analyze the influence of K C on the robot translational and rotational displacements. Those two indices are denoted ν p and ν r and defined as follows:

ν p = δp KC -δp KC max δp KC , δp K C (10)
and

ν r = max{|δr xKC -δr xKC |, |δr yKC -δr yKC |, |δr zKC -δr zKC |} (11)
where δp KC and δp KC are the point-displacement of the REE obtained with (3) and ( 4) assuming that matrix K C is not null and null, respectively. δr xKC , δr yKC , δr zKC and δr xKC , δr yKC , δr zKC are the small rotations of the REE about x 0 , y 0 and z 0 axes obtained with (3) and ( 4) assuming that matrix K C is not null and null, respectively. Figures 3(a)-(b) illustrate the isocontours of ν p and ν r throughout the robot joint space (θ 2 , θ 3 ). Several areas appear, but ν p and ν r values remain very small as ν p ≤ 0.016 and ν r ≤ 0.025 deg throughout all the robot joint space. Nevertheless, let Z νp and Z νr be the zones in which the influence of K C on K θ is a minimum with regard to ν p and ν r , respectively. To come up with good results, the robot configurations have to be chosen in Z νp and Z νr .

C. Evaluation of the joint stiffness values

From (4) and assuming that K C is negligible with respect to K θ thanks to an appropriate robot configuration, (3) can be rewritten as

ω = J -T K θ J -1 δd (12)
Hence, the 6 × 1 robot end-effector displacement vector δd takes the form

δd = JK θ -1 J T ω (13)
From ( 13), it turns out that

δd =           6 j=1 x j J 1j i=6 i=1 J ij ω i . . . . . . . . . . . . 6 j=1 x j J 6j i=6 i=1 J ij ω i           (14)
x j being the jth joint compliance, i.e, x j = 1/k θj , j = 1 , . . . , 6. Let the joint compliances 6 × 1 vector x be

x = 1/k θ1 1/k θ2 1/k θ3 1/k θ4 1/k θ5 1/k θ6 T (15)
By isolating the components of vector x in ( 14), the joint compliances can be expressed with respect to the robot EE displacements as follows:

A x = δd ( 16
)
A can be derived from ( 4) and expressed as follows:

A ij = J ij 6 k=1 J kj F k ( 17
)
A ij is the term of the ith row and the jth column of matrix A. F 1 , F 2 and F 3 are the components of the force and F 4 , F 5 , F 6 are the components of the moment exerted on the REE along x, y and z axes and expressed in F 0 . It is noteworthy that a 6 × 1 wrench vector, a 6 × 1 REE displacement vector and a 6 × 6 A matrix are evaluated for each test. The equations system ( 16) becomes overdetermined when several tests are taken into account.

Assuming that n tests are considered, n > 1, matrix A is not of size 6 × 6 anymore but of size 6n × 6. As matrix A is not square anymore, the joint compliance vector x can not be calculated with [START_REF] Symoro+ | The software package SYMORO+[END_REF]. The joint stiffness values are obtained thanks to a minimization of the Euclidean norm of the approximation error of equations system [START_REF] Symoro+ | The software package SYMORO+[END_REF]. As a result,

x = A T A -1 A T δd (18)
Several tests can be considered with this approach in order to evaluate the joint stiffness values. Accordingly, if all joints are stressed substantially at least once among all the tests, their stiffness value will be accurately evaluated.

IV. EXPERIMENTAL SETUP

As shown in Fig. 4 the experimental setup is composed of the robot, a laser tracker, retroreflectors and a mass connected to the end-effector by means of a chain and a spring balance. The latter helps the user evaluate the wrench exerted on the REE. The repeatability of the KR240-2 robot is equal to ±0, 12 mm and its workspace radius is about 2700 mm [START_REF] Kuka | Dossier de spécification[END_REF].

V. JOINT STIFFNESS VALUES

A. Robustness of the method

As the joint stiffness identification requires the measurement of the EE's displacement, the repeatability of this deformation has been checked. The mean uncertainty (i.e. 3 times the standard deviation) represents about 1.3% of the measured deformation, which is acceptable. In order to analyze the robustness of the method, ( 16) has been solved by means of (18). Figure 5 illustrates joint stiffness values k θ2 , k θ3 , k θ4 , k θ5 and k θ6 obtained with this method as a function of the number of tests n, n = 1, . . . , 23. Let us note that the n sets of tests are chosen randomly amongst the 23 available ones and a test can not appear two times in a given set. We can notice that the larger the size of the set of tests, the better the convergence of joint stiffness values and the more reliable the results. It is apparent that the variations in the obtained joint stiffness values is reasonably small, i.e., the method for the joint stiffness values identification is robust, as long as the number of tests considered for their evaluation is higher than six. Let us note that this conclusion was found in [START_REF] Lecerf-Dumas | Joints Stiffness Identification of Serial Robots Dedicated to Machining Operations[END_REF], but was only validated by means of numerical simulations.

B. Sensitivity of the results to measurement errors

To analyze the sensitivity of the results to measurement errors, all parameters defining the 23 tests have been modified by considering errors in the initial parameters. Due to the experimental setup, several sources of errors can be detected:

• The Faro Tracker Laser uncertainties, which are about ±0.03mm, in the distance between the retroreflector and the source.

• The error in the spring balance, which is ±0.1kg

• The error in joint coders, which is ±0.01 deg The errors in all the parameters are supposed to follow a normal law. As a consequence, Table II gives the nominal stiffness value of each joint as well as their error. For instance, the stiffness value of the second joint is equal to 6.6 10 6 Nm/rad while its evaluated error is about ±1 10 5 Nm/rad, i.e., 8% of the nominal stiffness value.

In Figures 6 and7 the tests are organized with respect to the zones Z 1c , Z 2c and Z 3c defined in Table I. Moreover, the line segments around the circles depict the error in the calculated REE displacement due to measurement errors. The longer the segment, the higher the error in the calculated REE displacement. It appears that errors in the calculated REE displacement are quite smaller than the displacement itself, namely, the joint stiffness identification is with respect to measurement errors.

Over the 25 tests, the average difference between the theoretical and measured displacements is about 0.1 mm, and the maximum gap is equal to 0.6 mm. The method can predict about 80% of the displacement of the EE. In order to explain the un-corrected 20% of the displacement of the EE, the link stiffnesses have been assessed. As links 2 and 3 are the largest ones, their flexibility should be the main source of errors in addition to the joint compliances. Consequently, their deformations under several loadings have been measured and compared to the EE displacement. Results show that deformations of link 3 are responsible for a maximum of 4.8 % of the EE displacement (when the link is horizontal and the load on the EE is at the maximum). As link 2 is far form the EE, the influence of its deformations on the latter is more important: maximum 21 %. So a maximum of 25 % of the EE displacement, depending on the robot configuration and applied load, can be due to link flexibilities. Therefore, it is a limit of the identification method proposed in this paper. Figure 7 illustrates the calculated and measured rotations of the REE about x, y and z axes and expressed in F 0 . The circle denotes the calculated, i.e., theoretical, rotation of the REE while the cross denotes its measured rotation. Over the 25 tests used to check the model, the average difference between the theoretical and measured rotations is about 0.005 deg around x and y, and about 0.01 deg around z. This gap is due to the fact that the sixth actuated joint was not as stressed as the fourth and fifth ones.

Z 1c Z 1c Z 2c Z 2c Z 3c Z 3c
Z 1c Z 1c Z 1c Z 1c Z 1c Z 1c Z 2c Z 2c Z 2c Z 2c Z 2c Z 2c Z 3c Z 3c Z 3c Z 3c Z 3c Z 3c (

VI. CONCLUSIONS AND FUTURE WORKS

A. Conclusions

This paper dealt with a new methodology for joint stiffness identification of serial robots. First the kinematic model is obtained in order to determine the optimal robot configurations according to the condition number of its kinematic Jacobian matrix. Then, its stiffness modelling was presented by means of its Cartesian stiffness matrix K X and its Complementary stiffness matrix K C . To simplify the identification of the joint stiffness values, the robot configuration tests are optimized in order to minimize the influence of the Complementary stiffness matrix. This approach is original and avoids any least square minimization that turned out to be often used but highly dependent on the starting point. The experimental setup and the experimental procedure were also presented. The Kuka KR240-2 robot was used as an illustrative example throughout the paper. The proposed methodology provides a good approximation of the real joint stiffness values of serial robots. It turned out to be robust, namely, few sensitive to measurement errors. The advantages of the method are its robustness, its few time consumption, its adaptability to any serial robot, and its ease of use.

B. Future works

Firstly, it is noteworthy that in the presented method the links and transmissions of the robot were supposed to be quite stiffer than the joints and not known as it is usually the case for industrial robots. Future works deal with the improvement of the proposed methodology in order to identify the link stiffnesses in addition of the joint stiffnesses of industrial robots. Secondly, at the moment, if the wrench applied on the REE is known, it is possible with the proposed methodology to predict about 80% of the EE displacement. All tasks that require both high precision and high stiffness, such as trimming, deflashing, degating, sanding and sawing of composite parts, can be improved by the proposed methodology. It is for example possible to optimize the task placement in the reachable workspace with regards to stiffness performance of the robot. Finally, future works also aim at determining the elastodynamic model and performance of the robot in order to predict its behaviour during high speed machining operations. Moreover, the dynamic parameters of the robot will be identified in addition to geometric and stiffness parameters.

VII. ACKNOWLEDGMENT

The experiments were conducted with the help of FARO company that is dutifully acknowledged.

  Subsection III.B) Selection of a robot configuration in Z with respect to K θ , i.e., Loading of the robot end-effector (forces and moments) Measurement of the displacements (translations and rotations) of the end-effector (Section IV) Evaluation of the joint stiffness values (Subsection III.C) No Yes Is the number of required tests reached? Measurement of the end-effector pose

Fig. 1 .

 1 Fig. 1. Joint stiffness values identification

Fig. 2 .

 2 Fig. 2. Contours of the inverse condition number of J N : (a) in the robot Cartesian workspace and (b) in the joint space (θ 2 , θ 3 )

Fig. 3 .

 3 Fig. 3. Isocontours of (a) νp and (b) νr in the robot joint space (θ 2 , θ 3 )

Fig. 4

 4 Fig. 4. Experimental Setup

Fig. 5 .

 5 Fig. 5. Joint stiffness values as a function of the number of tests used for their evaluation.

Fig. 6 .

 6 Fig. 6. Theoretical and measured REE translational displacements for all the tests (mm): (a) Validation with the tests used for the joint stiffness identification; (b) Validation with the other tests

Fig. 7 .

 7 Fig. 7. Calculated and measured rotations of the REE expressed around x, y and z axis of F 0 (deg): (a) Validation with the tests used for the joint stiffness identification; (b) Validation with the other tests

  (b) characterizes the singularities in which the arm is folded. The choice of appropriate robot configurations for the identification of the joint stiffness values can be made from Figs.2(b), namely, θ 2 and θ 3 should be chosen in the light areas, named Z 1c , Z 2c and Z 3c in TableI.

B. Optimal robot configurations according to the influence of K C on K X

Joint stiffness values are evaluated in

TABLE I OPTIMAL

 I

ROBOT CONFIGURATIONS DEFINED IN THE JOINT SPACE Zone θ 2

The Kuka KR240-2 robot used for experimental tests is located in Université de Bordeaux 1