Abstract
BACKGROUND:
One of the aspects that influences the sitting comfort is the distribution of the pressure applied to the skin by the seat surface. In the scientific literature, many studies show experimental activities in order to evaluate the influence of pressure distribution at the seat-human interface on the comfort evaluation. The main limitation in seat design is based on the difficulties to predict the contact pressures distribution without prototypes because of the complex interaction among body muscles, wearing, human’s anthropometric characteristics, shape and materials of the seat. Moreover, the same human can assume different postures on the same seat, and different people, seated on the same chair, can assume different postures even if they have the same anthropometric percentile.
OBJECTIVE:
The aim of this study is to propose a mathematical model evaluating interaction loads between human segments and seat segments.
METHOD:
In this model, a human body represented by 8 segments is placed on a 6 segments seat with posture dependent on seat segments and on position of the coccyx on seat and feet on floor. Human segments can be configured in length and weight and friction between body and seat is considered. A model validation study based on an experimental comparison with contact pressures is also presented.
RESULTS:
The experiment showed that there is a remarkable recursion of some stress values of the articular joints of the pelvis, hip and knee. By imposing these values in the calculation model, it is possible to determine, for each chair configuration, which postures will be assumed by a person, and to make a preliminary assessment of the level of comfort possible.
Physiological and postural comfort
The word “comfort” refers to a state of well-being perceived by an individual during any activity, and involves factors such as temperature, brightness, noise, ventilation, assumed posture, level of anxiety, level of fatigue, or anything that alters human physiology. The Vink-Hallbeck model [1] of comfort perception shows how the factors that act on comfort can be grouped into few large categories that refer to external aspects during the use of the product, to the product, and to the subjectivity of the user.
The perception of the comfort of a chair depends, in an objective manner, on the human assumed posture that depends, in a still objective manner, on how the chair is designed, but also on the subjective way in which the person decides to sit.
Another fundamental factor is the duration of the interaction: there are many studies [2] between the micro-movements of the person and the level of perceived discomfort. Macro movements are instead a consequence of the type of human activity on the chair, but also a sign of the need to relax muscles that have guaranteed the posture up to that moment or to lighten the level of pressure localized in the areas of contact that causes a reduction in blood circulation. Hence, a prediction model of posture must take into account that there is not a unique comfortable posture but a range of satisfactory postures.
The comfort of a chair is a topic of considerable importance in the field of transport, but not only, considering that each of us carries out many activities (working, eating, studying) sitting on a chair or relaxing sitting on armchairs. The design of a chair, whatever it is, must adequately predict the level of comfort perceived by the user.
Currently it is difficult to predict the comfort of a chair and, in most cases, experiments with prototypes of the products are needed to try to overcome the effects of experimental reliefs on the perception of comfort [3]. There are two main lines of thought: the first believes that the factor to consider, in the search for constructive geometry, is the contact pressure while the second directly measures the assumed posture of the various parts of the body.
In the first case we focus mainly on the back of the thigh and on the buttocks, areas in which most of the load is discharged [4–7]. We try to limit the average pressure as much as possible by increasing the contact surface. For example, the study by Noro et al. [7] starts from the idea that from the posture assumed by those who practice Zen meditation, which is maintained long time, indications can be obtained for the design of a session for a specific application. A chair was created that reproduces the same contact pressures obtained on meditation cushions that optimize posture by providing support to the lumbar area, taking into account the differences linked to surgical activity.
In the case of posture analysis, the focus is mainly on the position of the back, legs and head [8–17]. Figure 1 shows how excessive inclinations generate shear stresses on muscles and skin that limit, once again, the passage of blood. The inclination of the back slightly affects the extent of the shear stress, while it greatly influences the geometry assumed by the spine, with minor consequences such as headache, shortness of breath, pain in the neck, wrists, back and vision problems, as well as real diseases: dorsal hypercyphosis, epicondylitis, carpal tunnel, loss of elasticity of the optic nerve, myopia. The most deleterious cases are those with inclined chair.

Shear stress vs. chair angles [7].
A previous study indicated that 3 hours of seated position (body sitting) without interruptions lead to a reduction in the physiological vasculature in the body by 33%(reduction in the number of vessels that allow the passage of blood) and that this prolonged position is associated with an increase in cardiovascular diseases [18]. It can therefore be said that assuming a correct posture is essential to avoid the aforementioned back problems and high cutting efforts, but for the purpose of comfort it is also necessary to distribute the loads in the best possible way and find configurations in which the muscles are activated the least possible [7].
The aim of this work is to study the relation among posture, articular moments and comfort through a mathematical model evaluating interaction loads between human and chair. This model is based on a static analysis, in which the body and the chair are seen in profile and are considered as set of segments on a two-dimensional plane; human articulations are represented by joints that allow rotations but not translations. The posture depends on the positions of the coccyx on seat and of the feet on floor. A self-developed Python program was used to implement the model and the results were compared to experimental data, made using a pressure pad. It has been found a relation between anthropometry of a human and the moments of three joints (sacral joint, hip and knee) imposed by muscles activation to sit in comfort.
There are different kind of chair, depending on the context in which they are used. They differ in various aspects but the one of greatest interest to us is the geometry. An automotive seat follows the body’s shape from the trunk downwards leaving the legs free; the chaise longue of a psychologist also supports these one, while a generic kitchen chair usually does not provide head support.
We used a scheme that allows us to characterize every kind of chair; they can be used up to six segments: headrest, backrest, upper part, backrest, lumbar part, seat, support for legs and footrest. The inclination compared to the floor and the length of the generic segment “i” of the chair are respectively equal to
To simulate in the best way the different assumable postures, a human body has been schematized with 8 segments (Fig. 2): the head and neck, the upper trunk, the lower trunk, the buttock, the thigh, the leg, the sole of the foot and the toes.

Schematisation of a human body with 8 segments: 0 –head and neck; 1 –upper trunk in contact with the backrest; 2 - trunk part with no contact; 3 –leg part always in contact (buttock); 4 –upper leg (thigh); 5 –lower part of the leg; 6 –sole of the foot; 7 - toes. The blue circles are the articulation (joints).
The reason to consider buttock and thigh separately (two different segments) allows us to analyse also that cases in which, for the moderate height of the seat, instead of stretching out foot forward the thigh are lifted from the sitting plan: the buttock, in these cases, however remains in contact. The same goes for the foot, it is also possible to vary the foot position that changes depending on whether a person is sitting with legs forward/upright or backwards (Fig. 3), so the forepart of the foot is always in contact with the respective support (footrest or floor). The weight and the height of the considered person are divided on the various segments based on percentiles of Table 1 to obtain weights

a) Foot totally in contact (legs forward/upright); b) Foot in contact but with the sole lifted (legs backwards).

Body segment parameters.
Percentile weights and lengths of the various parts of the body [19]
As said, some segments have been divided (foot, upper leg, trunk); their lengths and weights are fractions of the total value that pertain the overall segment (Table 1). It has been seen that, generally, toes have length and weight equal to 1/3 of those of the whole foot. The weight of arms is summed to the one of the upper trunk whereas the weight of thighs, legs and feet is counted twice. The trunk’s length is divided into the upper and the lower trunk part in proportions 1/3 and 2/3 to make difference between the lumbar and the thoracic parts.
Each segment is subject to the loads coming from the joints

Loads on a segment.

Loads conversion from segment i to segment i + 1.
The inclination of the generic anatomical segment compared to the floor has been called
The weight W (i) of the various parts of the body acts in the middle of the segments at a distance from the respective joint B (i) equal to
Depending on the size of the body segments and on the chair configuration, for those anatomical segments that eventually rest on the chair, the overlapping parts between chair segments and body segments are considered as contact sections.
For a body segment in contact the reaction force
The body posture depends on where the person chooses to position the buttock on the sitting plane; so, the position of the other parts of the body is subsequently defined, also in relation to chair geometry. If the posture obtained is not satisfactory in terms of comfort, the position is remodulated compared to the seat until the most comfortable posture is reached.
The model calculates the posture starting from the seat coverage percentage which, multiplied by the length of the seat segment, provides the contact line

Back on seat parameter.

Human seated at the extreme of the chair.
The second postural parameter imposed is the leg angulation
Depending on the upper trunk position and/or the headrest configuration, the head angle and the contact area are calculated. Three possible scenarios are identified (Fig. 9): a) Trunk longer than the backrest and headrest backwards with an angle greater than 45 °; b) Trunk longer than the back and headrest backward with an angle smaller than 45 °; c) Trunk shorter than the backrest, headrest forward, the contact occurs only with the top of the head.

Samples of head posture.
Once the posture is defined and the extensions of the contact surfaces between the body and the chair segments are calculated, it is calculated the positions lR (i) in which are applied the contact forces R (i) . In particular, they act in the middle point of the contact length, defined as part of the chair section on which an anatomical segment or part of it rests. For each body segment i:
if the contact length is exactly equal to LengSed (i) , the part of the chair is occupied for the 100%. This means that the anatomical segment’s length is equal or greater than the one of the respective sections of the chair (LengBodySeg (i) ≥LengSed (i) ), and the contact starts from the joint B (i) to which reference is made. Then lR (i) = LengSed (i) /2. if the contact length in less than that of the chair section, we can have: Anatomical segment’s length is smaller than that of the respective chair section (LengBodySeg (i) ≤LengSed (i) ) and the contact starts from the joint B. As the latter is the reference point for lengths, the distance from it is null and we have lR (i) = LengBodySeg (i) /2: Anatomical segment’s length is smaller than that of the respective chair section (LengBodySeg (i) <LengSed (i) ) and the contact does not start from the joint B (i) ; in this case, to the latter relationship, it must be summed the distance between the joint B (i) and the starting point of contact; Anatomical segment’s length equals or is greater than that of the respective chair section (LengBodySeg (i) ≥LengSed (i) ) but the contact takes place at a not null distance from B (i) ; to the chair section’s length it must be subtracted this distance; R (i) is applied at half of that value.
Once the posture and the contact forces position are determined, we can analyse loads and equilibrium conditions considering weights and frictional forces between the foot and the footrest and between the body segments and the corresponding seat segments (Fig. 5).
For each segment, all the equilibrium conditions are calculated compared to the local reference system, imposing that in the joints between segment and segment it must result the equality of the resulting forces and moments on the two sections. The segments head and toes have both a free extreme where forces and moments assume null value. The frictional force is Ra (i) = Rn (i) *Mu (i) .
From the count of equations and variables, they result to be indeterminate 6 values for which it is necessary to make some hypotheses: we decided to evaluate 4 hypothesis: we decided to evaluate 4 hypothesis: to impose null moments condition as ideal condition: not-natural results obtained because, to guarantee equilibrium, the chair and the floor/footrest should attract the body to obtain sufficient friction forces not to slip the human from the chair. to impose as ideal condition the one in which all moments are equal: each joint is used to sustain the weight of the body parts above him, so each joint has a different capacity to exercise moments compared to the others. impose known values in place of unknown moments but we do not know which values to use. make a study of moment’s variability in a wide range: this option contain the previous ones.
Since the study of the interaction between chair and posture to predict the comfort level of a seated person is an open problem without a unique solution, because for the same human on the same chair we observe very different postures, we decided to make a study of moment’s variability on different seated postures.
Joint’s moment analysis
To perform the joint’s moment analysis, an experimental phase was accomplished comparing pressure pad results with model results in order to find any recursion of moment values of the articular joints in assumed postures, highlighting comfortably seating drivers.
Knowing the comfort needs of a seated person means knowing which inclinations the various parts of his body need to assume and in which area he needs to have more support to reach a comfortable seating. This allows designing of any type of seat to accommodate a human in order to optimize it from the comfort point of view.
Experimental setup
The experimental phase implicated the use of the chair shown in Fig. 10 and a mat measuring the contact pressure. The mat is made of 480 sensors, where a single sensor dimension is 2×2cm2, distributed in a 20×24 matrix; we made an acquisition every 0.04 s so we have 1500 pressure states per minute. In order to limit the effects of initial transient phase and typical measure fluctuation in time, for each sensor a mean of values in 30 s was made starting from the second 15th.

Chair (left) and model of chair (right) used in experimental tests.
We calculated the mean pressure on the mat and the contact area extension considering only active sensors, where a single sensor dimension is 2×2cm2. The product of mean pressure and contact area is the total force acting on the seat by buttocks and legs. It can be compared with the normal reaction Rn (seat) , explicated by the seat on the said segments (Rn (seat) = Rn (3) +Rn (4) ), calculated by the model.
The tests were carried out on 17 different subjects; the pressures exercised on the sitting plan by each of them were measured for three different knee inclinations: 1) 90 °; 2) legs forward in the most comfortable position; 3) back legs still in the most comfortable inclination. Each subject was photographed, and the position of the pelvis compared to the chair and the values of the knee angles were taken from the photo.
As example, for 4 subjects and for knee angle values for vertical leg, stretched leg and leg under seat are presented in Table 2 the R mat mean and the ranges of results (minimum and maximum values) of the acquisitions made with the pressure mat.
Characteristics and experimental data for the four subjects
The mathematical model was applied varying the moments applied to the knees, hips and sacral joint from 0 to 100 kg*cm with step 5kg*cm, thus analysing 21×21×21 = 9261 possible combinations. Table 3 shows part of simulation results for one of considered subjects.
Load conditions of the joints corresponding to the experimental data for Subject 1
There is not headrest, so the head-neck segment is always upright (section 0, LengSed (headrest) = 0 cm); the backrest allows the contact only for the part indicated in yellow in the previous imagine (section 1, LengSed (backrest) = 26 cm); the blue part is, instead, the one where there is no contact because it’s empty (section 2, LengSed (lumbarsupport) = 12 cm).
The sitting plan, indicated in black, corresponds to the section 3 of length LengSed (seat) = 46 cm; the sitting plan is 41 cm from the ground, and this distance represents the section 4 (LengSed (supportforlegs) ) on which, however, there is no contact.
The footrest is missing so the section 5, on which the foot lean, correspond to the floor. His length is set as equal to that of the foot (sole + toes): LengSed (floor) = LengBodySeg (6) +LengBodySeg (7) .
The inclinations of the seat chosen, compared to the floor, are: Segment 0: absent; segment 1:88 °; segment 2: absent; segment 3:0 °; segment 4: it is represented by a distance but physically does not provide support; segment 5 : 0 °.
The friction coefficients have been set, hypothetically, all equal to 0.3 except for that of the foot, chosen equal to 0.4.
The experimental data obtained from the mat are compared with the sum of the normal force acting on the buttocks (Rn (3) ) and of that acting on the thigh (Rn (4) ) provided by the model. In particular, all the combinations of joints moments that result in the load value on the seat corresponding to the measured value with a certain tolerance (±3 kg corresponding to the load oscillations during the acquisition interval) have been identified.
Among these, the combinations for which the component relative to the thighs and that relating to the buttocks are equal (unless of the same tolerance value) have been identified since this condition corresponds to a better pressure distribution which induces greater comfort or less discomfort.
The moment applied to the sacral joint conditions the other two, therefore depending on the activation of the back there will be a consequent activation of the leg muscles.
Load conditions of the joints corresponding to the experimental data
Load conditions of the joints corresponding to the experimental data
Since the sacral and hip joints have the same axis of rotation and must both hold the weight of the upper part of the body, we assume that in conditions of comfort they exercise a similar level of effort. In this hypothesis the results are further filtered by choosing the solutions for which |M sacral –M hip |≤10 kg*cm, doubling the calculation step of the moments.
From the analysis of the data it results that, in the hypotheses carried out and comparing the simulations with the experimental results, we tend to always assume the same values of articular stress, which grow linearly in proportion to the weight, as shown in the Table 4, independently from the position of the legs stretched forward, straight or placed under the pelvis.
This is an important result because it means that the moments exercised by the joints follow some pattern. So, to find those schemes, the moment of the three reference joints have been plotted in function of the body parameters, weight and height, as shown in the Fig. 11. It can be seen that the moment on the sacral joint and on the hip vary about in a linear way with the body parameters: they can be approximated with linear functions; the moment of the knee, instead, seems to vary in a more chaotic way, but looking at the dependence on the height in the Fig. 12, it is clearly an exponential function (quadratic variation). No significant results can be found respect to the BMI index.

Moments of sacral joint, hip and knee in function of body parameters.

Moment of the knee in function of the height of the human.
A mathematical two-dimensional model has been developed able to determine the posture assumed by the human body on a chair and how the chair sustains the weight of the body. The human body is represented by 8 jointed rigid segments whereas the chair is represented by 6 rigid segments, so local deformations are not considered. This model allows the evaluation of many combinations of human joints moments able to keep a seated posture and the estimate of contact pressure on the sitting plane.
From the comparison between the model and the experimental data, we observed that there are different combinations of moment values which allow to maintain the same posture. This could explain also why a seated human tends to slightly change his posture in time or to differently contract muscles to promote cardiovascular circulation.
The experimentation allowed to highlight that there is a remarkable recursion of some stress values of the articular joints of the pelvis, hip and knee. By imposing these values in the calculation model, it is possible to determine, for each chair configuration, which postures will be assumed by a person, and to make a preliminary assessment of the level of comfort obtainable.
Conflict of interest
None to report.
