The Methods of Determining the Centre of Gravity of a Tilting Body on the Upper Ankle Joint and Weighing the Feet of a Living Human

Featured Application

Determining the correct position of the centre of gravity of the whole body and the leaning body can be very important in developing rehabilitation methods in medicine and training techniques for sports and military purposes.

Abstract

(1) Background: This paper focuses on the issue of examining the centre of gravity (CoG) of the entire body and its tilting segment at the upper ankle joint. (2) Methods: A custom-built measuring station was used to determine the CoG of the tilting body, and measurements were carried out on six individuals. Based on the theory of torques, the general centre of gravity, the centre of gravity of the tilting segment and the centre of gravity of the feet were calculated. (3) Results: A novel method was developed for determining the CoG of a tilting body at the upper ankle joint and for indirectly “weighing” the feet of a living human. It was demonstrated that the general body CoG and the CoG of a tilting segment are two distinct points. Based on the developed method, the centres of gravity of individual body parts were determined.

1. Introduction

In many studies, the terms centre of gravity or centre of mass are used interchangeably. These concepts are often confused and usually equated [1]; therefore, for clarity, both concepts and their relationship are explained below. The centre of gravity of a body (CoG) is defined as the point at which the resultant of the gravity forces of all body elements is applied, and the total gravitational moment acting on the body is zero, which causes the body to be in a state of equilibrium. This point is independent of the body’s position but depends on its shape and may lie outside it. Changing the shape of the body is equivalent to changing the position of the CoG. The centre of body mass (CoM) is a more general concept than the centre of gravity because a body always has a centre of mass regardless of whether it is in a gravitational field or not. It is a point that behaves as if all the body’s mass were at that point and as if all external forces acting on the elements of that body were applied to that point. If a force acts on this point, the body will accelerate linearly but will not rotate. The interchangeable use of the terms CoG and CoM in the context of research on the human body results from the fact that for objects of uniform density, in a uniform gravitational field, the centre of gravity coincides with the centre of mass. The smaller body’s size justifies this approximation in comparison to the size of the Earth and the distance of this body from its centre. Currently, there are several methods known for determining the centre of gravity of the human body in practice. These are as follows:

• The method of balancing the body (one-sided lever method) through placing horizontally on a special platform supported at one point at the level of the plantar side of the heel. The overall centre of gravity of the body measured in this way was first described by E. du Bois-Reymond in the 19th century [2].
• Dynamic method—movement analysis, which uses camera and marker systems (e.g., Vicon system, BTS) to track body movement. The software analyses the movement of individual body segments and determines the position of the centre of gravity in different phases of movement [2,3,4,5].
• Segmental weighing method, in which the mass and position of the centre of gravity of individual body parts (head, torso, limbs) are determined based on special anthropometric tables. Mathematical formulas are then used to determine the centre of gravity of the entire body [6].

The human body can assume various positions, so the CoG may change its position and even be located outside the body, for example when a person is bent over and reaches for their toes [7]. In an erect human, the general CoG is located at a point where the human body, when placed horizontally on a platform (equal to the length of a human body), supported at this point, balances itself. After carrying out a series of population measurements, it was assumed that the general CoG is located in the midline of the body, just in front of the second sacral vertebra at an average height of ~57% of a man’s height and ~55% of a woman’s height. The general variation in the human population ranges between 56 and 58% body height [2,8]. The line of gravity runs through the centre of gravity of the body, which, when viewed from the side, is located very slightly behind the heads of the femurs, and frontally runs through the centre of the sacrum and perpendicular to the ground at a point equidistant from the two heads of the femur [9,10]. This position changes with body structure, posture, age, and gender [11,12]. Infants have the highest general centre of gravity, which lowers in children and is lowest in adults. The location of the general CoG is related to the different distribution of weight in the human body; for example, men have a more developed and muscular shoulder girdle. Women have a more developed hip belt. In a young child, the general CoG is located higher than in an adult due to the disproportionately large mass of the head and smaller mass of the lower limbs. Sports activities also influence the change in the general location of the CoG. A gymnast with well-developed shoulder girdles and upper limbs may have a higher general CoG than a soccer player with well-muscled lower limbs [13].

Incorrect positioning of the general CoG causes several postural abnormalities and related clinical consequences [9]. In slim people with a poorly developed chest, the general CoG will be shifted towards the lower limbs. In people with high muscle mass in the arms and chest, the general CoG will shift towards the head, passing behind the line of the anterior superior iliac spine [13]. It has been shown that a non-physiological shift in the general CoG contributes to various pathologies. For example, patients suffering from chronic low back pain tend to have an excessively posteriorly positioned CoG [14]. They have reduced muscle strength in the lumbosacral spine in the upright position with a concomitant tendency to reduce lordosis. This abnormality increases the demand on muscles responsible for postural control to maintain the CoG projection of the tilting body within the centre of the base of support.

Accurate determination of the CoG in a dynamically moving human body is also crucial in military training programs. Proper weight distribution of equipment ensures optimal gravitational torque, balanced by efficient muscle energy use, while minimizing overload changes in the foot joints.

The paper presents a new approach for analysing the body’s centre of gravity. It highlights that the dynamics of the human body necessitate revising the current methods for determining the centre of gravity. It was showed that the body segment leaning on the upper ankle joint and supported on the foot has a higher centre of gravity than the general CoG. This is related to the generation of greater pressure forces on the upper ankle joint, as well as greater gravitational moments. Thus, defining the accurate centre of gravity of the tilting body is fundamental to understanding the interplay of torques in the human body [1]. This determines the correct pointing of the gravitational force arm concerning the joint axis of rotation, and therefore also the gravitational moment, which is counterbalanced by muscle moments.

2. Materials and Methods

2.1. Description of the Measurement Station

To measure the centre of gravity of the body, the one-sided lever method was used, in which the beam is supported at one point and can rotate around it. The lever is set into rotation by the torques acting on it. If these moments balance each other, the lever is in equilibrium. This property of the lever was used to determine the general centre of gravity of the body and the centre of gravity of the leaning body on the axis of the upper ankle joint. The human body, positioned on a rigid wooden board, and reaction forces were measured at the level of the top of the head (Figure 1A–C). During each measurement, the human arms and hands were placed alongside the body. Body weight was recorded using an electronic scale with a range of 0 to 100 kg.

Measurements were made in three situations:

(A)

A human body placed on a board with the support point at the level of the tuberosity of the calcaneal bone on one side and, on the other, the reaction force (F₁) was measured at the level of the top of the head using a scale. The feet were placed in the zero position (Figure 1A). In this way, the general centre of gravity of the body was determined.

(B)

The human body was placed on a board with the support point at the level of the axis of the upper ankle joint, while the weight of both feet was removed by independently supporting the feet at the level of the tuberosity of the calcaneal bone. The reaction force (F₂) was measured at the level of the top of the head using a scale (Figure 1B). In this way, the centre of gravity of the leaning body part on the axis of the upper ankle joint (when the body was in upright position) was determined (method 1).

(C)

The human body was placed on a board with the support point at the level of the axis of the upper ankle joint, with the feet hanging freely on the edge of the board. The reaction force (F₃) was measured at the level of the top of the head using a scale (Figure 1C). In this way, the centre of gravity of the leaning body part on the axis of the upper ankle joint (when the body was in upright position) was determined (method 2).

2.2. Weighing the Feet of Living People

To determine the centre of gravity of the leaning body, a specially designed measuring station was used, and measurements of the human body were carried out. Subsequently, based on the theory of torques, the centre of gravity of the leaning body and the centre of gravity of the feet were calculated using mathematical methods.

Having at one’s disposal measurements of the foot length (l₄); total body height from the ground to the top of the head (l₁); height from the axis of the upper ankle joint to the top of the head (l₂); the distance between the insertion of the Achilles tendon to the calcaneal tuberosity and the projection of the point of the axis of the upper ankle joint at the top of the lateral ankle (Ach); and the distance from the ground to the axis of the upper ankle joint (l₃), as well as having information that the centre of gravity of the feet is located 44% of foot length from the calcaneal tubercle [15], a method was developed to calculate the shortest distance from the centre of gravity of the foot to the axis of rotation of the upper ankle joint (Figure 2). This made it possible to determine the gravitational moment of the feet and subsequently to estimate their weight. Next, using the developed method, the gravitational moments of the feet of six men were measured to determine foot weight both in absolute and relative (percentage) terms. Measurements were performed on a sample of six individuals to estimate the approximate average result of the measurements and the measurement error to show that the proposed methodological approach is justified. However, to estimate the results more precisely, the sample size should be significantly increased.

2.3. Statistical Analysis

Statistical analyses were performed based on the R program, in particular the “stats” library. Graphical analysis was performed using the “ggplot2” library. The “irr” library of the R program was used to analyse the agreement between six measurements made by one person. Intra-rater reliability was assessed by having the same rater perform repeated measurements on a subset of 6 samples at six separate time points with at least 1 day between sessions. The ICC parameter was calculated.

The study was approved by the Bioethics Committee in Kraków, Poland (Approval Code: 222/KBL/OIL/2016, Approval Date: 12 December 2016) and conducted under the Declaration of Helsinki. This study of the centre of gravity of the tilting body is part of a broader research series focused on static foot deformities, particularly hallux valgus

3. Results

3.1. Determining the Gravitational Arm of the Feet Concerning the Upper Ankle Joint

The gravitational arm of the feet is the closest distance from the centre of gravity of the foot to the axis of rotation of the upper ankle joint (h_{CoG_4}) (Figure 2). The experimentally determined centre of gravity of an average human foot is located at a distance of approximately 42% of the foot’s length measured from the top of the heel bone. In the case of women, this value is approximately 40%, and for men, approximately 44% [15]. The moment arm of the foot’s gravitational force relative to the upper ankle joint was determined based on the Pythagorean principle, taking into account the basic dimensions of the foot, i.e., length (l₄), height (l₃), and the distance between the insertion of the Achilles tendon to the calcaneal tuberosity and the projection of the point of the axis of the upper ankle joint at the top of the lateral ankle (Ach) (1).

$$h_{CoG\_4}=\sqrt[2]{b^2+a^2}=\sqrt[2]{{[\left(l_4\ast 0.44\right)-Ach]}^2+{\left({\displaystyle \frac{1}{2}}{l}_3\right)}^2}$$

(1)

3.2. Determining the Position of the Centre of Gravity of the Body

Depending on the support point of the one-sided lever, the body’s centre of gravity is located in different places. If we consider the tuberosity of the calcaneal bone without a hinge connection at the level of the upper ankle joint as the point of support of the human body (i.e., as the point of rotation of the one-sided lever), the human body can be considered a “rigid body”. In this way, the human body’s general centre of gravity (CoG) is commonly determined for biomechanical research, both static and dynamic [16]. This approach is justified only in a static condition, with an upright body position, when the projection of the CoG falls on the axis of rotation of the upper ankle joint, and both uscular and gravitational moments are zero. In dynamic situations, e.g., when the human body leans forward or backwards, it is necessary to determine the location of the CoG without taking into account the weight of the feet, because the feet are not part of the leaning segment of the body; they function as an element of support base (element of the ground).

Below are three methods for determining the body’s centre of gravity (Figure 3A–C).

3.2.1. Determining the Location of the General Centre of Gravity of the Human Body

Given the force value F₁ = 55.1 kG and the human height l₁ = 1.82 m, and knowing the body weight W₁ = 94.2 kG, the location of the centre of gravity of the body (h_{CoG_1}) was calculated based on the principle of moments of force (M_W1, M_F1) in a one-sided lever (2) (Figure 3A).

$$M_{W1}=M_{F1}$$

(2)

$$h_{Co{G}_1}\ast W_1=l_1\ast F_1$$

$$h_{CoG\_1}={\displaystyle \frac{l_1\ast F_1}{W_1}}={\displaystyle \frac{1.82\mathrm{m}\ast 55.1\mathrm{k}\mathrm{G}}{94.2\mathrm{k}\mathrm{G}}}=1.0645\mathrm{m}$$

$$h_1=h_{CoG\_1}-l_3=1.0645\mathrm{m}-0.09\mathrm{m}=0.974\mathrm{m}$$

The general centre of gravity of the body in this case is at a height of 1.0645 m (h_CoG1) measured from the point of support, i.e., the sole of the feet, at the level of 58.49% of the individual’s body height (l₁). However, when measured from the axis of the upper ankle joint, it is at a height of 0.974 m (h₁).

3.2.2. Determining the Position of the Centre of Gravity of the Leaning Part of the Human Body on the Axis of the Upper Ankle Joint

• Excluding feet torques

To calculate the position of the centre of gravity of the leaning body, the total weight of the human body (W₁ = 94.2 kG) was reduced by the weight of both feet (2 * 1.38% of the weight of the whole body [8]), resulting in 91.6 kG (94.2 kG−2.599 kG). Given F₂= 52.28 kG and the lever arm length (l₂ = 1.73 m, calculated as 1.82 m−0.09 m), the direct position of the h₂ and h_{CoG_2} was directly calculated (3) (Figure 3B).

$$M_{W2}=M_{F2}$$

(3)

$$h_2\ast W_2=l_2\ast F_2$$

$$h_2={\displaystyle \frac{l_2\ast F_2}{W_2}}={\displaystyle \frac{1.73\mathrm{m}\ast 52.28\mathrm{k}\mathrm{G}}{91.6\mathrm{k}\mathrm{G}}}=0.987\mathrm{m}$$

$$h_{Co{G}_2}=h_2+l_3=1.077\mathrm{m}$$

The centre of gravity of the body in this case is located at a height of 0.987 m (h₂), measured from the fulcrum situated on the axis of the upper ankle joint. However, when measured from the sole of the feet, it is at a height of 1.077 m (h_CoG2 = h₂ + l₃) (0.987 m + 0.09 m), i.e., at the level of 59.17% of the height of the entire body (l₁).

• Taking into account the feet torques generated at the upper ankle joint—on one side by the feet and on the other by the rest of the body.

With the experimentally measured F₂ value of 52.2 kG and the weight of the feet being 2.6 kG (W₃) (2 * 1.38% of the total body weight [8]), and the gravitational force arm of the feet being 0.08 (h_{CoG_4}), as well as the length of the lever arm l₂ = 1.73 m (1.82 m−0.09 m), F₃ was calculated, followed by h₃ and h_{CoG_3} (4) (Figure 3C).

$$M_{W4}={M_{F2}-M}_{F3}$$

(4)

$$W_4\ast h_{Co{G}_4}={(F}_2\ast l_2)-{(F}_3\ast l_2)$$

$$F_3={\displaystyle \frac{{(F}_2\ast l_2)-(W_4\ast h_{Co{G}_4})}{l_2}}={\displaystyle \frac{\left(52.28\mathrm{k}\mathrm{G}\ast 1.73\mathrm{m}\right)-(2.6\mathrm{k}\mathrm{G}\ast 0.09\mathrm{m})}{1.73\mathrm{m}}}={\displaystyle \frac{90.444\mathrm{k}\mathrm{G}\mathrm{m}-0.234\mathrm{k}\mathrm{G}\mathrm{m}}{1.73\mathrm{m}}}=52.14\mathrm{k}\mathrm{G}$$

Using F₃, the distance from the axis of the upper ankle joint to the centre of gravity of the body (h₃) and the distance from the ground to this centre of gravity of the body (h_{CoG_3}) were calculated (5).

$$M_{W3}=M_{F3}$$

(5)

$$h_3\ast W_3=l_2\ast F_3$$

$$h_3={\displaystyle \frac{l_2\ast F_3}{W_3}}={\displaystyle \frac{1.73\mathrm{m}\ast 52.14\mathrm{k}\mathrm{G}}{91.6\mathrm{m}}}=0.984\mathrm{m}$$

$$h_{Co{G}_3}=h_3+l_3=1.074\mathrm{m}$$

The centre of gravity of the body in a horizontal position with the support point at the level of the upper ankle joint axis with the feet weighing (without backrest) generates a torque that relieves the part of the body located on the opposite side of the upper ankle joint axis (Figure 3C). This locates the centre of gravity of the human body at a distance of 0.984 m (h₃) from the axis of rotation of the upper ankle joint. When a person is in a vertical (standing) position and the body leans forward or backwards, the body weight is not “unloaded” by the feet, and therefore the centre of gravity is moved more cranially. When measuring the position of the centre of gravity from the ground (including the feet), it is at a height of 1.074 m (h_{CoG_3}), which corresponds is 59.01% of the height of the entire body (Figure 3C). To determine the centre of gravity of a body leaning relative to the axis of rotation of the upper ankle joint, the calculated centre of gravity point for the body in a horizontal position (grey dot) should be moved by the value “x” (6). Then the centre of gravity CoG₃ (grey dot) will coincide with CoG₂ (pink dot) (Figure 3C).

$${(l}_2+x)\ast F_3=l_2\ast F_2$$

(6)

$$x={\displaystyle \frac{l_2\ast F_2}{F_3}}-l_2={\displaystyle \frac{1.73\mathrm{m}\ast 52.28\mathrm{k}\mathrm{G}}{52.14\mathrm{k}\mathrm{G}}}-1.73\mathrm{m}=0.0046\mathrm{m}$$

$$h_{CoG\_2}=h_3+l_3+x=0.984\mathrm{m}+0.09\mathrm{m}+0.0046\mathrm{m}=1.078\mathrm{m}$$

The difference between h_{CoG_2} calculated using the method with supported feet (Figure 3B) and h_{CoG_2} calculated using the method that accounts for the gravitational moment of the feet (Figure 3C) was 0.001 m. This small discrepancy is due to measurement errors. The difference in the position between the general centre of gravity of the human body with the support point on the tuberosity of the calcaneal bone (h_{CoG_1}) and the centre of gravity of the leaning human body with the support point at the level of the upper ankle joint (h_{CoG_2}) is 0.013 m (7).

$$h_{Co{G}_2}-h_{Co{G}_1}\approx 0.013\mathrm{m}$$

(7)

• Consequences of a different location of the centre of gravity

The higher centre of gravity of the tilting part of the body at the upper ankle joint increases the gravitational torques, because CoG₂ can “shift” further when tilting forward compared to CoG₁, and therefore has a larger gravitational arm (Figure 4A–C). CoG₁ can extend the furthest forward to the position when its throw falls on the heads of the metatarsals. After exceeding this position, the body loses balance.

The difference between gravitational moments is approximately 0.7866 kGm (~7.712 Nm), based on the demonstrative case. The difference between the torque values (M_CoG1 = r₁ * F₂ and M_CoG2 = r₂ * F₂, r₁ < r₂) are also significantly different. Although this difference is much smaller than the maximum torques generated in the upper ankle joint, it is still significant enough to indicate active muscle engagement. This level of torque may correspond to a moderate load during exercises or low-intensity movement. In physiotherapy and rehabilitation, such resistance level may occur during isokinetic exercises or targeted joint training following injury. For diagnostics, such a torque may appear when testing the strength of the lower limbs in a weakened person.

3.2.3. Determining the Weight of the Feet Using the Indirect Method

Based on the principle of torque equilibrium and having the measured values of the F₁ (Figure 3B) and F₂ (Figure 3C) forces, and with the foot gravity arm determined (Results section 1), the weight of the feet (W₄) was calculated using the indirect method (8).

$$W_4\ast h_{Co{G}_4}={(F}_2\ast l_2)-{(F}_3\ast l_2)$$

(8)

$$W_4={\displaystyle \frac{{(F}_2\ast l_2)-{(F}_3\ast l_2)}{h_{Co{G}_4}}}$$

For men’s foot dimensions, e.g., l₄—0.25 m, l₃—0.09 m, Ach—0.044 m, a—0.045 m, i b—0.07 m, the arm of the gravity was as follows (9):

$$h_{CoG\_4}=\sqrt[2]{{0.07}^2+{0.045}^2}=0.0832\mathrm{m}$$

(9)

Based on experimentally measured values of forces F₂ and F₃ and the known length of the human body from the upper ankle joint to the top of the head (l₂), and the distance from the centre of gravity of the feet to the axis of rotation of the upper ankle joint (h_{CoG_4}), the weight of the feet was calculated (10).

$$W_4={\displaystyle \frac{{(F}_2\ast l_2)-{(F}_3\ast l_2)}{h_{Co{G}_4}}}={\displaystyle \frac{(52.28\mathrm{k}\mathrm{G}\ast 1.73\mathrm{m})-(52.14\mathrm{k}\mathrm{G}\ast 1.73\mathrm{m})}{0.0832\mathrm{m}}}=2.91\mathrm{k}\mathrm{G}(3.09\%\mathrm{b}\mathrm{o}\mathrm{d}\mathrm{y}\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s})$$

(10)

The weight of the feet was experimentally determined in a group of male volunteers (

Table 1. Foot weight calculated by the indirect method in six men. F₂—force measured at the level of the top of the head without a gravitational moment of the feet, F₃—force measured at the level of the top of the head with a gravitational moment of the feet, l₂—body height without feet, h_{CoG_4}—distance from the axis of the upper ankle joint to the centre of gravity of the feet, W₄—weight of the feet.

	F2 [kG]	F3 [kG]	l2 [m]	hCoG4 [m]	Body Mass [kG]	W4 [kG]	Foot Mass [% of Body Mass]
P1	52.28	52.14	1.73	0.0832	94.2	2.91	3.09
P2	56.65	56.49	1.75	0.0991	102.1	2.81	2.75
P3	50.27	50.13	1.78	0.0879	89	2.95	3.32
P4	52.37	52.21	1.74	0.0962	91.9	2.87	3.12
P5	41.72	41.61	1.69	0.0791	75.2	2.48	3.31
P6	45.70	45.59	1.71	0.088	80.9	2.03	2.51
Mean (SD)	49.83 (5.33)	49.69 (5.31)	1.73 (0.03)	0.089 (0.007)	88.88 (9.62)	2.68 (0.36)	3.02 (0.32)
95% CI	[44.2, 55.4]	[44.1,55.2]	[1.7, 1.77]	[0.081, 0.097]	[78.7, 98.9]	[2.29, 3.051	[2.678, 3.356]
Margin of_error_95CI	5.59	5.57	0.03	0.007	10.09	0.37	0.36

The intraclass correlation coefficient (ICC) was calculated and demonstrated high consistency (ICC = 0.983), indicating excellent intra-rater reliability. This means a very high agreement between measurements performed by the same rater. Only 1.7% of the variance is due to measurement errors, the rest to real differences between the assessed objects.

). The average weight of the feet was 2.69 kG, accounting for approximately 3.02% of total body weight.

4. Discussion

The body’s centre of gravity (CoG) and centre of body mass (CoM) are often used interchangeably. However, authors do not always realise that these are not the same concepts. Their interchangeable use in human body analysis is acceptable because the human body has approximately uniform density, is relatively small compared to the mass of the Earth, and functions in a uniform gravitational field.

It is common to apply the general CoG determined in passive conditions [16,17] to dynamic situations, which is inappropriate because the tilting segment of the body has a different centre of gravity with a different gravity value and spatial location. Therefore, it is not possible to analyse the biomechanics of the dynamic human body by analysing the dynamic human body’s biomechanics as though it were a rigid body, because the vertical, supported human body tilts at the level of the axis of rotation of various joints. This is particularly evident during full support of the human body on the feet, with the axis of rotation at the level of the upper ankle joint. At that point, the centre of gravity shifts, as the mass of the feet is no longer part of the leaning body segment. This manuscript addresses a simplified scenario—body tilt with support on both feet. In any other body position during the movement of the human body, the analysis of tilt should refer to the specific joint at which the single-plane hinge motion occurs. During gait, the body alternately shifts support between the feet; thus, only the mass of one foot should be excluded from the leaning body mass. In the case of the take-off phase of gait, from the moment of lifting the heel, the foot, except for the toes, participates in deflecting the body weight, and the axis of rotation runs mainly through the first metatarsophalangeal joint. In an extreme case, when standing on the tips of the toes, as is the case with a ballerina, the entire body weight is tilted because the axis of rotation is at the level of the distal phalanx of the hallux. Studies that apply the general CoG to dynamic human body research misrepresent the actual forces and torques involved [18], which translates into the design of physiotherapeutic methods, training programs for athletes and soldiers [16], and even surgical procedures.

In previous studies, the average weight of the feet was determined by the direct method through cadaver foot weighing and then determining their percentage share in the total body weight. This study presents an indirect method for determining the weight of the feet based on torque balance within the lever system. In this way, it is possible to weigh the feet of living people and determine their percentage share in the total body weight. It may also be applied to estimate the weight of other body segments, such as the head.

Accurate determination of the centre of gravity has both theoretical and practical relevance. A higher centre of gravity of a human body during tilting on the axis of rotation in the upper ankle joint results in greater rotational moments than previously assumed. A greater gravitational moment means that greater muscle force is required at a constant lever arm length to generate a muscle moment that balances the gravitational moment. This insight forms the basis for revising rehabilitation and training protocols based on muscle force calculations. This may also be relevant when analysing load distribution on soldiers’ bodies, including the effect of backpacks or carried equipment.

Up to now, rehabilitation and training methods have been developed largely intuitively or without taking into account that the foot is a support platform for the tilting rest of the body [19,20]. Many scientific reports are important in studying the shifting of the centre of gravity in the context of medical therapies. For example, monitoring the distance between the CoM and the limits of foot support allows for assessing balance and the risk of falling, especially in older people [21]. It has been noted that training to limit lateral swings of the centre of mass (CoG) can improve gait functions and the results of tests such as the TUG or Berg Balance Scale in patients with, for example, spinal cord injury [22]. Analysis of the centre of mass trajectory in patients, e.g., after hip replacement, helps to adjust rehabilitation protocols, taking into account gait asymmetry and compensations.

Our revised approach can significantly enhance the precision of rehabilitation design, sports training, and human load analysis during movement.

The limitation of our approach is that these are not high-precision measurements, because they are based on basic measuring devices and a system that is difficult to measure with high accuracy. Modern technologies enable precise real-time tracking of the body’s centre of gravity, allowing for dynamic and personalized training feedback. Based on our observations, this approach could significantly enhance the precision of future studies on human body dynamics. Apart from that, future efforts can focus on developing simulation software based on collected data to improve calculation accuracy helpful, for example, in planning surgical procedures to increase the rotational strength of muscles, e.g., in patients with muscle weakness.

5. Conclusions

• The overall centre of gravity of a human body considered as a rigid body is closer to the axis of the upper ankle joint than the centre of gravity of a tilting body segment.
• A higher-positioned centre of gravity in a leaning body places more strain on the upper ankle joint, which is due to the resultant force being a function of gravity and muscle force.
• Determining the position and value of the centre of gravity based on the assumption that the human body is rigid distorts the real loading conditions of the upper ankle joint by underestimating the values of muscle strength. This is due to the underestimation of the gravity arm, and therefore the gravitational moment, which is counteracted by the muscular moments with constant arm lengths of the muscle forces.

Thanks to the correct determination of centre of gravity (CoG) in the dynamically changing human body, the identification of key biomechanical parameters for analysing movement physiology and pathology is enabled, which can then be translated into the design of rehabilitation and training regimens as well as surgical procedures in orthopaedics.