Development of a Simplified Human Body Model for Movement Simulations

Abstract

The main goal of this paper is to develop a simplified model of the human body motion system that enables its application for movement simulations and the analysis of the kinematic and dynamic parameters occurring during the performance of activities. The model is established on the basis of the modified Hanavan model and consists of rigid solids with simple geometry that are connected mostly with spherical joints. Based on anthropometric data from the literature, a complete set of equations parameterizing the dimensions and mass of each segment was formulated. The equations depend on only two body measurements (height and mass). The model is built in the Adams system as a 3D numerical dynamic model and tested using data gathered with an IMU sensors system. A volunteer lifting an object with a bent spine from the ground with both hands is used for this purpose. Three angles (from the IMUs) are applied to each model’s joint to best simulate human movement and to analyze the angular displacements, velocities, and torques. These results are consistent with theoretical expectations and assumptions, thus proving that reproducing human movements with the developed model is possible and that it also allows various parameters of the human body to be obtained.

1. Introduction

The development and application of human body models are inextricably connected to the analysis of human movements. This is important in many fields, including medicine, sport, and robotics. Biomechanics, as a field of science, is constantly developing due to the desire to learn the principles governing both the movement of the human body and the application of various measurement equipment and techniques. Gait is often measured with accurate, but rather expensive, and requiring large space, sets of cameras in commercial systems like Vicon [1,2], Contemplas [3], OptotrakCertus [4], and often with markers placed on the human body [5]. Human movement can also be measured with extensible wires that may be fastened to various body parts [6], as well as with the use of wearable sensors like IMUs (an inertial measurement unit) [7] for testing gait on a treadmill [8] or for knee joint characterization [9]. Other more specific movements are also measured, i.e., a backward tucked somersault [10] or human gait with Nordic walking poles [11], which frequently apply a particularly developed measurement system.

Data from measurements are often used in models for motion simulation, visualization, analyzing movement, and finding further kinematic and dynamic parameters. For example, the research in [12] presents a reproduction of human gait with the use of Nordic walking poles using a model built in the Adams system (multibody simulation software). Data based on measurements from the Optotrak system were used. Again in the Adams program, data obtained with electrogoniometers were applied to simulate a model of human body gait with an exoskeleton [13].

Very precise and complicated human body models often involve particular body parts or joints, like the human knee joint model presented in [14], which was built based on computed tomography, magnetic resonance, and 3D-video-fluoroscopy. In another instance [15], to model the static and dynamic states of loading for bones in the skeletal system, medical images from PET scans and computer tomography were used. However, in the case of modeling the whole human body motion system, many concepts have been created, including models by Hanavan [16], Hatze [17], and Yeadon [18], as well as a model built in the so-called AnyBody system [19].

The Hanavan model is parameterized based on anthropometric data describing the dimensions of the human body (a minimum of 25 measurements are required to build the model). The model assumes symmetry of the body segments and consists of 15 rigid solids with simple geometric shapes. Each segment has a uniform density and is characterized by the position of the center of mass (COM) and moments of inertia with regard to the three main axes of rotation. The limbs are connected to the trunk using spherical joints with zero mass [16].

The Hatze model consists of 17 segments. It is similar to the Hanavan model, but has the right and left shoulder elements added. Each segment is divided into many plates—smaller rigid solids with their own density and complex shapes (e.g., parabolic plates and hollowed cylindrical sections). The model assumes no body symmetry and takes into consideration gender and individual factors such as pregnancy or being overweight. Therefore, as many as 242 individual measurements are required, including 160 diameters and the circumference of the ellipses used to model limbs. It is considered one of the most complicated and accurate human body models [17].

The Yeadon model assumes symmetry and consists of 11 segments divided into 40 rigid solids, each with a uniform density. The segments’ shapes are not very complex, but 95 body measurements are required to create the model. Each joint has at least one rotation; however, for the neck, ankle, and wrist joints, no movements are considered [18,20].

The last mentioned model (Anybody) is different from previous models. It is a complex musculoskeletal model that takes into account the muscles, flexibility, and deformation of the body (the segments are not rigid), thus reflecting the actual shapes and densities of human body parts. It can be individually adapted for every person but requires more computational power and, most importantly, a lot of specialist knowledge to configure and simulate the model [19].

Many human body models have been considered over the years, but obtaining a particular design that is suitable for various applications, including rehabilitation, biomechanics, robotics, and virtual reality, is still a subject of research [21]. Complex models, like Hatze [17] or Anybody [19], while providing high fidelity, often demand significant computational resources, hindering their use in real-life cases. Moreover, despite the existence of relatively simple models like Hanavan and Yeadon, which yet require a considerable number of measurements, a further simplified model is still necessary for time-demanding applications and cases where ease of use is crucial. This study aims to address this need by developing a simplified human body model suitable for performing kinematic and dynamic analysis of movement activities that maintains the necessary basic level of anatomical detail while significantly reducing the model’s complexity.

Therefore, the main contribution of this paper is the development of a simplified human body model with a set of parametric equations that requires only two body measurements (height and mass). The following part of the paper presents in Material and Methods, Section 2.1, the developed model consisting of simplified geometric solids that are connected mainly with spherical joints. The paper then shows in Section 2.2, an exemplary experimental 3D dynamic numerical model (built-in Adams 2020 software) that would allow visualization of movement. A set of inertial sensors is described in Section 2.3 as being used for an experiment where a volunteer performs a particular human activity—lifting an object with a bent spine from the ground with both hands. In Section 2.4, the IMU gathered data are applied, and displacements of individual body parts are implemented for each joint of the model to perform a motion simulation. In the Section 3, an analysis of kinematic and dynamic parameters, with the outcomes presented as plots and numerical results, is performed. The paper is completed with a Section 4 presenting a summary and comparison with existing models and future works. In the end, the Conclusions highlight the main paper’s contributions, outlining the developed model’s features, advantages, and limitations, as well as possible applications.

2. Materials and Methods

2.1. The Developed Human Body Model

A simplified human body model for movement simulations is described in this article. The development of the model initially required the interpretation and simplification of the human body in terms of kinematics and dynamics. Above all, this involves the number of segments and the number and type of connections (joints). The model’s main assumptions are that it should be parametric, simple to use (a small number of necessary measurements), and as universal as possible, even at the cost of reduced individualization.

In the model, 17 rigid solids are distinguished (Figure 1a), as proposed in the Hanavan model. The Hanavan model was chosen as the basis due to its established use in biomechanics research and its relatively comprehensive representation of human anatomy. Furthermore, it exhibits a level of complexity that aligns well with the desired level of detail for the intended simplified approach. The difference lies in the addition of the pelvis and neck (parts 8 and 9). Moreover, the two parts of the torso (indicated as 3 and 4) are initially separated so that the appropriate shapes and dimensions of these parts can be determined. However, they are connected to one solid (they do not move relative to each other, ultimately forming a rigid element). The model, therefore, contains 16 segments that are connected to each other in a movable way.

Human body joints are treated as spherical joints—class III kinematic pairs (p₃ = 13), and they follow common biomechanical interpretations. Only elbow joints are treated as class II kinematic pairs (universal/cardan joints p₂ = 2). Consequently, in the elbows,—2 possible rotational movements are taken into consideration—flexion/extension (F/E) and internal/external rotation (Rot), while in all the other joints—also abduction/adduction (A/A). For the purpose of the model’s analysis and interpretation of its mobility, the pelvis was considered to be connected with a spherical joint to the ground (immobile part). This means that the model’s mobility is equal to W_R = 6 × (17 − 1) – 5 × 0− 4 × 2 − 3 × 14 − 2 × 0 − 1 × 0 = 46, and therefore, in order to unambiguously determine the position of each member of the model, it is necessary to assign 46 angular parameters to it (apply 46 drives).

Particular emphasis is placed on the precise definitions of the shapes and dimensions of each designed segment of the body model (Figure 1b). Moreover, the dimensions are parameterized and dependent on only one value (body height). The segment shapes and equations of dimensions are listed in

Table A1. Description of the developed model’s individual segment shapes and dimensions (for each, a parametric equation, source, and value calculated for the model built in this article are indicated).

Body Part	Length [cm]	Width/Radius [cm]	Height/ Thickness [cm]	Shape
Calf (1′ and 1″)	$l_c=\left(0.285-0.039\right)H$ [22]	$r_c={\displaystyle \frac{1}{2\pi }}\sqrt{{\displaystyle \frac{m_c-0.0226M-0.016}{31.33l_c}}}$ [32]	-	Truncated cone
	46.002	5.397
Thigh (2′ and 2″)	$l_{thi}=\left(0.530-0.285\right)H$ [22]	$r_{thi}={\displaystyle \frac{1}{2\pi }}\sqrt{{\displaystyle \frac{m_{thi}-0.1032M+1.023}{12.76l_{thi}}}}$ [32]	-
	45.815	5.883
Abdomen (3)	$l_{ab}=\left(0.720-0.530\right)H$ [22]	$r_{ab}={\displaystyle \frac{0.174H}{2}}$ [22]	-
	35.530	16.269
Thorax (4)	$l_{tho}=\left(0.818-0.720\right)H$ [22]	$r_{tho}={\displaystyle \frac{0.259H}{2}}$ [22]	-
	18.326	24.217
Upper arm (5′ and 5″)	$l_u=0.186H$ [22]	$r_u=\sqrt{{\displaystyle \frac{m_u}{\rho \pi l_u}}}$ [22]	-
	34.782	4.094
Forearm (6′ and 6″)	$l_{for}=0.146H$ [22]	$r_{for}=\sqrt{{\displaystyle \frac{ m_{for}}{\rho \pi l_{for}}}}$ [22]	-
	27.302	3.399
Foot (7′ and 7″)	$l_{foot}=0.152H$ [22]	$w_{foot}=0.055H$ [22]	$h_{foot}=0.039H$ [22]	Triangular prism
	28.424	10.285	7.293
Pelvis (8′)	$l_p=0.163H$ [23]	$w_p=0.191H$ [22]	$h_p=0.05H$ [22]	Pyramid
	30.526	35.717	9.35
Neck (9)	$l_n=0.052H$ [22]	$r_n=0.0327H$ [23]	-	Cylinder
	9.724	6.112
Head (10)	$l_{he}=0.0508H$ [23]	$r_{he}=0.0425H$ [23]	$h_{he}=0.130H$ [22]	Ellipsoid
	9.500	7.950	24.310
Hand (11′ and 11″)	$l_{ha}=0.108H$ [22]	$r_{ha}=0.0294H$ [23]	$h_{ha}=0.0142H$ [22]
	20.196	5.500	2.650

(Appendix A). Generally, the modeled dimensions and masses are based on [22], whereas the shapes follow the suggestions of the Hanavan model [16]. The shapes of the body segments were assumed to be simple rigid solids, as follows: feet—a triangular prism, hands, and head—an ellipsoid, the remaining segments of the upper and lower limbs and the thorax and abdomen—a truncated cone, neck—a cylinder, pelvis—a double pyramid with a square base. Several dimensions that are missing in the above sources (e.g., neck or head radius) have been added based on the dimensions for a man in the 50th percentile—according to the Atlas of Human Measurements [23]. More precisely, the data used concerned an individual of Caucasian race, aged 20–60. Based on the values from this source, the missing dimension equations were also determined and were dependent only on the total human height (Table A1).

As for the dynamic aspects of the model, the masses of individual segments are mainly determined based on paper [22] and are presented in

Table A2. Description of the masses (parametric equations) for the individual segments of the developed model, including the values calculated for the model built and tested in this article [22].

Body Part	Equation for Mass [kg]	Calculated Mass [kg]
Foot (7′ and 7″)	$m_{foot}=0.0145M$	1.015
Calf (1′ and 1″)	$m_c=0.0465M$	3.255
Thigh (2′ and 2″)	$m_{thi}=0.100M$	7.000
Pelvis (8)	$m_p=0.142H\times \left(0.818-0.530\right)$	7.648
Abdomen (3)	$m_{ab}=0.139H\times \left(0.818-0.530\right)$	7.486
Thorax (4)	$m_{tho}=0.216H\times \left(0.818-0.530\right)$	11.633
Neck+Head (9 and 10)	$m_{he}=0.081M$	5.670
Upper arm (5′ and 5″)	$m_u=0.028M$	1.960
Forearm (6′ and 6″)	$m_{for}=0.016M$	1.120
Hand (11′ and 11″)	$m_{ha}=0.006M$	0.420

(Appendix A) in parametric equations, which are dependent on only one value (body mass). At this stage of the research work, the COM location for individual segments is not referred to in the literature data (for simplification purposes). It is, instead, determined geometrically by assuming a specific density and the mass of each segment that is distributed uniformly. The density of a segment can be calculated based on its mass and volume, which is further explained in the next subchapter.

The presented relationships (Appendix A, Table A1 and Table A2), therefore, constitute a complete set of equations that parameterize the dimensions and masses for each segment of the developed human body model based on only two body measurements (height—H, body mass—M).

The main features of the simplified model are as follows:

• sixteen moving segments after combining the two torso parts;
• rigid body segments with a uniform mass distribution;
• segments represented as simple, but varying between individual parts, geometric shapes (e.g., cylinders, prisms, cones);
• dimensions and masses of segments defined by parametric equations dependent only on 2 body measurements (height and mass);
• segments connected by spherical joints (universal joints for elbows);
• segment’s position of COM and mass inertial moments determined based on shape and calculated density (in Adams software and this way also parameterized).

As presented, the developed simplified model provides a balance between accuracy and complexity, making it suitable for movement simulations that focus on general human motion. Moreover, the changes in relation to other existing models, e.g., the Hanavan model, the advantages of the developed model, and the scope of applicability and its limitations, are further deliberated in the Section 4 and Section 5.

2.2. The Built Experimental Numerical Model

The developed simplified human body model is built in Adams software as a 3D numerical dynamic model (Figure 2a,b). This is in order to perform simulations and verify the developed model. Assuming the height (H = 187 cm) and total mass of the human body (M = 70 kg weight), the dimensions and masses of individual segments are determined according to the formulas in Table A1 and Table A2, where the results of these calculations are also provided. The numbers describing the individual segments (yellow solids) visible in Figure 2a correspond to those in Figure 1a. Joints are additionally indicated by inserting red spheres with negligible mass. As for the human motion standard—the developed model follows the International Society of Biomechanics (ISB) recommendations for anatomical coordinate systems and joint definitions, similar to the case presented in [4]. In order to facilitate the observation of some segments, characteristic elements (negligibly changing the mass and its distribution) were added to help determine the orientation of these solids: the head has nose and hollows symbolizing the eyes, the torso has a hole symbolizing the navel, and the hands have small protruding rods on the inside.

As described earlier, with the known mass and volume of each segment, the solids in the model were assigned appropriate densities. For this reason, the positions of COM and the mass moments of inertia for all the segments were simplified and followed the Adams calculated values of these parameters.

Due to the peculiarity of the software, the joint connections assumed as kinematic pairs of class III and II (elbows) were modeled respectively as 3 or 2 rotational pairs (class I). They have a common center of rotation but different (perpendicular) axes of rotation. More precisely, in the joints between the segments, 2 spheres (Figure 2) with negligible mass were placed and then connected with rotational pairs to each other and to the appropriate body segments. Accordingly, in the elbow joints, it was enough to use one sphere. As a result, the assumed mobility of the model’s individual parts is obtained. Furthermore, by applying a rotational drive to each kinematic pair, it is possible to simulate the movement of the human body in the model.

The presented numerical model, as well as further experimental/simulation results, refer to a human volunteer with a height H = 187 cm and body mass M = 70 kg. The experimental measurements were carried out with the volunteer using the IMU sensors system.

2.3. Movement Experiment Performed with the IMU System

In order to simulate the motion of the developed model in Adams software, it was necessary to assign displacements (drives) in each kinematic pair. To obtain appropriate motion data, it was decided to conduct an experiment with the aid of a volunteer wearing a set of inertial sensors from an STT iSen IMU system v2020 (Figure 3a). This system can measure human body movements without complicated equipment or any kind of interference with the human body. The system details are provided in [24,25], and one of its case studies for gait analysis is presented in [26]. Using straps and according to the manufacturer’s recommendations, the wireless IMU sensors are placed on the volunteer’s specific body spots (Figure 3b), directly on the skin or clothes. Each inertial sensor provides global orientations with regard to its own housing, which corresponds to the adequate body segment’s orientation. Sensors main features include: accuracy of Pitch/roll < 0.5° (RMS) and Heading < 2.0° (RMS), 3-axis gyroscope: ±2000°/s, 3-axis accelerometer: ±16 g, 3-axis magnetometer: ±1300 μT, maximum sampling rate: 400 Hz, dimensions: 56 × 38 × 18 mm, weight: 46 g. Measurements from each IMU sensor are time-stamped for data synchronization, but temporal synchronization in multi-sensor IMU systems [27,28] needs to be taken into consideration when dealing with possible inaccuracies. In addition, when it comes to biomechanical analysis, the software of the iSen system v2020 supplies skeleton rotation. Similar to the developed model, the ISB recommendation standards are generally used for the IMU system definition of biomechanical joint angles, with details provided by the manufacturer [24]. However, because the sensors are not perfectly placed along human bones, a particular process must be carried out to compute sensor-to-bone calibration (biomechanical calibration)—the patient/sportsman is asked to stay in a given position (such as the T-stance). Due to this, the system enables movements in each joint, in the form of three biomechanical angles, to be determined. These were collected during the experiment described below and used in subsequent simulation studies.

The performed experiment used the “Full body with hands” measurement protocol with 16 sensors and T-stance as the initial calibration (Figure 4a). The movement performed in the experiment involved lifting an object with a bent spine (a light rectangular box placed within reach) from the ground using both hands (Figure 4b). Therefore, the additional goal of measuring, modeling, and analyzing this type of movement is also realized.

2.4. Simulation Performed with the Numerical Model

As stated in subchapter 2.2, in order to test the operation of the developed human body model, a simulation was carried out on its numerical dynamic model built in Adams software. Data collected from the measurements with the IMU system (Section 2.3, the experiment of lifting an object with a bent spine from the ground with both hands) were implemented into the numerical model to reproduce the movement. In Adams, the drive for each kinematic pair (for each joint’s movement) was performed using Adams Motion with AKISPL (akima fitting method function). Data files containing the motion curves (splines α(t)—angle in time) obtained from the IMU system and iSen software were imported to the function. The unit °/rad and/or sign +/− were appropriately changed. In some cases, like for the shoulders, the measurement also had to be corrected by ±90° in order to be properly implemented into the model. For example, the equation of motion for the right knee Abduction/Adduction (Equation (1)) had the following form:

−AKISPL(time, 0, RKnee_A_A, 0) × 1d

(1)

At the current stage of research, the approach used by the manufacturer of the IMU sensors was applied in the model in order to visualize the movement. To be exact, the pelvis was connected with a spherical joint to the ground (immobile element); therefore, no detailed interactions of the feet with the ground were simulated. However, to compensate for the lack of impact of body mass on the lower limbs, forces were added to the feet—approximately 350 N to each (about half of that of body mass). Moreover, the weight of the lifted rectangular box was negligible; therefore, in the simulation, the model does not lift any object, and no additional weight is applied. In addition, due to the differences between the developed human body model and the model used by the IMU system, some simplifications and approximations were introduced for the purpose of the presented simulation. First of all, when performing measurements on a human, one sensor was used for the head and neck. Therefore, in the presented simulation, the neck was attached to the torso, and thus moved with it. Secondly, the system does not provide data on the internal/external rotation of the wrist, which means that in the simulated model, this movement was kept at 0. Lastly, in the case of some angles that were measured by the IMU system, partially inappropriate (not corresponding to the actual movement) data were obtained. According to the system manufacturer, such irregularities can occur in the system during measurements of large angle changes and are caused by the method of calculating the angles, which is based on projections of the limb axis on the biomechanical plane. For this reason, a correction was implemented for the flexion/extension and abduction/adduction of the shoulder joints. The correction involved adding the STEP function to the drive, from which the given position was obtained at a specified time. A similar problem, caused by a large flexion of the torso, occurred in the case of the flexion/extension movement of the torso in relation to the pelvis, as well as of the head in relation to the neck. For these instances, approximate parabolic functions that simulate motion similar to the observed one were determined from 9.91 s to 13.1 s and implemented directly in the data of the imported files with motion curves. For example, the equations of motion for the right shoulder’s flexion/extension (Equation (2)) and torso’s flexion/extension (Equation (3)) had the following forms:

−AKISPL(time,0,RShoulder_F_E, 0) × 1d + STEP(time, 9.81, 0.0, 11.07, 97.0d) + STEP(time, 11.07, 0.0, 13.82, −17.0d)

(2)

−15.7089 × time² + 361.622 × time − 2031.15

(3)

The need for corrections was not, therefore, due to the incorrect modeling of the human body but solely to the inappropriate results obtained from the IMU system. This was due to the imperfect angle calculation method used in the company system. For this reason, when using IMU measurements to simulate the model’s motion in the future, the data should be based on quaternions defining the angular position of the segments and not on the joint angles. The introduced estimates allowed the correct movement of the model, close to that observed in reality, to be achieved. Moreover, the applied approximations do not hinder the obtained outcomes and, above all, the results of the evaluation of the developed model. The movement of lifting an object from the ground with both hands with a bent spine and the data concerning this movement serve as an example for testing the model.

3. Results

The numerical model in Adams moved according to the implemented motions based on the biomechanical angles calculated using the software of the IMU system’s manufacturer. The progress of the simulation can be observed in Figure 5a–d, where the sequence of movements is presented. According to the assumptions and observations, at the end of the simulation, the model’s lower limbs, trunk, and head almost returned to the initial position (straight position), while the upper limbs changed their orientation and final positions due to the box being held in front of the person. The entire experiment, which lasted for about 14 s, was reproduced in Adams, starting with nearly a 10 s preparation and calibration in the T-stance (as visible in Figure 4a). For this reason, the first 9 s were omitted in the graphs, and the analysis of the results focused on the actual studied movement—in the range of 9.5 s to 14 s. Moreover, only some of the obtained results, focusing mainly on the upper and lower limbs, are presented in the plots (Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11 and Figure 12), with the most important outcomes summarized as numerical values. The following plots present, for each particular joint, the angular displacement or moment of force as three waveforms for the joint movement, where F/E stands for flexion/extension, A/A stands for abduction/adduction, and Rot stands for internal/external rotation. As previously mentioned, the presented results follow ISB standards for human motion. Joint angles are measured using coordinate systems based on defined anatomical planes (sagittal, frontal, and transverse) and axes, as well as by applying the right-hand rule for the definition of coordinate systems.

For the hip joints, the F/E movements achieve similar waveform shapes and values for the left and right limbs, with min. and max. values of −5.84° and 93.90° for the left side (Figure 6a); and −3.84° and 93.86° for the right side (Figure 6b). The A/A and Rot achieved minor values when compared to the main motion F/E.

In the case of the knee joint (Figure 7a), a large increase in the F/E angle from about 10 s to 13 s was observed. It corresponds to the tested movement of lifting an object from the ground. A negative value at the end of the simulation indicates a small hyperextension of the knee. The minimum and maximum values of the achieved angle were 0.06° and 51.62° for F/E at the left joint, −1.69° and 54.29° at the right joint, −2.20 °and 0.46° for A/A at the left knee, and −8.04° and 1.48° at the right knee, respectively. For the ankle joint, the maximum and minimum achieved values were: F/E at the left ankle −7.17° and 2.29°, at the right ankle −6.58° and 3.13° (Figure 7b); A/A for the left leg is −8.00° and −2.75°, while for the right leg, it was −7.62° and −3.70°.

In the case of the shoulders, both graphs are similar to each other for all three movements in terms of the characteristics of the waveforms and the achieved values of the angle. The largest change in the angle can be observed for the A/A movement, where the extreme values are −8.91d° and 93.39° for the left side and −7.54° and 84.94° for the right side. The results correspond to the simulated movements of a person grabbing an object and straightening up while still holding the arms straight in the front. The minimums and maximums obtained were −5.02° and 44.66° at the left shoulder for F/E, and −17.28° and 35.64° at the right shoulder. An important fact is that in the case of shoulder joints, corrections were applied to the F/E and A/A movements obtained from the IMU sensor system. Due to the fact that the movement was still based on the results from the sensors, the introduced corrections appear natural and are practically indistinguishable in the graphs, i.e., it was possible to obtain the correct final position/orientation of the limbs (Figure 5d), by introducing corrections, while at the same time maintaining the smoothness and continuity of the movement (Figure 8a). This indicates both the reasonability of the modifications and their correctness—they do not disturb the natural movement or the obtained results.

The graph presenting the angles for the elbow joint (Figure 8b) lacks the A/A movement because, as explained earlier, the model assumes the elbow to be a Cardan joint (there are only two movements). At the beginning of the simulation, the model was in the T-stance position, and the palm surfaces of the hands were facing down parallel to the ground plane. During movement, the forearm was rotated so that the hand could obtain the proper orientation to grip the box. This can be observed as a large change in the values of the Rot angle for the elbow with a min. and max. of: −75.07° and −1.56° in the left joint; −80.42° and −9.30° in the right. For the F/E plots, the min. and max. are respectively equal to −10.93° and 2.52° for the left limb and −10.54° and −0.42° for the right limb. In the case of the wrist joint, a zero change in the Rot angle was observed. As clarified earlier, this motion was locked in this particular simulation because the applied IMU system did not include the wrist Rot.

The movement of the torso is also measured at the thorax connection with the pelvis (Figure 9a). Visible is the parabolic part for F/E movement (max. 50.04°), according to the correction given in (Equation (3)).

Comparing the graphs from Adams with those obtained during the IMU measurements allowed for the certification that the movement in the model was accurately reproduced (min. and max. values of the angles were very close). The angular velocities of particular joint movements are not presented in this article, but were also measured. Among all the human body segments, the upper limbs, as expected, moved at the highest angular velocity. For instance, velocities for the right and left shoulders were very similar, and the highest values were obtained for A/A motion—about 150°/s. Moving the arms from the T-stance to the front was performed with high speed, but when the hands approached the object on the ground, the velocity decreased in order to precisely grip the box.

The moment of force for each joint movement was obtained from the Adams model using the torque measurement function applied to each motion. First, the torques applied to move the thorax are shown (Figure 9b) with high values for F/E movement—max. 137.24 Nm.

Both lower limbs performed very similar F/E movements in all joints. As a result, loads that were almost symmetrical were obtained (Figure 10). Additionally, all the values for F/E (Figure 10 and Figure 11) do not change sign (remain constantly positive or constantly negative); therefore, the moments of force act with a constant sense (due to the continuous need to support body weight). Of all the lower limb joints, the hips were subject to the greatest loads, and the moment of force for F/E assumed initial values of about 50 Nm. A similar regularity was observed for F/E in the other lower limb joints (Figure 11). This is due to the fact that forces were applied to the feet (each about 350 N), imitating the effect resulting from body weight. For the hips, the F/E moments of the force reached min. and max. values of 30.90 Nm and 144.85 Nm for the left limb and 28.21 Nm and 136.20 Nm for the right limb. The extremes for the A/A movement were 4.18 Nm and 37.44 Nm for the left joint (Figure 10a), 2.96 Nm, and 58.90 Nm for the right joint (Figure 10b).

For the knee joints, the moment min. and max. extremes were: 31.90 Nm and 60.36 Nm for F/E of the left knee (Figure 11a); 31.22 Nm and 62.36 for F/E of right knee; −30.34 Nm and −4.88 Nm for A/A of left; −31.93 Nm and −10.08 Nm for A/A of right. For the ankle joints, the torque values for A/A and Rot were small, while for F/E, these values were quite stable and constantly around −50 Nm (Figure 11b).

The moments of force for the left (Figure 12a) and right shoulders had similar absolute values and waveforms. However, the values were not as large as those for the previous joints. The torques for Rot were close to 0, while both for F/E and A/A had a very changing character with values ranging from around –18.0 Nm to 17.5 Nm (F/E) and from about –13.5 Nm to 12.0 Nm (A/A).

In the case of elbows, the graphs of the left (Figure 12b) and right connections are also very similar and generally do not exceed 5 Nm. The moments of force for the wrists were the lowest in the model, and did not even reach 1 Nm. This is due to the fact that the hand is the lightest in relation to the other segments.

Table 1. Extreme values of the angular displacements and moments of forces for the part of the developed model obtained from the simulation based on measurements using the IMU system.

Joint	Left/Right	Measured Movement	Angle Min. [°]	Angle Max. [°]	Torque Min. [Nm]	Torque Max. [Nm]
Hip	Left	F/E	−5.84	93.90	30.90	144.85
		A/A	1.80	9.71	4.18	37.44
		Rot	−0.05	16.40	−11.17	7.39
	Right	F/E	−3.84	93.86	28.21	136.20
		A/A	−2.09	8.58	2.96	58.90
		Rot	−6.65	3.41	−10.06	9.87
Knee	Left	F/E	0.06	51.62	31.90	60.36
		A/A	−2.20	0.46	−30.34	−4.88
		Rot	−6.69	2.12	−7.35	−2.52
	Right	F/E	−1.69	54.29	31.22	62.36
		A/A	−8.04	1.48	−31.93	−10.08
		Rot	−7.88	2.68	2.07	7.52
Ankle	Left	F/E	−7.17	2.29	−52.14	−51.72
		A/A	−8.00	−2.75	−0.51	3.43
		Rot	−3.64	0.66	−0.27	0.33
	Right	F/E	−6.58	3.13	−52.16	−51.48
		A/A	−7.62	−3.70	−4.99	0.73
		Rot	−5.25	0.64	−0.69	0.50
Pelvis	-	F/E	−47.34	6.58	14.18	157.84
		A/A	−12.53	6.21	−75.74	86.78
		Rot	−7.46	2.15	−106.79	18.77
Thorax	-	F/E	1.59	50.04	−18.40	137.24
		A/A	−2.71	4.68	−54.49	21.78
		Rot	−7.81	4.93	−17.98	17.97
Head	-	F/E	−6.16	35.15	−3.46	7.35
		A/A	−3.27	28.19	−2.20	2.00
		Rot	−5.83	21.86	−0.12	0.13

shows a summary of the obtained minimum and maximum values (in the simulation) for the angular displacements and moments of force. The sign for the moment of force is maintained to evaluate the motion’s direction and if it alters.

To summarize, according to the measured movement, very high results of F/E are obtained for the hip (nearly 94°), knee, and thorax (above 50°). Significant values of A/A are only in the shoulder (around 90°, resulting from arm movement from the T pose to the body front), and noteworthy numbers of Rot are obtained only for the elbow (as much as −80°). The moment of the force values also agreed with the theoretical loads that could appear in the human body during the simulated movement. Omitting the connection of pelvis with ground, the highest value of torque was obtained for the F/E of the Thorax in connection with the pelvis (around 137 Nm). The next highest was for F/E of the hip, exceeding 144Nm. The highest for A/A was also in the hip (nearly 59Nm). Torques for Rot are generally much smaller than for F/E or A/A, the highest for Thorax (nearly 18Nm). Overall, the movements obtained were very close to those observed in reality, and the results were consistent with the assumptions. This proves that it is possible to reproduce movements using the developed human body model and that measurements from IMU sensors can be used for this purpose. More importantly, the developed model allows for the simulation and analysis of various parameters with regard to both kinematics (movement) and dynamics (moment of force).

4. Discussion

The main objective of this research was to develop a simplified model of the human body movement system that could be used to simulate movement and to analyze the kinematic and dynamic parameters present during the performance of various activities. The developed model consists of simplified geometric solids that are mostly connected by spherical joints. On the basis of anthropometric data, a comprehensive set of equations was formulated that parameterized each segment’s dimensions and mass with regard to only two body measurements (height and mass).

Subsequently, for testing and evaluation, the model was built in Adams software as a 3D dynamic numerical model, based on an example height of 187 cm and a body mass of 70 kg. This enabled the simulation of movement and detailed analysis. The movement was reproduced with data obtained from an experiment with a volunteer who was lifting an object from the ground with both hands with a bent spine . The measurement was performed using a set of inertial sensors with software (STT iSen IMU system). Overall, the IMU system worked properly and showed correctly measured movements, but in the case of some body parts with significant rotations in three dimensions, the exported data (joint biomechanical angles) had some inaccuracies caused by the manufacturer’s software calculation method. In these few cases, it was necessary to apply a correction to the obtained values so that the final effect would be as close to reality as possible. This solution was chosen because applying a correction to a movement measurement was simpler and provided better results (closer to reality) than the attempts to completely independently reproduce the desired movement.

In order to accurately and correctly reproduce human movement, three motions based on the measured biomechanical angles (from the IMU system) were applied to each joint in the model. The implemented movement enabled the analysis of the kinematic and dynamic parameters of the human body, such as displacements, velocities, and angular accelerations, as well as the moments of force occurring in individual joints. The obtained values were consistent with the theoretical expectations and assumptions. Therefore, despite the need for further experimental validation of the findings, this proves that

• the developed model can be correctly used for the analysis of human movement;
• the built-in Adams exemplary numerical model is suitable for simulating and visualizing motion, thus enabling not only angular displacements in joints but also angular velocities and moments of forces between body parts to be obtained;
• the data from the IMU system can be applied to the model as input data for simulating the desired/measured movement.

The ideal model should be characterized by having a structure and shapes of segments as simplified as possible while at the same time maintaining the body element’s dimensions, COM positions, and ranges of motion. This would ensure that the simulations are easy to perform and also provide accurate results. The model developed in this work was created based on existing methods of presenting the human musculoskeletal system—it reproduces body parts in a simplified way, focusing mainly on the skeleton and joints while omitting details about muscles and tendons. Therefore, it differs significantly from the complex musculoskeletal models, such as those created in Anybody [19] or Matlab-based BoB Biomechanics software [29], which take into account elements like tissue elasticity and accurate body segment forms. However, the computational demands of these models limit their usability in real-time scenarios or applications, requiring a large amount of processing power and specialist knowledge for simulation and configuration.

The developed model follows certain ideas and solutions from the Hanavan model. Both models assume full symmetry of the body segments, which are connected by spherical zero-mass joints. The segments are treated as single rigid bodies with simple shapes and uniform density. However, significant changes were also introduced in the simplified model. First of all, although the models are parameterized using anthropometric data, the Hanavan model requires the measurement of as many as 25 body dimensions, while the simplified model associates all the values with the height and mass of a human. Moreover, differences also concern the partitioning into individual body segments: 15 in Hanavan, while the simplified model contains 17 segments, including 16 connected in a movable way. Taking all the presented features into consideration, the developed model may be called a modified Hanavan human body model. A further comparison with several existing models is presented in

Table 2. Comparison of the developed model’s main features with several existing model solutions.

Name of Model	No. of Measurements/Segments	Geometry of Segments	Features of Solids	Type of Connections	Additional Features
Hanavan model	25/15	Single solids with simple shapes	Rigid solids Uniform density Specified COM position	Spherical joints with zero mass	Assumes symmetry of body segments
Hatze model	242/17	Divided into many plates—smaller complicated solids	Rigid solids Accounts for varying densities	Segments have origin coordinate systems	Assumes no symmetry Considers gender, factors such as pregnancy or overweight
Yeadon model	95/11	Divided into a total of 40 solids	Rigid solids Uniform density	Each joint has at least 1 rotation	Assumes symmetry For neck, ankle, and wrist joints—no movements
Pecolt model	42/14	Single solids Shapes replicate only distances between connections	Rigid solids Uniform density Specified COM and moment of inertia	Connections by visco-elastic elements	Not exactly parametric Based on the literature, anthropometric parameters for each segment
Nagano model	48/16	Single solids Prisms with a rectangular base	Rigid solids Uniform density Specified COM and moment of inertia	15 hinge and spherical joints Total of 35 DOF	Based on individually provided anthropometric parameters for each segment
Developed model	2/16	Single solids Simple shapes (the torso consists of 2 segments)	Rigid solids Uniform density	Spherical joints with zero mass and two universal joints (elbows)	Assumes symmetry of body segments

: Hanavan [16], Hatze [17], Yaedon [18], Pecolt [30], and Nagano [31]. All models divide the human body into rigid solids with a generally uniform density. The main differences are the number of required human body measurements, as well as the total number of segments and solids contained in the model. Some consider gender and factors like pregnancy or being overweight.

The developed model represents a significant simplification compared to the existing models described in Table 2. While these models often require numerous measurements (ranging from 25 in Hanavan to 242 in Hatze) and incorporate complex segment geometries and varying densities, the developed model relies on only two parameters (height and mass). Furthermore, based solely on these two easily obtainable anthropometric measurements, the developed model achieves full parameterization of segment dimensions and masses. This is another significant advantage over models that rely on numerous and potentially less accessible measurements. At the same time, the developed model also offers an advantage over models like Pecolt and Nagano, which may oversimplify segment shapes, potentially leading to inaccuracies. The simplified model, with a drastic reduction in the required measurements to enhance the model’s usability, allows for faster model creation and application, making it a valuable tool for preliminary analyses and rapid prototyping. However, this simplification and parameterization, which depend only on two parameters, comes at the cost of potentially reduced model accuracy and limited applicability to individuals with various body shapes and sizes. It is difficult to determine the accuracy and performance of the models since they depend on a variety of factors, including model complexity, data quality, parameter estimation, and validation. Generally, simpler models with fewer segments and DOF are easier to develop and analyze, but may not accurately capture the complex biomechanics of human movement. More complex models, with a greater number of segments and joints, can provide more realistic simulations, but are computationally expensive, especially when real-time performance is required. Furthermore, the performance and accuracy of existing models can only be generally evaluated since detailed data concerning these parameters are difficult to obtain and even more challenging to interpret and compare, as models present various accuracies regarding numerous features. For instance, it is reported that the Hanavan model provides data about the center of gravity within 0.7 inches from expectations, and the moments of inertia are anticipated within 10% of the experimental results [16]. Meanwhile, the Yeadon model reported around 2% error in specifying the inertia parameters [18]. Even for the Hatze model, which is considered one of the most accurate, the numerical data are quite general, reporting that the overall accuracy of the model is better than 3% [17]. Therefore, the presented comparison of models involves design features, while the evaluation and comparison of performance and accuracy should be performed in the future.

The main model’s limitations and trade-offs of simplifications are as follows:

• parameterization using only two parameters may not accurately capture the anatomical variations of individuals;
• application of single rigid solids may limit the accuracy of results for kinematics since the elasticity of human tissue, and articulations is not included;
• uniform density of segments may lower the accuracy of the results for dynamics.

The model is to some extent universal, but its current scope of applicability and limitations concern the fact that the model refers to people of Caucasian race, adults aged 20–60 years; the model is for men. Its modification to make it adequately useful for women may be the subject of further research and should not be problematic, as the parameterization formulas are mostly based on gender-independent anthropometric data [22,32]. Moreover, the correctness and universality of the additional parametric relationships derived from data for a man in the 50th percentile [23] (Table A1) still need to be verified.

In the case of using a larger number of precise body measurements, the model’s accuracy of simulations and calculations would increase, but this would make its application more difficult (measuring many parameters). Moreover, introducing additional parameters would allow for greater individualization of the model with regard to specific types of body structure, e.g., taking into account, the dependence on different values of the centile (not only the 50th) or the calculated BMI coefficient in anthropometric formulas. However, a very detailed reproduction of the individual human body was not the aim of this study, which instead tried to limit the number of values necessary for model parameterization in order to obtain a simple model that is quick to use as a reference for assumed typical body measurements and which allows results to be obtained with satisfactory accuracy (depending on the application, the acceptable level should be determined). Therefore, the model may not fit precisely for individuals with atypical parameters (not typical BMI), being overweight, etc. The correctness of the model’s operation and its suitability for reproducing measured movements should also be further investigated, e.g., by simulating other activities and using other sensors or sources of data for the simulated movements. In this way, it may also be possible to improve the accuracy of the obtained results.

In the future, one of the key steps for research continuation will be to include the anatomical position of each segment’s COM in the model and then parameterize it again in relation to the smallest possible number of human body measurements (preferably only height and weight). It will also be necessary to compare the results of the dynamic analysis of such a model with the current solution. More importantly, the application of the formulas presented in this work will allow the development of a fully mathematical model of the human body in the future. This would enable kinematic and dynamic parameters to be calculated without the use of Adams or any other multibody simulation software. It would be enough to use a mathematical calculation program such as Matlab or Excel after prior validation and comparison of the obtained results. Another issue is whether the internal/external rotation of the wrist joint should be included in the model. This is generally recognized by biomechanics, but does not occur in everyday activities; therefore, omitting it may be a way to further simplify the model.

In addition, in future attempts to link the model motion simulations with the results from the IMU sensor system, it is necessary to eliminate the need to apply corrections to the obtained values. These corrections, according to the manufacturer, resulted from the method of calculating the biomechanical angles in the joints. One solution could be to use more sensors to measure movements in problematic places or to use data on the orientation of human body segments (directly exported quaternions from the IMU system) instead of data on joint angles. This study aimed to explore the potential of using IMU-based data for the developed model. However, it should also be considered that besides offering certain advantages in terms of portability and ease of use, IMU-based systems have drawbacks. Their accuracy can be influenced by factors such as sensor noise, drift, and signal processing. Due to the limitations of IMU systems, data from optical motion capture systems should be incorporated in future studies.

Moreover, the current study focuses on a single subject with specific characteristics (height 187 cm and mass 70 kg), which may significantly limit the reliability of the current findings and generalizability for broader applications. Therefore, a plan for future research to assess the model’s performance and accuracy should include the following steps.

Firstly—Trials with diverse groups of volunteers to obtain more representative results:

• Recruit volunteers varying in height, weight, body shape, age, and gender to ensure statistically significant results;
• Include a variety of daily activities and tasks;
• Couple volunteers should perform the same activities to assess inter-subject variability and improve the generalizability of the findings;
• Incorporate data from optical motion capture systems (e.g., Vicon) as the gold standard to provide more accurate data for evaluation;
• Collecting data simultaneously with IMU sensors would allow us to directly compare and validate IMU results and their applicability to the model;
• Obtaining human body torques with proper measurement equipment (e.g., torque sensors, Biodex system, and measurement exoskeletons) would allow us to assess the model’s correctness in this aspect.

Secondly—Simulations for a wider range of anthropometric data:

• Include variations in height, weight, and body proportions for the model. This would allow us to assess the model’s sensitivity to these variations and evaluate the model’s generalizability across a more diverse population;
• Compare the model results with those measured for volunteers representative of a particular set of weight and height in order to evaluate the model’s accuracy.

Thirdly—Statistical analysis to assess the accuracy and reliability of the model:

• Compare model predictions with experimental data using appropriate metrics (e.g., root mean square error and correlation coefficients);
• Determine the sensitivity and the universality of the model in predicting different aspects of human movement.

Performing these planned experiments and simulations in the future will allow us to assess the model’s accuracy and significantly enhance its validity, reliability, and generalizability for a broader application. Until this validation is completed, the model’s applicability is limited in the main aspects concerning its usage for a wide range of individuals (sets of height and weight) and for performing various movements and tasks. However, based on the obtained results and conclusions, the preliminary assumptions about the model’s applicability can be stated.

5. Conclusions

To sum up, in the course of research, it was possible to successfully develop a simplified model of the human body. The application of Adams software and the IMU sensor system enabled an example activity (lifting an object from the ground with both hands with a bent spine) to be simulated, and the movement parameters to be analyzed. Currently, this model represents a good approximation of the human body and its kinematic and dynamic parameters. The main model’s simplifications and advantages over existing solutions and, at the same time, the paper’s main contributions include:

• a significant reduction in the number of measurement parameters (just two: height and mass) required for model creation;
• a complete set of parametric equations for each segment’s dimensions and mass (based on the available data parameterizing the features of the human body and supplementing them with anthropometric data).

As stated, the developed model is universal (to some extent) and can be scaled and used multiple times. This universality is achieved by minimizing the need for detailed individual measurements while striking a balance between simplicity and accurate representation of the human body. However, the broader applicability for the range of individuals and the performance of the model still needs to be fully proven in future planned studies. Based on the current state of research, it is estimated that the model can be used for different people and reproducing many activities. Moreover, it also allows a number of parameters for a standard human body to be achieved, but in relation to two easily obtainable main individual characteristics (height and weight). It can also serve as a tool for visualizing movements, such as those measured with IMU sensors, which was already demonstrated by one volunteer.

For these reasons, the potential fields of application of the model for analyzing the human body and its movements are medicine (especially rehabilitation devices and strategies), sports (biomechanics of movement), and robotics (humanoid machines and human-robot interactions). The use of the developed model by engineers/biomechanists may lead to the development of various devices that support people, which could improve their quality of life in the future.