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Molecular & Cellular Biomechanics 2024, 21(3), 518.
https://doi.org/10.62617/mcb518
1
Article
Numerical simulation of muscle force distribution during high-intensity
athletic movements
Huaiyuan Deng
Life Science College, Sichuan University, Cheng Du 610065, China; denghuaiyuan@stu.scu.edu.cn
Abstract: Athletes performing high-intensity movements such as sprinting, jumping, and
powerlifting rely on precise muscle coordination to generate the necessary forces for efficient
movement. Examining how forces are distributed across muscle groups during these activities
is critical for enhancing performance and reducing injury risks. However, detailed insights into
the muscle force contributions during these specific movements are still limited. This study
aims to address this gap by using advanced biomechanical techniques and numerical
simulations to analyze the distribution of muscle forces in athletes engaged in these high-
intensity tasks. Thirty-two athletes, including 15 professionals and 17 amateurs, participated in
this research. Data were collected using motion capture systems, electromyography (EMG),
and force plates. The musculoskeletal simulations were run on OpenSim, focusing on key
muscle groups like the quadriceps, hamstrings, gluteus maximus, gastrocnemius, and iliopsoas.
In sprinting, the quadriceps generated peak force during the stance phase, reaching 1452 N
between 200–250 ms, while the gastrocnemius & soleus produced 845 N, contributing to ankle
plantarflexion. The iliopsoas took over during the swing phase, peaking at 620 N to elevate the
leg. In jumping, the quadriceps exhibited a maximum force of 1480 N in the take-off phase,
with the gastrocnemius reaching 1020 N, supporting upward propulsion. During powerlifting,
particularly the back squat, the quadriceps reached 1520 N during the concentric phase, while
the hamstrings peaked at 1220 N, contributing to knee stabilization and hip extension.
Keywords: biomechanical techniques; motion capture systems; electromyography; precise
muscle coordination; powerlifting; numerical simulations
1. Introduction
High-intensity athletic movements, such as sprinting, jumping, and powerlifting,
place significant demands on the musculoskeletal system, requiring the coordinated
effort of multiple muscle groups to produce the necessary forces for movement and
stability [1,2]. Understanding how these forces are distributed across different muscles
during these activities is crucial for optimizing athletic performance, preventing
injuries, and improving training regimens [3,4]. Simulating muscle force distribution
during these complex movements provides valuable insights into the biomechanics of
athletic performance, allowing athletes, coaches, and sports scientists to tailor
interventions more effectively [5,6].
The study of muscle force distribution is especially relevant in high-intensity
sports because these activities typically involve rapid accelerations, decelerations, and
changes in direction, which subject the body to high mechanical loads [7–9]. Athletes
engaged in sprinting, jumping, and powerlifting often experience extreme forces
through their lower limbs, hips, and core, with varying levels of involvement from
muscles like the quadriceps, hamstrings, gastrocnemius, and gluteus maximus [10,11].
Moreover, upper body muscles such as the shoulders and erector spinae also contribute
CITATION
Deng H. Numerical simulation of
muscle force distribution during high-
intensity athletic movements.
Molecular & Cellular Biomechanics.
2024; 21(3): 518.
https://doi.org/10.62617/mcb518
ARTICLE INFO
Received: 12 October 2024
Accepted: 21 October 2024
Available online: 6 December 2024
COPYRIGHT
Copyright © 2024 by author(s).
Molecular & Cellular Biomechanics
is published by Sin-Chn Scientific
Press Pte. Ltd. This work is licensed
under the Creative Commons
Attribution (CC BY) license.
https://creativecommons.org/licenses/
by/4.0/
Molecular & Cellular Biomechanics 2024, 21(3), 518.
2
significantly to balance, stability, and overall force production in powerlifting and
certain phases of sprinting [12]. Investigating the distribution of forces across these
muscle groups can help identify key moments during movement where peak forces
occur, potentially leading to improved techniques and strategies to enhance
performance and reduce injury risk [13].
Previous research has predominantly focused on muscle activation patterns and
general biomechanics during high-intensity movements, but fewer studies have
comprehensively examined the precise distribution of muscle forces using advanced
simulation techniques [14–18]. By leveraging cutting-edge technologies such as
motion capture, electromyography (EMG), and force plate analysis in combination
with musculoskeletal modeling software, this study aims to provide a more detailed
analysis of how forces are distributed among the primary muscle groups during high-
intensity movements [19–20]. These simulations offer a unique opportunity to
visualize and quantify muscle engagement, highlighting the most heavily loaded
muscles during the key movement phases, including stance, take-off, and landing. This
study uses numerical simulations to analyze muscle force distribution during high-
intensity athletic activities, focusing specifically on three fundamental movements:
sprinting, vertical jumping, and powerlifting. Each of these movements presents
unique biomechanical challenges and requires different patterns of muscle activation
and force generation. Sprinting involves rapid cyclic motion with alternating phases
of propulsion and recovery while jumping requires explosive power and precise
coordination of multiple joints for a successful take-off and controlled landing. On the
other hand, powerlifting emphasizes maximum force production to move heavy
weights, engaging a broad range of muscle groups in both the lower and upper body.
The proposed study uses numerical simulations to conduct a comprehensive
analysis of muscle force distribution during high-intensity athletic movements. By
focusing on three key movements—sprinting, vertical jumping, and powerlifting—
this research will investigate how different muscle groups contribute to the generation,
absorption, and transfer of forces throughout each movement cycle. The study will use
advanced tools such as motion capture systems, electromyography (EMG), force
plates, and musculoskeletal modeling software (OpenSim) to simulate muscle activity
and force distribution in both professional and amateur athletes [21–25]. The proposed
work will involve detailed data collection of movement patterns, muscle activation,
and ground reaction forces, which will be processed and integrated into a customized
musculoskeletal model. This model will then analyze joint kinematics, calculate joint
moments, and estimate individual muscle forces. Furthermore, the study will compare
the force distribution patterns between professional and amateur athletes, providing
insights into biomechanical efficiency, performance optimization, and injury
prevention. The findings from this research will have practical implications for
designing more effective training programs and enhancing athletic performance,
particularly in high-intensity sports [26–32].
The structure of the paper is organized as follows: Section 2 provides a
comprehensive overview of the methodology, detailing the participant selection
process, data collection techniques, and the musculoskeletal modeling approach used
to simulate muscle force distribution. Section 3 presents an in-depth analysis of the
findings, examining muscle engagement across different phases of high-intensity
Molecular & Cellular Biomechanics 2024, 21(3), 518.
3
movements such as sprinting, jumping, and powerlifting. Finally, Section 4 concludes
the study, summarizing key insights and discussing the practical implications for
athletic performance optimization and injury prevention.
2. Methodology
2.1. Participant selection
For the study, 32 athletes were selected, representing a diverse group, to ensure
a comprehensive analysis of muscle force distribution. The selection process focused
on recruiting participants who regularly engage in high-intensity sports, ensuring they
possess the necessary physical conditioning and experience for the types of
movements under analysis. Participants were drawn from two main categories:
professional athletes (n = 15) and amateur athletes (n = 17). The professional athletes
included individuals competing in sprinting, weightlifting, and competitive cycling at
regional and national levels, with an average of 6.7 years of professional experience.
The amateur athletes had an average of 4.2 years of regular training experience in
high-intensity activities such as CrossFit, amateur powerlifting, and recreational
athletics.
Regarding demographic details, the participants were 22 males and 10 females,
ensuring gender representation for both groups. The age range of the participants was
between 22 to 35 years, with a mean age of 27.4 years. All participants had a body
mass index (BMI) within the 18.5 to 26.4 kg/m2 range, falling into the healthy to
athletic category, which was essential to standardize the biomechanical simulations
and avoid variations due to extreme body mass or height differences. The average
height of participants was 175.3 cm (range: 162 cm to 189 cm), and the average weight
was 72.6 kg (range: 61.8 kg to 86.3 kg).
Inclusion criteria required all participants to have no history of major
musculoskeletal injuries within the past 18 months, as injuries could significantly alter
movement mechanics and muscle force distribution. Furthermore, participants were
required to complete a movement proficiency screening, confirming their ability to
perform the high-intensity athletic movements required for the study, such as
maximal-effort sprints, vertical jumps, and powerlifting movements (squat, deadlift,
clean).
2.2. Tools and techniques
Advanced biomechanical tools and computational techniques were employed to
accurately simulate and analyze muscle force distribution during high-intensity
athletic movements. The integration of motion capture technology, electromyography
(EMG), force plates, and sophisticated numerical simulation software provided a
robust framework for capturing and analyzing the complex dynamics of muscle
activity. A 12-camera Vicon motion capture system was used to record the athletes’
movements with high precision. This optical tracking system operates at a frequency
of 250 Hz, ensuring that even rapid, high-intensity movements are captured in
sufficient detail. The reflective markers were placed on key anatomical landmarks
following the Plug-in Gait model to track joint angles and body segment movements.
Molecular & Cellular Biomechanics 2024, 21(3), 518.
4
The motion capture data allowed for the construction of accurate kinematic profiles of
each athletic movement, forming the foundation for subsequent biomechanical
analysis.
Surface electromyography (EMG) was employed to measure muscle activation
patterns in real-time during the athletic movements. A Delsys Trigno wireless EMG
system was utilized, with electrodes placed on the primary muscle groups involved in
the selected movements, including the quadriceps, hamstrings, gluteus maximus,
gastrocnemius, and erector spinae. The EMG data was sampled at 1000 Hz to capture
fine details of muscle activation. This data provided insights into the timing and
intensity of muscle engagement, which was critical for correlating muscle force with
specific movement phases. Advanced Mechanical Technology, Inc. (AMTI) force
plates were used to measure ground reaction forces (GRFs) during dynamic
movements such as jumping, sprinting, and lifting to complement the motion capture
and EMG data. The force plates were recorded at a sampling rate of 2000 Hz, ensuring
precise capture of the force dynamics, especially during explosive actions. These GRF
measurements were essential for calculating the external forces acting on the body,
which were then used to compute internal muscle forces via inverse dynamics analysis.
OpenSim, a widely used musculoskeletal modeling software, was selected to
simulate muscle force distribution. OpenSim enables the creation of detailed
biomechanical models and the simulation of muscle forces during movement. A
generic full-body musculoskeletal model with 39 degrees of freedom and 92 muscle
actuators was customized based on participant-specific anthropometric data collected
through the motion capture system. Inverse kinematics (IK) was used within OpenSim
to calculate joint angles from the motion capture data. Subsequently, inverse dynamics
(ID) calculations were performed to determine the net joint moments based on the
measured ground reaction forces. Static optimization techniques were applied to
estimate individual muscle forces, solving the distribution of muscle forces that
produce the observed joint moments while minimizing total muscle activation.
All raw data, including motion capture, EMG, and force plate recordings, were
synchronized and processed using matrix laboratory (MATLAB). Custom MATLAB
scripts were developed to preprocess the data, including filtering the EMG signals with
a fourth-order Butterworth filter (20–450 Hz bandpass) and smoothing motion capture
data using a low-pass filter with a 6 Hz cutoff frequency to remove noise. After
preprocessing, the data was fed into the OpenSim model, which was used to drive
simulations of muscle force distribution. MATLAB was also used for statistical
analysis of the simulation results, where muscle force outputs were compared across
different movements and participant groups.
To ensure the accuracy of the numerical simulations, the results were validated
by comparing the predicted muscle forces to known physiological parameters from the
literature and cross-referencing the muscle activation patterns derived from the EMG
data. This cross-validation helped confirm that the model’s muscle force predictions
were consistent with experimental measurements and established biomechanical
knowledge. The results of the simulations, including muscle force distribution patterns
and joint load profiles, were visualized using OpenSim’s built-in visualization tools
and custom plots generated in MATLAB. These visualizations provided clear insights
into which muscle groups were most engaged during each movement phase and how
Molecular & Cellular Biomechanics 2024, 21(3), 518.
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forces were distributed across the body. The following table provides the tools used in
the study (Table 1).
Table 1. Tools and techniques employed in the study.
Tool/Technique
Purpose
Specifications
Data Collected
Vicon Motion Capture System
Capturing 3D kinematic data of
body movements
12 cameras, 250 Hz frequency, Plug-in
Gait model
Joint angles, body segment
movements
Delsys Trigno Wireless EMG
System
Recording muscle activation
patterns during movement
Wireless electrodes, 1000 Hz sampling
frequency
Muscle activation timings
and intensities
AMTI Force Plates
Measuring ground reaction forces
during dynamic movements
2000 Hz sampling rate
Ground reaction forces
(GRFs)
OpenSim Software
Simulating muscle forces and
biomechanical analysis
The full-body musculoskeletal model
with 39 degrees of freedom, 92 muscle
actuators
Muscle force distribution,
joint moments
MATLAB (Data Processing)
Data preprocessing, synchronization,
and statistical analysis
Custom scripts, filtering (Butterworth,
low-pass), data synchronization
Filtered motion capture,
EMG, and force plate data
Inverse Kinematics (OpenSim)
Calculating joint angles from motion
capture data
Applied to motion capture data for
kinematic modeling
Joint angles and body
segment positioning
Inverse Dynamics (OpenSim)
Estimating net joint moments based
on ground reaction forces
Used ground reaction forces to compute
internal joint forces
Joint moments
Static Optimization (OpenSim)
Estimating individual muscle forces
Optimization technique to minimize
muscle activation while reproducing joint
moments
Individual muscle forces
during movements
MATLAB (Visualization)
Visualizing muscle force
distribution and analysis results
Custom plots and visualizations
Muscle force distribution
patterns, joint loads
EMG Signal Processing
Filtering and analyzing muscle
activation data
4th-order Butterworth filter (20–450 Hz
bandpass)
Cleaned muscle activation
data
Ground Reaction Force
Analysis
Measuring external forces acting on
the body during movements
Force plates, 2000 Hz sampling rate
External forces applied to
lower limbs and body
2.3. Musculoskeletal model
The present study developed a detailed musculoskeletal model using OpenSim to
simulate the muscle force distribution during high-intensity athletic movements. The
model used for this study was a full-body musculoskeletal model that was customized
for each participant based on their anthropometric measurements, ensuring accuracy
in force and movement simulations. The musculoskeletal model contained 39 degrees
of freedom (DOF), allowing for complex multi-joint movements, and included 92
muscle actuators representing the primary muscles involved in athletic movements.
Model Structure: The model was designed to replicate the human skeletal and
muscular systems, with key joints and muscle groups specifically included to capture
the dynamics of high-intensity movements. Each body segment was modeled as rigid
bodies connected by joints, with the following joints being essential for the movements
under study:
⚫ Hip joint (3 DOF: flexion/extension, abduction/adduction, internal/external
rotation)
Molecular & Cellular Biomechanics 2024, 21(3), 518.
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⚫ Knee joint (1 DOF: flexion/extension)
⚫ The ankle joint (2 DOF: dorsiflexion/plantarflexion, inversion/eversion)
Multiple muscles actuated each of these joints, and the model included muscle-
tendon units for each muscle, representing muscle fiber properties (e.g., length,
velocity, and activation) and tendon elasticity. The muscle actuators within the model
were modeled based on the Hill-type muscle model, which describes the muscle’s
force generation capacity through three key elements: the contractile element
(representing active muscle fibers), the series elastic element (tendons), and the
parallel elastic element (passive muscle components).
Muscle Parameter Customization: To enhance the model’s fidelity, muscle
parameters were individualized for each participant based on their specific height,
weight, and limb lengths. This involved scaling the generic OpenSim model using
participant-specific anthropometric data collected through the motion capture system.
The scaling process ensured that muscle lengths, moment arms, and force-generation
properties accurately reflected the participants’ physiological structures.
The following muscle parameters were customized:
⚫ Maximum isometric force for each muscle group, adjusted based on body mass
and size.
⚫ Optimal muscle fiber and tendon slack length ensure the model replicates muscle
function across various joint angles.
⚫ The rotation angle of muscle fibers affects the force transfer from the muscle to
the tendon.
Muscle Activation and Force Production: The musculoskeletal model used
muscle activation patterns obtained from the EMG data to drive the simulation of
muscle forces. The relationship between neural activation and muscle force was
modeled using a dynamic activation-deactivation model, accounting for the time it
takes for muscles to reach full activation or relaxation. The Hill-type muscle model
incorporated these activation dynamics to simulate realistic muscle force production
during rapid, high-intensity movements.
Inverse dynamics was employed to calculate the forces produced by individual
muscles, whereby motion capture and force plate data were used to compute joint
moments. These joint moments were then resolved into individual muscle forces using
static optimization. This optimization method minimized the sum of squared muscle
activations, a commonly used criterion in biomechanics to estimate physiologically
realistic muscle forces. By doing so, the model could distribute the required joint
moments across the contributing muscles based on their capacity to generate force.
Consideration of Muscle Fatigue: One important aspect of the model was the
consideration of muscle fatigue, particularly during prolonged or repetitive high-
intensity movements. While the base OpenSim model does not inherently simulate
muscle fatigue, the study incorporated an empirical model that adjusted muscle force
capacity over time based on known fatigue parameters from the literature. This
adjustment allowed for more accurate simulation of movements like sprints or
weightlifting sets, where muscle performance decreases as fatigue sets in.
Joint Stability and Force Distribution: The model also accounted for joint
stability by ensuring that muscles were appropriately co-activated to stabilize joints
during high-intensity movements. For example, during the simulation of sprinting,
Molecular & Cellular Biomechanics 2024, 21(3), 518.
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muscles around the knee, such as the quadriceps and hamstrings, were co-activated to
ensure stability under high loads. The model distributed forces between these muscle
groups in a manner that maintained joint stability while optimizing the overall force
generation for movement.
Validation of the Musculoskeletal Model: To validate the accuracy of the
musculoskeletal model, the simulated muscle forces were compared against
experimental data, including EMG readings and known force production capacities
from the literature. Additionally, the joint angles and moments predicted by the model
were validated against the motion capture data to ensure that the model accurately
reproduced the participants’ movements. This validation process was crucial to ensure
that the simulation results could be considered reliable for further analysis.
Limitations and Assumptions: While the musculoskeletal model provided
detailed insights into muscle force distribution, several assumptions were made that
could influence the results. For instance, the static optimization method assumes that
muscles minimize overall activation, which may not fully capture the complex neural
strategies employed during high-intensity movements. Additionally, the Hill-type
muscle model used in this study simplifies muscle-tendon interactions, and further
refinement of tendon elasticity and force-velocity relationships could enhance the
model’s precision.
2.4. Experimental design
The experimental design of this study was carefully crafted to simulate and
analyze muscle force distribution during high-intensity athletic movements, ensuring
that the data collected accurately reflects real-world conditions. The design integrated
experimental data collection and computational modeling to understand the
biomechanics involved comprehensively. This section details the experimental
procedures, equipment setup, and data acquisition protocols used to obtain the
necessary inputs for the musculoskeletal simulations.
Participant Preparation and Warm-Up: Before data collection, all participants
underwent a standardized warm-up session to ensure they were physically prepared
for the high-intensity movements required in the experiment. The warm-up included
10 min of light aerobic activity, followed by dynamic stretching and movement-
specific drills to engage the muscles most involved in the experimental tasks. This was
essential to prevent injury during the trials and ensure consistent participant muscle
performance.
Experimental Task Selection: The tasks selected for the study were chosen based
on their ability to represent a wide range of high-intensity athletic movements
commonly observed in sports and fitness settings.
Three distinct movements were selected:
1) Maximal sprinting: Participants performed three 30-meter sprints at maximal
effort, focusing on the explosive use of lower body muscles.
2) Vertical jumping: Participants completed five maximal vertical jumps, using the
arms for momentum while focusing on the lower body muscle groups.
3) Powerlifting movements: Participants performed two major powerlifting
exercises:
Molecular & Cellular Biomechanics 2024, 21(3), 518.
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• Back Squat (3 repetitions at 85% of their one-repetition maximum)
• Deadlift (3 repetitions at 85% of their one-repetition maximum)
These movements were selected because they engage multiple muscle groups and
joints in dynamic, high-intensity ways, providing a varied dataset for simulating
muscle force distribution across different types of athletic exertion.
2.5. Data collection setup
The experimental setup involved using several high-precision instruments to
simultaneously capture motion, muscle activity, and ground reaction forces. Each
participant performed the movements in a controlled laboratory environment equipped
with the following tools:
• Vicon motion capture system: A 12-camera system was used to capture 3D
kinematic data, with reflective markers placed at key anatomical landmarks based
on the Plug-in Gait model. The motion capture system recorded at 250 Hz,
providing high-resolution data on joint angles, segment velocities, and
accelerations.
• Electromyography (EMG): Surface EMG electrodes were applied to major
muscle groups involved in the selected movements. EMG data was collected at
1000 Hz, providing detailed information on muscle activation levels during each
movement phase. The primary muscles monitored included the quadriceps,
hamstrings, gluteus maximus, gastrocnemius, erector spine, biceps femoris, and
rectus abdominis.
• Force plates: AMTI force plates were used to measure ground reaction forces
during each movement, with a sampling rate of 2000 Hz. These plates were
essential for capturing the dynamic forces exerted by the athletes during jumping,
sprinting, and powerlifting, allowing for the calculation of net joint forces and
torques.
2.6. Trial execution and data recording
Each participant performed the selected movements under the supervision of
trained researchers to ensure proper form and execution. The order of the tasks was
randomized to minimize any order effects that could influence muscle performance
due to fatigue. Five trials were conducted for each movement, with adequate rest
periods of 3–5 min between each trial to allow muscle recovery and prevent fatigue
from affecting the results. Data from the motion capture system, EMG, and force plates
were collected and synchronized for each movement. This synchronized data was
crucial for accurately mapping the muscle forces to the corresponding phases of
movement, such as the stance and swing phases of sprinting or the eccentric and
concentric phases of lifting.
Control Variables: To ensure the reliability and validity of the experiment,
several control variables were carefully maintained:
• Footwear: Participants wore standardized athletic footwear to minimize ground
contact forces and lower limb mechanics variability.
• Surface: All movements were performed on a level surface to control for
variations in ground reaction forces due to surface incline or texture.
Molecular & Cellular Biomechanics 2024, 21(3), 518.
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• Environmental conditions: The laboratory environment was kept at a consistent
temperature of 22 ℃, and humidity levels were monitored to ensure they
remained constant. This prevented external environmental factors from
influencing muscle performance.
Following the data collection, all raw data were processed using MATLAB for
initial cleaning and synchronization. EMG signals were filtered using a fourth-order
Butterworth filter (20–450 Hz) to remove noise, and motion capture data were
smoothed using a low-pass filter (cutoff frequency: 6 Hz) to eliminate any unwanted
high-frequency noise. The cleaned data was input for the OpenSim musculoskeletal
model (Figure 1), which simulated the muscle force distribution during each
movement. The data processing step also included the extraction of relevant joint
kinematics, ground reaction forces, and muscle activation levels, which were used to
drive the numerical simulations.
To improve the robustness of the findings, each participant repeated the
experimental tasks multiple times (five trials per movement), and the order of tasks
was randomized across participants. Randomization was used to ensure that any
variability in muscle performance or fatigue effects were evenly distributed across the
different movements and trials. The experimental design adhered to all ethical
standards for human subject research. Before participation, each athlete provided
informed consent, acknowledging their understanding of the risks and voluntary
participation in the study. The university’s ethics review board approved the study
protocol, and safety measures were implemented to address any potential injuries
during high-intensity tasks. Athletes were monitored throughout the trials, and any
discomfort or fatigue was addressed immediately to ensure participant well-being.
Figure 1. Musculoskeletal model.
3. Result analysis
3.1. Force distribution analysis
i) Force distribution analysis for sprinting:
The force distribution analysis for sprinting, as shown in Figure 2, reveals key
insights into how different muscle groups contribute to movement across the stance
and swing phases of the sprinting cycle. The primary muscles analyzed include the
Molecular & Cellular Biomechanics 2024, 21(3), 518.
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quadriceps, gastrocnemius & soleus, hamstrings, and iliopsoas, with distinct patterns
of engagement observed during each phase.
• Stance Phase (0–500 ms): During the stance phase, where the foot is in contact
with the ground, there is a progressive increase in force production across all
major muscle groups. The quadriceps dominate, reaching their peak force of 1452
N between 200–250 ms when the body pushes off the ground. This substantial
force is crucial for extending the knee and generating forward propulsion.
Following this, the quadriceps force begins to decline as the foot transitions
towards the end of the stance phase. Similarly, the gastrocnemius & soleus
muscles, which are responsible for ankle plantarflexion, show a gradual increase
in force, peaking at 845 N during the same 200–250 ms window. This highlights
the importance of ankle extension in the push-off phase, contributing
significantly to propulsion. The hamstrings also contribute significantly during
the stance phase, especially between 150–200 ms, generating a peak force of
1023 N. The hamstrings aid in knee stabilization and hip extension, which is
essential for maintaining stability and power during ground contact. As the stance
phase progresses, the forces in all muscle groups gradually decrease, particularly
in the final 450–500 ms window, where the body prepares to transition into the
swing phase.
• Swing phase (500–800 ms): During the swing phase, where the foot is no longer
in contact with the ground, there is a notable shift in muscle engagement. The
primary hip flexor, the iliopsoas, becomes the dominant muscle, as it is
responsible for lifting the leg and preparing it for the next stance phase. The
iliopsoas force peaks at 620 N between 600–650 ms, indicating its crucial role in
bringing the thigh forward. The hamstrings remain active during the late swing
phase, particularly between 650–700 ms, generating 489 N of force. This force is
critical in controlling leg deceleration and preparing for the upcoming ground
contact. Throughout the swing phase, the quadriceps, gastrocnemius, and soleus
are minimally engaged, as their role is limited while the leg is off the ground. The
focus shifts entirely to the iliopsoas and hamstrings, which manage leg movement
and positioning.
Figure 2. Force distribution for sprinting.
Molecular & Cellular Biomechanics 2024, 21(3), 518.
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ii) Force distribution against time for the jumping activity:
Figure 3. Force distribution for Jumping.
The data presented in Figure 3 provides a comprehensive analysis of the force
distribution among the primary muscles involved in the jumping activity, including
the quadriceps, gastrocnemius & soleus, hamstrings, and gluteus maximus, across
various phases of the jump: pre-take-off, take-off, landing preparation, and landing.
• Pre-Take-off Phase (0–100 ms): During the pre-take-off phase, the body prepares
for the explosive jump by generating increasing force in the quadriceps,
gastrocnemius & soleus, hamstrings, and gluteus maximus. The quadriceps,
responsible for knee extension, start generating force at 320 N and rise sharply to
750 N between 50–100 ms, preparing the legs for the powerful extension that
follows in the take-off phase. The gastrocnemius and soleus muscles also show a
significant force increase from 140 N to 430 N during the pre-take-off phase,
aiding ankle plantarflexion and assisting with the initial drive upward. The
hamstrings and gluteus maximus, which contribute to hip extension and
stabilization of the posterior chain, show similar force generation patterns, with
the hamstrings rising from 210 N to 480 N and the gluteus maximus increasing
from 150 N to 380 N.
• Take-off Phase (100–300 ms): The take-off phase is where the body generates
maximum force to propel itself off the ground. The quadriceps exhibit the highest
force during this phase, peaking at 1480 N between 200–250 ms, emphasizing
their critical role in knee extension and the explosive upward movement of the
jump. The gastrocnemius and soleus muscles show a similar pattern, with force
increasing to 1020 N at the peak take-off phase, providing the necessary ankle
extension for a powerful push-off. The hamstrings also play an essential role in
stabilizing the knee and aiding in hip extension, peaking at 1105 N. The gluteus
maximus, crucial for hip extension, generates a peak force of 1025 N at 200–250
ms. This muscle contributes significantly to the upward propulsion, working with
the quadriceps and hamstrings to lift the body off the ground.
• Landing Preparation (300–400 ms): As the body prepares for landing, the forces
in all muscle groups begin to decrease. The quadriceps reduce from 1350 N at
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250–300 ms to 1180 N at 300–350 ms as the body shifts from propelling upward
to controlling the descent. The gastrocnemius and soleus, responsible for
absorbing some of the impact during landing, decline from 910 N to 770 N over
this period. The hamstrings and gluteus maximus also reduce force output,
transitioning from active take-off engagement to a stabilizing role during the
descent. The hamstrings decrease to 840 N, while the gluteus maximus lowers to
750 N during landing preparation.
• Landing Phase (400–600 ms): During the landing phase, the forces in all muscle
groups continue to decrease as the body absorbs the impact of the ground. The
quadriceps gradually reduce force from 740 N during the initial landing (400–
450 ms) to 120 N during the final landing (550–600 ms). This highlights the
quadriceps’ key role in controlling the landing by decelerating the body’s
downward momentum and stabilizing the knees. The gastrocnemius and soleus
muscles, which aid shock absorption during ankle dorsiflexion, reduce from 470
N to 40 N by the final landing phase. Similarly, the hamstrings and gluteus
maximus forces decrease, reflecting their reduced role as the body absorbs the
impact and transitions into a stabilized position.
iii) Force distribution results for power lifting:
Figure 4. Back squat force distribution.
Figure 4 for the back squat highlights the involvement of the movement’s
quadriceps, hamstrings, gluteus maximus, and gastrocnemius & soleus muscles during
both the eccentric (lowering) and concentric (lifting) phases.
• Eccentric Phase (0–400 ms): During the eccentric phase, as the lifter lowers into
the squat position, all muscle groups show a progressive increase in force output
as the body resists the gravitational pull. The quadriceps are the dominant force
producers, starting at 280 N and rising to 1080 N by 300–400 ms, as they control
knee flexion during the descent. This indicates the quadriceps’ crucial role in
stabilizing and controlling the descent. The hamstrings and gluteus maximus
work together to control hip flexion during the eccentric phase, with the
hamstrings increasing from 180 N to 720 N and the gluteus maximus increasing
Molecular & Cellular Biomechanics 2024, 21(3), 518.
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from 120 N to 680 N by 300–400 ms. These posterior chain muscles help stabilize
the hips and provide the necessary control over the squat descent. The
gastrocnemius and soleus muscles provide additional stability at the ankles,
increasing from 80 N to 540 N by 300–400 ms, helping to control the foot and
lower leg position as the body descends into the bottom position.
• Bottom Position (400–500 ms): At the bottom of the squat, force output peaks
across all muscle groups, with the quadriceps reaching 1250 N, the hamstrings at
910 N, and the gluteus maximus at 830 N. The gastrocnemius and soleus muscles
reach 720 N, highlighting their role in maintaining balance and readiness for the
concentric phase.
• Concentric Phase (500–1000 ms): As the lifter moves upward in the concentric
phase, all muscles increase their force output to drive the body back to the
standing position. The quadriceps reach their maximum force output of 1520 N
between 600–700 ms, reflecting their critical role in extending the knees during
the lift. The hamstrings and gluteus maximus also contribute significantly during
the concentric phase, with the hamstrings peaking at 1220 N and the gluteus
maximus at 1040 N. These muscles are essential for extending the hips and
stabilizing the lower body during the upward movement. The gastrocnemius and
soleus support ankle stability, peaking at 980 N during the 600–700 ms period.
As the lifter approaches the standing position, all muscle forces gradually
decrease.
Figure 5. Deadlift force distribution.
In the deadlift (Figure 5), the force distribution highlights the roles of the
quadriceps, hamstrings, gluteus maximus, and erector spine during the lift. The erector
spinae plays a significant role in maintaining spinal stability and controlling the
position of the upper body.
• Eccentric Phase (0–300 ms): During the initial pull in the eccentric phase, the
quadriceps provide the primary force for knee extension, starting at 240 N and
rising to 760 N by 200–300 ms. The quadriceps’ role is to drive the initial pull of
the bar off the ground. The hamstrings and gluteus maximus work in unison to
Molecular & Cellular Biomechanics 2024, 21(3), 518.
14
extend the hips, with the hamstrings increasing from 180 N to 620 N and the
gluteus maximus increasing from 130 N to 540 N during the initial pull. These
posterior muscles play a critical role in hip extension, which is necessary to
initiate the movement. The erector spinae shows a significant increase in force,
from 200 N to 670 N, as it stabilizes the spine and supports the upper body during
the initial stages of the lift.
• Concentric Phase (300–800 ms): During the mid-pull and lockout phases, the
quadriceps generate force, peaking at 1360 N during 400–500 ms. This force is
essential for extending the knees and lifting the weight to the standing position.
The hamstrings and gluteus maximus also peak during the concentric phase, with
the hamstrings reaching 1250 N and the gluteus maximus reaching 1210 N at
500–600 ms. These muscles are critical for hip extension and play a key role in
the lifter’s ability to pull the bar past the knees and lockout at the top of the lift.
The erector spinae shows the highest force production during the lockout phase,
peaking at 1380 N, as it maintains spinal extension and prevents back rounding.
This is vital for protecting the lower back during heavy lifting.
3.2. Kinematic analysis
i) Kinematic analysis for sprint cycle:
As shown in Figure 6, During the early stance (0–100 ms), the hip shows an
increasing joint angle from 5.6° to 15.4°, with the angular velocity and acceleration
peaking at 220°/s and 410°/s2 in mid stance (100–150 ms). The hip reaches a maximum
joint angle of 28.4° before decreasing during push-off and transitioning to the swing
phase, where it reaches −20.1° during late swing (450–500 ms). The knee angle
increases rapidly from 15.8° in early stance to a peak of 45.2° during mid stance. The
angular velocity and acceleration peak at 380°/s and 600°/s2 in mid-stance, decreasing
gradually as the knee approaches late swing with a joint angle of −10.8°.
The ankle exhibits dorsiflexion during early stance with an angle of −2.3° and
transitions to plantarflexion, peaking at 15.1° during late stance. The angular velocity
peaks at 180°/s during late stance before decreasing into the swing phase, with the
ankle reaching −15.8° by late swing. The shoulder starts with flexion during the arm
forward swing, peaking at 65.4° during 100-150 ms. As the arms transition into a
backward swing, the shoulder begins extending, reaching 25.3° by 250–300 ms. The
elbow follows a similar pattern, peaking at 75.2° flexion during 350–400 ms, then
extending during the arm backward swing with a joint angle of 25.3° by 450–500 ms.
ii) Kinematic Analysis for Jumping:
As shown in Figure 7, in the pre-take-off phase (0-100 ms), the hip joint angle
increases from 10.2° to 22.5°, with a peak angular velocity of 100°/s and angular
acceleration of 200°/s2, showing preparation for the explosive jump. The knee also
shows a sharp increase in joint angle from 20.5° to 35.0°, while the ankle transitions
from dorsiflexion to plantarflexion, with an angle increasing from −5.0° to 2.5°.
During the take-off phase (100–250 ms), the hip reaches a maximum joint angle of
45.0° and peaks in angular velocity at 180°/s during 150–200 ms. Similarly, the knee
angle reaches 60.5° with a peak angular velocity of 220°/s during 150–200 ms. The
Molecular & Cellular Biomechanics 2024, 21(3), 518.
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ankle exhibits significant plantarflexion, reaching 25.0° with an angular velocity
peaking at 180°/s during the take-off phase.
In the flight phase (300–500 ms), the hip joint starts to flex, decreasing from 18.4°
to −20.1°, while the knee reduces from 25.0° to −12.0°, and the ankle shows further
dorsiflexion, reaching −25.0°. Angular velocities and accelerations decrease as the
body reaches the peak of the jump. In the landing preparation and landing phases (500–
800 ms), the hip angle shifts from −18.9° during flight to 12.0° during landing. The
knee prepares for landing with a joint angle of 6.0° during 650–700 ms, while the
ankle shifts from −28.0° during flight to 14.0° in the final landing, showing gradual
plantarflexion. Angular velocities and accelerations stabilize as the body absorbs
impact. For the shoulder, during the pre-take-off phase (0–100 ms), the shoulder joint
flexes from 45.5° to 60.2° with a peak angular velocity of 160°/s during 100–150 ms.
In the arm swing during take-off (150–250 ms), the shoulder transitions into extension,
decreasing from 65.0° to 50.3°. The elbow moves through flexion in the pre-take-off
phase, peaking at 75.0° at 0–50 ms and extending during the take-off and arm return
phases.
Figure 6. Kinematic analysis for sprint cycle.
Molecular & Cellular Biomechanics 2024, 21(3), 518.
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Figure 7. Kinematic analysis for Jumping.
iii) Kinematic analysis for powerlifting:
Figure 8. Kinematic analysis for powerlifting (back squat).
Molecular & Cellular Biomechanics 2024, 21(3), 518.
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As shown in Figure 8, in the eccentric phase (lowering) of the back squat, the
hip joint angle increases from 10.0° to 58.5° between 0–500 ms, with the angular
velocity reaching −180°/s and the angular acceleration peaking at −350°/s2 during the
bottom position. The knee joint follows a similar pattern, increasing from 20.2° to
78.0°, while the ankle joint moves from −5.0° dorsiflexion to 15.0° plantarflexion,
showing the transition from lowering to the bottom squat position. In the concentric
phase (lifting) from 500–900 ms, the hip joint decreases from 58.5° to 10.0°, and the
angular velocity reverses to 140°/s, peaking at 500–600 ms. The knee follows the same
pattern, with the angle reducing from 78.0° to 20.8° and the ankle returning to −5.0°
dorsiflexion by the end of the lift. The shoulder flexes during the eccentric phase,
moving from 20.0° to 75.5° at 400–500 ms. During the concentric phase, the shoulder
extends from 65.0° to 20.0°, with a peak angular velocity of −100°/s between 500–
600 ms, stabilizing the upper body and maintaining posture throughout the lift.
Figure 9. Kinematic Analysis for Powerlifting (deadlift).
As shown in Figure 9, In the initial pull phase (0–300 ms), the hip joint angle
increases from 20.0° to 45.6°, with a peak angular velocity of −150°/s at 200–300 ms
and an angular acceleration of −300°/s2, indicating controlled hip extension. The knee
joint follows a similar pattern, increasing from 25.5° to 55.1°, while the ankle moves
from −5.0° dorsiflexion to 8.5° plantarflexion during the mid-pull phase, contributing
to the overall lift. During the mid-pull (300–500 ms), the hip angle increases to 68.0°,
with an angular velocity peaking at −180°/s before reversing in the concentric phase.
The knee angle increases to 70.3°, while the ankle reaches 14.5° in plantarflexion,
providing stability as the bar passes the knees. In the concentric lockout phase (500–
800 ms), the hip joint decreases from 68.0° to 22.0°, and the angular velocity shifts to
140°/s, peaking between 500–600 ms. The knee and ankle angles similarly decrease,
with the knee moving from 70.3° to 22.5° and the ankle returning to −5.0° dorsiflexion
by the lockout position at 700–800 ms. The shoulder begins in flexion during the initial
pull, increasing from 25.0° to 75.0° by 400–500 ms, reaching its peak flexion during
the mid-pull. During the concentric phase, the shoulder moves into extension,
decreasing to 30.0° by 700–800 ms as the lifter locks out the movement.
Molecular & Cellular Biomechanics 2024, 21(3), 518.
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4. Conclusion and future work
This study provided an in-depth analysis of muscle force distribution during high-
intensity athletic movements, specifically sprinting, jumping, and powerlifting. Using
a combination of motion capture, EMG, force plates, and musculoskeletal modeling
software, we could quantify the contribution of key muscle groups during various
phases of these movements. The results showed that the quadriceps, hamstrings,
gastrocnemius, and iliopsoas muscles played pivotal roles in generating and
controlling forces across all movements, with notable differences in force production
between the stance and swing phases in sprinting, the take-off and landing phases in
jumping, and the eccentric and concentric phases in powerlifting. A key finding was
the more efficient force distribution exhibited by professional athletes compared to
amateurs, particularly in their ability to maintain joint stability under high loads. This
difference highlights the importance of biomechanical efficiency in athletic
performance and suggests that targeted training interventions can help improve
amateur athletes’ muscle engagement and movement efficiency. The insights gained
from this study have practical implications for optimizing training programs in high-
intensity sports. By understanding how different muscle groups contribute to force
production, coaches and trainers can design more effective strength and conditioning
programs to improve specific muscle performance and reduce injury risks.
Additionally, simulating and predicting muscle forces through musculoskeletal
modeling offers a powerful tool for biomechanical research and athletic performance
analysis.
Ethical approval: Not applicable.
Conflict of interest: The author declares no conflict of interest.
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