# Whole-body musculo-skeletal model V1

Galo Maldonado, Philippe Souères, Bruno Watier

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Galo Maldonado, Philippe Souères, Bruno Watier. Whole-body musculo-skeletal model V1. [Technical Report] Rapport LAAS n° 18233, Université de Toulouse 3 Paul Sabatier; LAAS-CNRS. 2018. hal-01841355

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Whole-body musculo-skeletal model V1

Galo Maldonado, Philippe Souères and Bruno Watier

LAAS-CNRS, Université de Toulouse, CNRS, UPS, Toulouse, France
CONTENTS

I **Introduction** 2

II **Methods** 2

II-A Skeletal model 2

II-B Joints modeling 3

III **Marker set** 11

IV **Muscles modeling** 12

IV-A Lower limbs muscles 12

IV-B Upper limbs muscles 13

IV-C Trunk and head muscles 13

**References** 14
# I. INTRODUCTION

The main goal of this project was to build a basic musculo-skeletal model of the human body in order to be able of analyzing and simulating human motion. To this end, an OpenSim [4] musculo-skeletal model was modified and augmented based on previous works of the literature. The resulting model is also compatible with Pinocchio [3], an open source C++ library for efficient rigid multi-body dynamics computations based on revisited Roy Featherstone's algorithms. This allows users for creating powerful simulations of whole-body human-based motions with anthropomorphic systems. Using Pinocchio with the model permits also to use state-of-the-art libraries written in C++ or python (e.g. from robotics, machine learning, ...).

The first version of the whole-body model was modified and built based on the following specific criteria:

* The model should express the main elementary motions of humans performing parkour [11], [12].

* The model has to be used for the analysis and generation of anthropomorphic motion [13]. This implies that the model should be more complicated than a humanoid robot model for instance, but not as a complex as a complex human model.

* The model should be whole-body and three dimensional as sportive practicers require whole-body coordination for accomplishing complex motions.

* The model has to include surface joint stabilizer muscles that favor the study of muscular activity in highly dynamic motion. For example the agonist-antagonist muscles that perform abduction-adduction, flexion-extension or plantar flexion-dorsiflexion.

In the sequel we provide a technical report of the skeletal and muscular modeling. This model is freely available for download at https://github.com/GaloMALDONADO/ospi along with all the libraries to parse the model to use it with Pinocchio. Some examples of utilization and motion data are also provided.

# II. METHODS

In this section we aim at providing the description of the anthropomorphic model, of the joints modeling, angle conventions and ranges of motions.

## A. Skeletal model

The model includes 42 degrees of freedom (Table I), 18 joints and 19 segments. The pose (position and orientation) of a reference frame attached to the pelvis is expressed with respect an intertial world frame (Fig 1).

<figure><img src="image_1.png" /><figcaption>Fig. 1: Kinematics chain of the model. In order to model hinge joints (2 DoF), extra segments were added (talus and calcaneus, ulna and radius). The visual elements are based on the running model of Hammer [8].</figcaption></figure>
The skeleton is modeled as a friction-less articulated multi-body dynamic system as shown in Fig 2. The pelvis, thighs, shanks and feet segments mass and inertia were set according to the model of [1] where data was obtained based on the studies of [14]. In this model, the length of the segments was taken from [5] model. The same model was used in [8] for simulating running motions. Upper limb anthropometry are based on the running model of [8] which was estimated based on the regression equations of [10] and [9]. Antrhopometry of the torso and head segments (including the neck) were estimated from the regression equations of [6], [7].

<figure><img src="image_2.png" /><figcaption>Fig. 2: Kinematics chain of the model. The numbers inside the colored balls indicate the number of degrees of freedom between segments. In order to model hinge joints (2 DoF) with Pinocchio, extra segments were added (talus and calcaneus, ulna and radius) to the model.</figcaption></figure>

## B. Joints modeling

The characteristics of the joint modeling are presented in Table I. Fig 2 show how joints are linked from parent to child segments in the kinematic chain. Euler XYZ body-fixed rotation angles are used to express the orientation using OpenSim.
The joint modeling adapted from the literature is described below:

* Each lower extremity has 7 DoF. The hip is modeled as a ball-and-socket joint, the knee is modeled as a hinge joint, the ankle is modeled as 2D hinge joints (flexion-extension and inversion-eversion), and the toes are modeled with one hinge joint at the metatarsals. Lower extremity joint definitions and the pelvis ones are based on [5] corrected in [2].

* The pelvis joint is modeled as a free-flyer joint to permit the model to translate and rotate in the 3D space. This 6D joint is attached to the free-floating base (root frame) of the under-actuated systems. The lumbar motion is modeled as a ball-and-socket joint and the neck joint is also modeled as a ball-and-socket joint. Joint definitions are based on [1].

* Each arm is modeled with 8 DoF. The shoulder is modeled as a ball-and-socket joint, the elbow and forearm rotations are modeled with hinge joints to represent flexion-extension and pronation-supination [9], the wrist flexion-extension and radial-ulnar deviations are modeled with hinge joints, and the hand fingers are modeled with one hinge joint for all fingers. Joint definitions are based on [8].

For further details about the location of each coordinate system with respect to bony landmarks, see [1].

<table><caption>TABLE I: Synovial joints and free flyer joint of the whole body model.</caption><tbody><tr><th colspan="5">Lower limb joints</th></tr><tr><th></th><th>Hip</th><th>Knee</th><th>Ankle</th><th>Toes</th></tr><tr><th>Type</th><td>ball and socket</td><td>hinge</td><td>hinge (×2)</td><td>hinge</td></tr><tr><th colspan="5">Upper limb joints</th></tr><tr><th></th><th>Shoulder</th><th>Elbow</th><th>Wrist</th><th>Fingers</th></tr><tr><th>Type</th><td>ball and socket</td><td>hinge (×2)</td><td>hinge (×2)</td><td>hinge</td></tr><tr><th colspan="5">Trunk and head joints</th></tr><tr><th></th><th>Pelvis</th><th>Lumbar</th><th>Neck</th><th></th></tr><tr><th>Type</th><td>free flyer</td><td>ball and socket</td><td>ball and socket</td><td></td></tr></tbody></table>

In the sequel we present some illustrations showing the ranges of motion of the model and the respective angle conventions.
<figure><img src="image_3.png" /><figcaption>Fig. 3: Shoulder joint conventions and range of motions.</figcaption></figure>

(a) Maximum shoulder extension (−) equal to 90 deg, anatomical pose and maximum shoulder flexion (+) equal to 180 deg.

(b) Maximum shoulder abduction (−) equal to 180 deg, anatomical pose and maximum shoulder aduction (+) equal to 35 deg.

(c) Maximum shoulder internal rotation (+) equal to 100 deg, anatomical pose and maximum shoulder external rotation (−) equal to 100 deg.
<figure><img src="image_4.png" /><figcaption>Fig. 4: Elbow joint conventions and range of motions.</figcaption></figure>

(a) Maximum forearm supination equal to 110 deg, anatomical pose and maximum forearm pronation equal to 110 deg.

(b) Maximum elbow extension which is the same as the anatomical pose and maximum elbow flexion equal to 170 deg.

<figure><img src="image_5.png" /><figcaption>Fig. 5: Wrist joint conventions and range of motions.</figcaption></figure>

(a) Maximum radial deviation equal to 25 deg, anatomical pose and maximum ulnar deviation equal to 35 deg.

(b) Maximum wrist extension equal to 90 deg, anatomical pose and maximum wrist flexion equal to 90 deg.

<figure><img src="image_6.png" /><figcaption>Fig. 6: Fingers joint conventions and range of motions.</figcaption></figure>

(a) Maximum fingers flexion (+) equal to 90 deg, anatomical pose and maximum fingers extension (−) equal to 10 deg.
<figure><img src="image_7.png" /><figcaption>Fig. 7: Neck joint conventions and range of motions.</figcaption></figure>

(a) Maximum neck extension (−) equal to 60 deg, the anatomical pose and maximum neck flexion (−) equal to 60 deg.

(b) Maximum neck right bending (+) equal to 45 deg, the anatomical pose and maximum neck left bending (−) equal to 45 deg.

(c) Maximum neck right rotation (−) equal to 80 deg, the anatomical pose and maximum neck left rotation (+) equal to 80 deg.
<figure><img src="image_8.png" /><figcaption>Fig. 8: Lumbar joint conventions and range of motions.</figcaption></figure>

(a) Maximum lumbar extension (+) equal to 30 deg, anatomical pose and maximum lumbar flexion (−) equal to 90 deg.

(b) Maximum lumbar right bending (+) equal to 30 deg, anatomical pose and maximum lumbar left bending (−) equal to 30 deg.

(c) Maximum lumbar right rotation (−) equal to 30 deg, anatomical pose and maximum lumbar left rotation (+) equal to 30 deg.
<figure><img src="image_9.png" /><figcaption>Fig. 9: Hip joint conventions and range of motions.</figcaption></figure>

(a) Maximum hip extension (−) equal to 30 deg, anatomical pose and maximum hip flexion (+) equal to 120 deg.

(b) Maximum hip abduction (−) equal to 50 deg, the anatomical pose and maximum hip adduction (+) equal to 30 deg.

(c) Maximum hip external rotation (−) equal to 45 deg, the anatomical pose and maximum hip internal rotation (+) equal to 35 deg.

<figure><img src="image_10.png" /><figcaption>Fig. 10: Knee joint conventions and range of motions.</figcaption></figure>

(a) Maximum knee flexion (−) equal to 140 deg, anatomical pose and maximum knee extension (+) equal to 10 deg.
<figure><img src="image_11.png" /><figcaption>Fig. 11: Ankle joint conventions and range of motions.</figcaption></figure>

(a) Maximum ankle dorsiflexion (+) equal to 20 deg, anatomical pose, maximum ankle plantarflexion (−) equal to 50 deg.

(b) Maximum ankle eversion (−) equal to 50 deg, anatomical pose and maximum ankle inversion (+) equal to 30 deg.

<figure><img src="image_12.png" /><figcaption>Fig. 12: Toes joint conventions and range of motions.</figcaption></figure>

(a) Maximum toes extension (+) equal to 90 deg, anatomical pose and maximum toes flexion (−) equal to 45 deg.
### III. MARKER SET

The model includes a whole-body marker set with 48 markers placed on anatomical bony landmarks (13) selected based on the recommendations of the International Society of Biomechanics (ISB) [17], [18].

<figure><img src="image_13.png" /><figcaption>Fig. 13: Marker set depicted on the whole body skeletal model</figcaption></figure>

<table><caption>TABLE II: Marker set</caption><thead><tr><td>Marker</td><td>Name</td><td>Location</td></tr></thead><tbody><tr><td>SEL</td><td>Selenius</td><td>Between the eyebrows and above the nose.</td></tr><tr><td>OCC</td><td>Occipital</td><td>Back and lower part of the skull.</td></tr><tr><td>TEMP</td><td>Temporal</td><td>On the sides and base of the skull.</td></tr><tr><td>STR</td><td>Sternum</td><td>On the center of the chest.</td></tr><tr><td>A</td><td>Acromion process</td><td>Located on the lateral part of the shoulder, right above the shoulder joint.</td></tr><tr><td>C7</td><td>Seventh cervical vertebrae</td><td>Cervical area of the spinal cord.</td></tr><tr><td>T10</td><td>Tenth thoracic vertebrae</td><td>Thoracic area of the spinal cord.</td></tr><tr><td>SUP</td><td>Clavicle</td><td>Center of the clavicle.</td></tr><tr><td>LHE</td><td>Lateral humerus</td><td>Palpated on lateral sides of distal end of humerus.</td></tr><tr><td>MHE</td><td>Medial humerus</td><td>Palpated on medial sides of distal end of humerus.</td></tr><tr><td>US</td><td>Ulna</td><td>Long protuberance on lateral aspect of elbow.</td></tr><tr><td>RS</td><td>Radius</td><td>Long protuberance on medial aspect of elbow.</td></tr><tr><td>MH5</td><td>Fifth metacarpal</td><td>Long protuberance on proximal end of little finger metacarpal.</td></tr><tr><td>MH2</td><td>Second metacarpal</td><td>Long protuberance on proximal end of index finger metacarpal.</td></tr><tr><td>FT3</td><td>Middle finger</td><td>Over the tip of the medial finger.</td></tr><tr><td>ASIS</td><td>Antero superior ilac spine</td><td>Over the antero superior ilac spine.</td></tr><tr><td>PSIS</td><td>Posterior superior ilac spine</td><td>Over the posterior superior ilac spine.</td></tr><tr><td>GT</td><td>Greater trochanter</td><td>Lateral aspect of thigh just distal to hip joint.</td></tr><tr><td>LFE</td><td>Lateral femoral condyle</td><td>Lateral aspect on distal end of femur.</td></tr><tr><td>MFE</td><td>Medial femoral condyle</td><td>Medial aspect on distal end of femur.</td></tr><tr><td>ATT</td><td>Antero tibial tuberosity</td><td>Long protuberance on proximal end of femur.</td></tr><tr><td>SPH</td><td>Sphiron</td><td>Large protuberance on medial aspect of ankle.</td></tr><tr><td>LM</td><td>Lateral malleolus</td><td>Large protuberance on lateral aspect of ankle.</td></tr><tr><td>CAL</td><td>Calcaneus</td><td>Over the heel bone.</td></tr><tr><td>MFH1</td><td>Firs foot metatarsal</td><td>Long protuberance on proximal end of first toe metatarsal.</td></tr><tr><td>TT2</td><td>Second Toe</td><td>Long protuberance on second distal interphalangeal joint.</td></tr><tr><td>MFH5</td><td>Fifth foot metatarsal</td><td>Long protuberance on proximal end of first toe metatarsal.</td></tr></tbody></table>
## IV. MUSCLES MODELING

The musculoskeletal model (Fig. 14) has been assembled to perform whole-body analysis of 3d human motion.

<figure><img src="image_14.png" /><figcaption>Fig. 14: Musculoskeletal model. The visual elements are based on the running model of Hammer [8].</figcaption></figure>

The model contains 48 superficial muscles (Fig. 14) that represent the more relevant joint stabilizer muscles to study sport movements. The Muscles are modeled using hill-type models based on the works described in [15], [16] which are used in OpenSim [4]. The muscles and their principal mechanical actions in the execution of sport movements, are presented in Table III for the lower limb muscles, in Table IV for the upper limb muscles and in Table V for the trunk and head muscles.

### A. Lower limbs muscles

Twenty three superficial muscles that stabilize the hip, knee and ankle joints were selected based on a functional analysis of the muscles mechanical action in the execution of jumps and landing techniques (Table III).

<table><caption>TABLE III: Lower body muscles of the whole body model and their mechanical action</caption><thead><tr><th colspan="2">Lower limb muscles</th></tr><tr><th>Muscle</th><th>Main Functions</th></tr></thead><tbody><tr><td>(1) Gluteus medius</td><td>Abduct an rotate medially the thigh at the hip.</td></tr><tr><td>(2) Sartorius</td><td>Flex, abduct, and rotate laterally the thigh at the hip. Flex the leg at the knee.</td></tr><tr><td>(3) Tensor fasciae latae</td><td>Extend the thigh at the hip.</td></tr><tr><td>(4) Biceps femoris</td><td>Flex and rotate the leg laterally at the knee. Extend the thigh at the hip.</td></tr><tr><td>(5) Semitendinosus</td><td>Flex and rotate the leg medially at the knee. Extend the thigh at the hip.</td></tr><tr><td>(6) Vastus lateralis</td><td>Extend the leg at the knee.</td></tr><tr><td>(7) Vastus medialis</td><td>Extend the leg at the knee.</td></tr><tr><td>(8) Lateralis gastrocnemius</td><td>Plantar flex the foot at the ankle.</td></tr><tr><td>(9) Medialis gastrocnemius</td><td>Plantar flex the foot at the ankle and flex the leg at the knee.</td></tr><tr><td>(10) Soleus</td><td>Plantar flex the foot at the ankle.</td></tr><tr><td>(11) Tibialis posterior</td><td>Plantar flex the foot at the ankle. Slight inversion of the foot at the ankle.</td></tr><tr><td>(12) Tibialis anterior</td><td>Dorsiflex the foot at the ankle. Slight inversion of the foot at the ankle.</td></tr></tbody></table>
## B. Upper limbs muscles

Twenty one superficial muscles that stabilize the shoulder, elbow and wrist joints were selected based on a functional analysis of the muscles mechanical action in the execution of climbing techniques (Table IV).

<table><caption>TABLE IV: Upper body muscles of the whole body model and their mechanical action</caption><thead><tr><th colspan="2">Upper Limbs</th></tr><tr><th>Muscle</th><th>Main Functions</th></tr></thead><tbody><tr><td>(13) Anterior deltoideus</td><td>Abduction, flexion and medial rotation of the forearm at the shoulder joint</td></tr><tr><td>(14) Posterior deltoideus</td><td>Abduction, extension and lateral rotation of the upper arm at the shoulder joint</td></tr><tr><td>(15) Medial deltoideus</td><td>Abduction of the upper arm at the shoulder joint</td></tr><tr><td>(16) Pectoralis major</td><td>Flexion, adduction and medial rotation of the upper arm at the shoulder joint</td></tr><tr><td>(17) Latisimus dorsi</td><td>Extension, adduction, horizontal abduction, flexion from an extended position, and medial rotation of the upper arm at the shoulder joint</td></tr><tr><td>(18) Triceps brachii longus</td><td>Extension of the forearm at the elbow joint. Also adducts and may assist in extension of the shoulder joint.</td></tr><tr><td>(19) Triceps brachii lateralis</td><td>Extension of the forearm at the elbow joint.</td></tr><tr><td>(20) Biceps brachii longus</td><td>Supination and flexion of the forearm at the elbow joint.</td></tr><tr><td>(21) Brachioradialis</td><td>Flexion of the forearm at the elbow joint</td></tr><tr><td>(22) Carpi radialis flexor</td><td>Flexion and radial abduction of the hand at the wrist joint</td></tr><tr><td>(23) Carpialis extensor</td><td>Extension and radial abduction of the hand at the wrist joint.</td></tr></tbody></table>

## C. Trunk and head muscles

Four superficial muscles that stabilize the lumbar and neck joints were selected based on a functional analysis of the muscles mechanical action in the execution of the sport techniques V. The sternocledomastoid and the trapecius ascendus muscles were used for studying the motion of the head. Nevertheless, the trapecius ascendus muscle is also important for the scapulae movement in the execution of climbing techniques.

<table><caption>TABLE V: Trunk muscles of the whole body model and their mechanical action</caption><thead><tr><th colspan="2">Trunk</th></tr><tr><th>Muscle</th><th>Main Functions</th></tr></thead><tbody><tr><td>(24) Erector spinae longissimus</td><td>Extension of the lumbar spine at the lumbar joint</td></tr><tr><td>(25) Rectus abdominis</td><td>Flexion of the lumbar spine at the lumbar joint</td></tr><tr><td>(26) Sternocledomastoid</td><td>Oblique rotation and flexion of the head at the neck joint</td></tr><tr><td>(27) Trapecius ascendus</td><td>Scapulae motion and extension of the head at the neck joint</td></tr></tbody></table>
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