A Kinematic and Dynamic Analysis of the American

Football Overhead Throwing Motion

Anthony Beeman

Over the past several years there have been increased interest in overhead throwing mechanics.

Recently, several methodologies and experiments have been developed by Champan [1], Rash [2], Dillman [3], and Bruce [4] to determine the kinematics of overhead throwing motions as well as the resulting joint torques.

Overhead throwing places extremely high stresses on the shoulder joint.

These high stresses are repeated many times and can be lead to a wide range of overuse injuries.

A better understanding of dynamics of the football pass can provide sports medical professionals useful information in prevention, treatment, and rehabilitation of football-related football injures.

Introduction & Background

NFL Quarterback in the Pre Pass Triangle Phase [6]

Benefits of Using DH Parameters Simple way to model robot links and

joints. Can be transformed to any coordinate

system. Can handle any possible combination

of joints and links. This method is commonly used in

robotics to define a robotic tool tip position, velocity, and acceleration as a function of each link’s◦ The DH parameter method chains

revolute and prismatic joints to model robotic kinematics.

◦ Setting up Abaqus connectors elements identical to the DH parameters will ensure proper compound joint rotations as a function of time.

Theory & Methodology

DH Parameter Link Example [10]

In order to establish a systematic method for biomechanical model the overhead throwing motion it is necessary to establish a convention for representing links and joints.

The human arm can be represented as a sequence of rigid body links which are connected by the shoulder and elbow joints.

In 1955 Denavit and Hartenberg developed a systematic method, DH method, for describing the position of orientation of successive links.

Denavit–Hartenberg (DH) parameters- DH parameters consists of four parameters associated with a particular convention for attaching reference frames to the links of a spatial kinematic chain, or robot manipulator.

Parameters θ- The angle from the xi-1 to xi

measured about zi

d- the distance from the xi-1 to xi measured along the zi axis

a- the distance from the zi to zi+1 measured along the xi axis.

α- The angle from zi to zi+1 measured about xi

An Abaqus FEM can be set up using the DH parameters in order to develop complex biomechanics models.

DH Parameters

DH Parameter Link Example [10]

A planar two bar mechanism was selected to model the kinematic systems to simplify the problem by constraining the motion to two degrees of freedom.

The planar two bar mechanism is composed of two rigid bodies, the upper arm and fore arm, which are connected to a ground. Each link is connected with revolute joints and is free to rotate about the z axis.

Mathcad/Excel files were created to calculate joint velocities & accelerations◦ Joint velocities shall be used as

connector velocity boundary conditions within the FEA

A 4 step Abaqus FEA was created to model the planer two bar mechanism using DH-parameterization.◦ Each degree of freedom can be

modified independently and provides rotations as expected.

DH Parameterization

Throwing Motion Represented as a Planar 2 Bar Mechanism

Link α

[rad]

d

[in]

θ

[rad]

a

[in]

1 0 0 θ1 L1

2 0 0 θ2 L2

Planar Two Bar Mechanism DH Parameters

Kinovea Software was utilized to analyze film of various NFL quarterbacks throwing the football.

Kinovea’s angle measurement tool was utilized to determine joint angles at key positions in the overhead throw

Kinovea’s Angle Measurements

Kinovea’s Angle Measurement Tool

Abaqus, was used to create the Finite Element Model and perform the kinematic analysis.

The Finite Element Model was constructed utilizing a series of hinge and beam connector elements.

Inertial mass properties were included in the model by separating the beam elements into two equal segments.

Display bodies were included in order to provide a physical representation of the human arm as it transitions from each of the four phases of the throwing movement.

Stationary parts such as the head, left arm, and lower body were modeled for information but motion was restricted for this analysis.

Kinematic Modeling

Abaqus FEM

Connector Chain Ground link constrains the model in six degrees of freedom (u1=u2=ur1=ur2=ur3=0).

◦ The ground constraint is set as a boundary condition within the FEM. Hinge connector element is coupled to the ground reference point and the shoulder reference point, s.

◦ The hinge connector element has one available degree of freedom (UR1) located about its local x axis.

◦ This available degree of freedom can be used to input calculated shoulder joint rotational velocities. Hinge connector element is connected to a rigid beam connector element which is coupled to a reference point located at the

center of gravity of the upper arm. Then, an additional beam connector element is linked between the center of gravity of the upper arm to the elbow.

Hinge connector element connects the end of the second beam element to the start of the lower arm beam element.

◦ Elbow hinge connector element has one degree of freedom which can be used to input calculated elbow joint rotational velocities.

A series of beam connector elements are added in series to represent the length of the lower arm with a CG located at the location of the lower arm center of gravity.

Cartesian + rotation connector element connects the wrist to the ground location of the shoulder.

◦ Connector is used to track the wrist location relative to the shoulder throughout each FEM analysis time step.

◦ Cartesian + rotation connector element has six available degrees of freedom and does not add any stiffness to the FEM.

Abaqus Connector Schematic

Abaqus Connector Schematic

The Abaqus Finite Element analysis is comprised of four unique steps in order to simulate the kinematics of throwing a football.

These steps include:◦ Foot contact◦ Maximum external rotation◦ Ball release◦ Follow through step

Each step was modeled as static general step with non-linear geometry turned on. ◦ Note: It is important to note that non-linear geometry was turned on in the FEM because large

displacements take place. This ensures the FEM accurately determines the final position of the elements after large displacements occurs.

The table below illustrates each of the four steps created in the FEM, the time duration, and the number of output database frames for each step.

Abaqus Analysis Steps

Variable

Step 0 Step 1 Step 2 Step 3 Step 4

Initial

Step

Foot

Contact

Maximum

External

Rotation Ball Release

Follow

Through

Time (sec) 0 1.0 0.5 0.25 0.25

Increment size 0 0.10 0.05 0.05 0.05

Number of

Output

Database

(ODB) frames

- 10 10 5 5

Abaqus FEM

Foot Contact M.E.R. Release

Wrist position as a function of time was created utilizing output data from the connector element relative position (CP) keyword. ◦ The CP keyword allows the user to

analyze relative distances between two fixed or moving objects.

X Position During the foot contact step (FC) the wrist is

farthest from the shoulder in preparation to throw the football.

As the arm progresses from the maximum external rotation (MER), ball release (BR), and follow through (FT) steps the x position with respect to the shoulder gradually increases.

Y Position The maximum height of the wrist occurs at

0.3 seconds after initial foot contact (FC). At the end of the maximum external

rotation step (MER) and the ball release step (BR) the vertical displacement of the arm is only 0.314".

After ball release the wrist height quickly decreases during the follow through step.

Wrist Position

Wrist X Position as a Function of Time

Wrist Y position as a function of Time

Joint Torques At initial foot contact the shoulder torque is 79 in-

lbs and the elbow torque is 0 in-lbf.

◦ The 0 in-lbf elbow torque result is based off the assumption that the ball, upper arm, and hand CG acts along the same vertical axis as the elbow joint.

After initial foot contact, the deltoid muscle is used to force the elbow above and ahead of the shoulders until it reaches the "zero position".

The zero position is defined as the location where there is zero strain on the rotator cuff muscles and occurs 0.35 seconds after initial foot contact.

◦ Improper biomechanics in the extension phase can result in additional strain on the rotator cuff which over time can lead to injury.

After 0.5 seconds after initial foot contact the arm is at the maximum external rotation (MER) which results in a 41 in-lbf torque at the shoulder and a 28 in-lbf torque at the elbow.

As the quarterback transitions from the maximum external rotation step to the ball release step (BR) the elbow torque decreases as it extends to the zero position.

After ball release, the arm propels forward placing significant torque on the shoulder and elbow joints at 158 and 59 in-lbf of torque respectively

Joint Torques as a function of Time

The DH parameter method is a suitable model for addressing the motion of human kinematics that are arranged in series.

This is accomplished by creating a series of rotational or prismatic joints.

The figure to the right illustrates a five degree of freedom upper limb model.

This model consists of two joints which include the shoulder and elbow joint.

Shoulder Joint The shoulder joint is represented with a

series of three prismatic joints which control the shoulder’s:◦ the flexion/extension◦ abduction/adduction◦ internal/external rotations

Elbow Joint Elbow is represented with a series of two

prismatic joints which control:◦ flexion/extension of the fore arm ◦ pronation/supination angle of the wrist

and forearm.

Expanded DH Model

Link α [rad] d [in] θ [rad] a [in]

1 0 0 θ1 0

2 -1.57 0 θ2 0

3 1.57 L1θ3 0

4 -1.57 0 θ4 0

5 1.57 L2θ5 0

6 0 0 θ6 0

The results from this paper illustrate the power and flexibility of the DH method in combination with Abaqus connector elements by showcasing their ability to model joints in the human arm.

Using the expanded DH methodology, researchers can utilize Abaqus to develop a complex over head throwing motion model in order to determine optimum joint angles when making an over head throwing motion.

This information could be used to help reduce injury, improve accuracy, and efficiency when throwing the football.

Conclusions

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References