Anthony Beeman

 Since the project proposal submittal on 9/21/15 I began work on the Abaqus Kinematic model utilizing join, hinge, and beam elements.  Building the model- A model was successfully created using the join, hinge, and beam connectors with 0 pivot errors. ◦ Zero pivot errors occur in Abaqus when the model is over constrained at a specific degree of freedom. This can provide inaccurate results as the model will still run to completion.  With the model successfully created I began applying one angle per analysis step and validated the connector was being utilized properly. The FEM behaved as expected.  Next, I applied up to three rotations per joint per analysis step. This resulted in a much different final joint location than expected. ◦ I assumed the angles would be projection angles or Euler angles.  Conclusions- Abaqus does not parameterize compound angles as I expected. Abaqus Joint Connector Model

 Knowing that Abaqus could rotate 1 angle per analysis step accurately I began looking for alternative methods to parameterize the model.  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.  This method is commonly used in robotics to define a robotic tool tip position, velocity, and acceleration as a function of each link’s joint angles and time.  The DH parameter method chains revolute and prismatic joints to model robotic kinematics. ◦ Therefore, setting up the Abaqus connectors identical to the DH parameters would ensure proper compound joint rotations as a function of time. DH Parameter Link Example

 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 files were created to calculate joint velocities, accelerations, and joint torques. ◦ 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. Throwing Motion Represented as a Planar 2 Bar Mechanism

 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 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 have been 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.  The series of Abaqus connector representing the throwing arm are illustrated to the right  Stationary parts such as the head, left arm, and lower body were modeled for information but motion was restricted for this analysis. Abaqus FEM

 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. Variable Step 0 Step 1Step 2Step 3 Step 4 Initial Step Foot Contact Maximum External RotationBall Release Follow Through Time (sec) Increment size Number of Output Database (ODB) frames

Foot ContactM.E.R. Release

 Add more detail to each report section  Discuss Results from the FEM ◦ X & Y position as a function of time ◦ X & Y Force as a function of time  Shoulder  Elbow ◦ Joint Torque as a function of time  Explain how DH parameterization is an excellent option when modeling complex biomechanical movements.  Explain how to increase the number of degrees in freedom in the throwing motion to increase model accuracy. 5 DOF Arm Modeled Using DH Parameters