1. Anthony Beeman

2.  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 3-1-3 Euler angles.  Conclusions- Abaqus does not parameterize compound angles as I expected. Abaqus Joint Connector Model

3.  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

4.  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

5.  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

6.  Add display bodies to the FEM  Provide FEA and Mathcad output results to the report  Add more detail to each report section  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