Anthony Beeman
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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
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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
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A planar
selected to
to simplify
the motion
two bar mechanism was
model the kinematic systems
the problem by constraining
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
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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
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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
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The Abaqus Finite Element analysis is comprised of four unique steps in order to simulate the kinematics of
throwing a football.
These steps include:
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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.
Step 0
Step 1
Step 2
Step 3
Step 4
Maximum
Variable
Initial
Foot
External
Step
Contact
Rotation
Ball Release
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
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10
10
5
5
Output
Database
(ODB) frames
Follow
Foot Contact
M.E.R.
Release
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Add more detail to each report section
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Discuss Results from the FEM
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X & Y position as a function of time
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X & Y Force as a function of time
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Shoulder
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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