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The Penn State Mechanism Collective Lab
SKILLS INVOLVED
SKILLS INVOLVED
Compliant Mechanism Design
MATLAB
Finite Element Analysis
Prototyping & Manufacturing
Experimental Testing
PROJECT OBJECTIVE
PROJECT OBJECTIVE
Constant force mechanisms (CFM) are a type of device that maintain a constant reaction force as the mechanism displaces, and have many applications in mechanism design. Compliant constant force mechanisms (CCFM) are a specific type of CFM that obtains is functionality through bending parts, resulting in increased lifetime and precision. However, most CCFM function strictly in compression, and can be complicated to design.
My objective is to employ a model for new type of CCFM that employs a simple design framework, and functions both in compression and in tension.
MODELING
MODELING
The design framework is composed into two modeling components: the Slider-Crank Model, which formulates the desired constant force curve, and the Pseudo-Rigid Body Model, which generates the geometry parameters that will follow that constant force curve.
The Pseudo-Rigid Body Model
The Pseudo-Rigid Body Model
Pseudo-rigid bodies (PRB) are used to relate the bending and movement of compliant mechanisms to the forces and displacement of rigid mechanisms.
By utilizing PRB relationships in MATLAB, we can generate a compliant structure with specific dimensions that is "functionally equivalent" to the rigid-link structure.
Finally, we can mirror this mechanism upon itself to eliminate the slider—resulting in a single-part tension-based CCFM, with an associated model.
The Slider-Crank Model
The Slider-Crank Model
Rigid links are easier to model than bending links. Therefore, the base model of this mechanism is a simple slider-crank, with its sliding end offset from its fixed end.
Using Newtonian methods, we can mathematically derive a system of equations between the displacement of the slider and the required force.
We can optimize the variables of this equation in MATLAB to generate a force-displacement plot that exhibits constant force over a specific range.
FINITE ELEMENT ANALYSIS
FINITE ELEMENT ANALYSIS
Finite element analysis in Ansys simulated the resultant forces and stresses of a sample configuration as periodic displacements were applied
Simulation results validated the model's predictive accuracy within 1.4%.
PROTOTYPING
PROTOTYPING
FDM
FDM
Excellent for rapid testing and iteration
Lacked the required tolerances for high-fidelity testing
SLA
SLA
High dimensional accuracy
Inconsistent material properties
Waterjet
Waterjet
High dimensional accuracy
Consistent material properties
Chosen process for high-fidelity testing
EXPERIMENTAL TESTING
EXPERIMENTAL TESTING
ASTM-standard tensile-test experiments was conducted upon three sample configurations to validate the model's predictive accuracy for constant-force and stress behavior.
Material Testing
Material Testing
The final test specimens were waterjet from sheets of polypropylene.
To ensure the most accurate results, the flexural modulus and yield strength of this material were experimentally determined following ASTM D790-19 standards for three-point bend testing.
Fixture Design and Machining
Fixture Design and Machining
The final specimen is to be tested on an industry-grade tensile testing apparatus. The system has no compatible test fixtures, so two custom test fixtures were specially designed and machined.
Mechanical Testing
Mechanical Testing
Mechanical testing followed ASTM-standard procedures for three-point bend tests utilizing ADMET hardware and MTESTQuattro software.
Three samples with the same dimensions were each run three times, resulting in a total of nine comparative tensile tests
DATA ANALYSIS
DATA ANALYSIS
Due to noise from the load cell, experimental data was run through a Savitzky-Golay filter using MATLAB software.
Statistical data analysis revealed that the experimental data had a 5.12% error from the predictive model, with a standard deviation of 3.19%. Accounting for manufacturing and testing error, this adequately validates the mechanism's performance.
PARAMETERIZATION STUDY
PARAMETERIZATION STUDY
Following the design, development, and testing of this specialized constant-force mechanism, a parameterization study was run to identify how different model inputs (geometry angles and lengths) affect the
output parameters (stiffness, constant-force, range of motion)
A MATLAB script was developed to auto-generate thousands of mechanism configurations, incrementing the input variables one at a time.
Results revealed that two input variables (θ20 and r2/r3) were the most impactful variables upon the output performance.
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