Mechanism Analysis – Dynamics and Static Behavior Study
Location: Mechanical Engineering, Purdue University, IN
Timeframe: Junior year of undergraduate
Introduction:
Understanding mechanism dynamics is fundamental to designing reliable mechanical systems in robotics, manufacturing equipment, and automated machinery. Proper analysis ensures motors are correctly sized, forces are accurately predicted, and systems operate safely under varying loads. The objective was to analyze the individual links of a mechanism under spring and damper attachments and determine which motor would be needed to provide the input torque of the system.
Design & Development:
My task was to use Equation of Motion, Graphical, and Force Analysis methods to determine the overall dynamics and static behavior of each link. These analyses were to be solved via MATLAB where applicable.
Analytical Methods:
I analytically analyzed each link through free body diagram analysis to determine system behavior at any specific instance. This involved deriving equations for forces, moments, and accelerations acting on each link throughout the mechanism’s range of motion.
Static Analysis:
I statically analyzed each link through free body analysis to determine the system behavior at equilibrium positions, identifying critical loading conditions and force distributions.
Graphical Analysis:
I graphically analyzed each link to determine link interactions at specific instances, using hand-drawn vector diagrams to visualize force components and verify analytical solutions.
Energy and Motion Analysis:
I utilized Equation of Motion methods to determine the work and energy properties of the mechanism, accounting for kinetic energy, potential energy (spring), and energy dissipation (damper). I compiled equations for each determination step within a loop in MATLAB, enabling automated analysis across the full range of input positions.
Challenges I addressed:
Creating a MATLAB script capable of analytically analyzing multiple input positions (from 0 to 360 degrees of the input link) and determining the positions, forces, and energies of each of the output links required careful indexing and vector management. Adjusting the system and determining the effects that the spring and damper had on the overall mechanism involved understanding energy storage and dissipation across motion cycles. Graphically determining each location of forces for each link of the mechanism by hand drawing required precision and understanding of vector composition. Determining the energy contribution of each aspect of the equation of motion (kinetic, potential, dissipated) and selecting the correct motor for the system while identifying potential shortcomings required synthesis of all analysis methods.
Evaluation:
The MATLAB script successfully analyzed the mechanism across the full 360-degree input range, generating force, position, and energy profiles for each link. The integration of analytical, static, and graphical methods provided cross-validation—discrepancies between methods revealed calculation errors and led to more robust solutions. The equation of motion analysis accurately predicted energy requirements throughout the cycle, with spring potential energy storage and damper dissipation matching expected theoretical behavior.
The motor selection analysis identified torque and power requirements based on the maximum instantaneous loads and continuous operating conditions. The script revealed that peak torque occurred at specific mechanism configurations where mechanical advantage was lowest, informing motor sizing beyond simple average load calculations. The spring-damper system analysis showed how energy storage could reduce peak power requirements but required careful tuning to avoid resonance conditions.
The graphical analysis by hand drawing, while time-intensive, provided critical intuition for understanding force flow through the mechanism that wasn’t immediately apparent from numerical solutions alone.
Conclusion:
This project strengthened my understanding of mechanism kinematics, dynamics, and energy methods that are essential foundations for robotic system design. The experience of developing MATLAB automation for repetitive calculations while maintaining physical intuition through graphical methods taught me the importance of combining computational tools with fundamental engineering analysis.
The skills I developed in free body diagram analysis, energy methods, and computational modeling directly informed my approach to path planning and motion analysis in graduate research. Understanding how springs and dampers affect system dynamics became particularly relevant in my later work on compliant robotic systems and trajectory optimization, where energy efficiency and dynamic response are critical design considerations.
Dhruv Lal 