Dynamics of Mechanical Systems

Dynamics of Mechanical Systems (IMEC-2540) is the second course in the Mechanical Systems area of the Mechanical Engineering program at Universidad de los Andes. It focuses on the dynamic behavior associated with the motion of particles and rigid bodies under the action of forces.

The course builds a solid understanding of the fundamental laws needed to carry out the dynamic analysis of two-dimensional systems, both at a given instant and over time. To this end, it makes extensive use of symbolic Python as a computational tool for modeling and simulating mechanisms along with their kinematic and kinetic variables.

Learning objectives

By the end of the course, students will be able to:

• Compute kinematic and kinetic variables related to the motion of particles and rigid bodies in two dimensions using analytical models.
• Analyze the motion of mechanical systems, both at an instant and over time, with the help of simulation models.
• Conduct experiments, compute uncertainties, analyze experimental data and draw conclusions based on the available data and models.

Course content

Module 1 — Kinematics

Review of prerequisite concepts, symbolic and numerical differentiation and integration in Python, absolute motion, fixed-axis rotation, relative velocity and acceleration between rigid bodies.

Module 2 — Kinetics

Mass and moment of inertia, Newton's laws, Newton-Euler (rectilinear and general motion), inverse dynamics, ODEs and forward dynamics, work and energy.

Module 3 — Vibrations

Particle vibration: free motion, damped free motion, forced motion and damped forced motion. Rigid-body vibrations.

Interactive labs

In addition to lectures, students apply what they learn in interactive labs and hands-on applications. These activities show the role of dynamics in mechanical engineering and build skills in conducting experiments, analyzing data and drawing conclusions.

Open the DSM labs (in Spanish)

Pre-labs

• Lab 1 — RR kinematics: RR robot (2D SCARA): FK, IK, Jacobian, position, velocity and acceleration profiles.
• Lab 2 — Motion classification: Accelerometer, signal filtering, numerical integration, MLPClassifier to classify movements.
• Lab 3 — Robot leg: Force analysis of a robot leg with variable drivers. CAD import and force computation.
• Lab 4 — Vibrations: Mass-spring-damper system. Transmissibility, isolation design, 1 and 2 DOF.

Lab bank

Additional labs covering topics such as the four-bar linkage, slider-crank, 3R serial robot, equations of motion, impact and collisions, multibody systems, energy methods, virtual work, the Duffing oscillator, modal analysis and FRF, vibration absorbers and beam vibrations.

References

• Meriam, J. L., Kraige, L. G., Bolton, J. Engineering Mechanics: Dynamics, 7th Ed., Wiley, 2012.
• Bedford, A., Fowler, W. Engineering Mechanics: Statics and Dynamics, 5th Ed., Prentice Hall, 2006.
• Hibbeler, R. C. Engineering Mechanics: Principles of Statics and Dynamics, 11th Ed., Pearson, 2006.
• Rao, S. Mechanical Vibrations, 6th Ed., Pearson Prentice-Hall, 2017.
• Rodríguez, C. F., Camargo, J. Dinámica Mecánica, 2nd Ed., Ediciones Uniandes, 2023.

Software

• Python — symbolic modeling and numerical simulation
• Autodesk Inventor — mechanism design and analysis
• Tracker — video analysis for dynamics experiments