University of Illinois at Chicago
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Dynamics of Mechanisms and Machines Lecture Notes

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Version 2 2024-04-13, 18:37
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posted on 2024-04-13, 18:37 authored by Ahmed ShabanaAhmed Shabana

These lecture notes are designed for a one-semester undergraduate course on the dynamics of mechanisms and machines taught at the University of Illinois at Chicago (UIC). The goal is to introduce undergraduate students to approaches used for the kinematic and dynamic analysis of mechanisms and machines that consist of interconnected components. The lecture notes focus on the analytical and computational approaches that form the basis of the computational algorithms implemented in the software used by the industry.

The notes start with an introduction to review basic concepts and provide mathematical preliminaries. After this introduction, the kinematic position, velocity, and acceleration equations are developed. Motion transmission using cams and gears are covered; and dynamics of mechanisms and machines, including balancing, Euler angles, and spatial Newton-Euler equations are discussed. The lecture notes are designed to provide the instructor with the flexibility to add or skip topics and/or assign class projects.

Computer algorithms used by the industry to solve complex mechanical and aerospace systems are based on the Lagrangian approach that does not require using free-body diagrams or cuts at the joints. The lecture notes are designed to introduce undergraduate students to this approach. For additional reading on this subject, the students are referred to the author’s textbook computational Dynamics, published by John Wiley & Sons.


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These lecture notes are for personal use and cannot be copied or distributed.


Shabana, A.A., 2024, Dynamics of Mechanisms and Machines Lecture Notes, University of Illinois at Chicago, Chicago, Illinois.

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