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2022 | Book

# Mechanical Simulation with MATLAB®

Authors: Prof. Dan B. Marghitu, Hamid Ghaednia, Jing Zhao

Publisher:

Book Series : Springer Tracts in Mechanical Engineering

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This book deals with the simulation of the mechanical behavior of engineering structures, mechanisms and components. It presents a set of strategies and tools for formulating the mathematical equations and the methods of solving them using MATLAB. For the same mechanical systems, it also shows how to obtain solutions using a different approaches. It then compares the results obtained with the two methods. By combining fundamentals of kinematics and dynamics of mechanisms with applications and different solutions in MATLAB of problems related to gears, cams, and multilink mechanisms, and by presenting the concepts in an accessible manner, this book is intended to assist advanced undergraduate and mechanical engineering graduate students in solving various kinds of dynamical problems by using methods in MATLAB. It also offers a comprehensive, practice-oriented guide to mechanical engineers dealing with kinematics and dynamics of several mechanical systems.

##### Chapter 1. Introduction
Abstract
The structure of the mechanical systems is analyzed: links, joints, degrees of freedom of the joint, degrees of freedom, independent contours, dyads. For the planar mechanisms the contour diagram and the dyads are introduced. Formulas for kinematics and dynamics of the rigid body are presented.
Dan B. Marghitu, Hamid Ghaednia, Jing Zhao
##### Chapter 2. Classical Analysis of a Mechanism with One Dyad
Abstract
The planar motion of a mechanism with three moving links is analyzed. Symbolical and numerical MATLAB are used for the kinematics and dynamics of the system. The classical vectorial equations for velocity and acceleration of the rigid body are used. The joint reaction forces and the moment applied to the driver link are calculated for a given position with Newton-Euler equations for inverse dynamics.
Dan B. Marghitu, Hamid Ghaednia, Jing Zhao
##### Chapter 3. Contour Analysis of a Mechanism with One Dyad
Abstract
Closed contour equations for velocities and accelerations are given for closed kinematic mechanisms. The contour equations are based on contour diagrams and take into consideration the relative velocities and accelerations between two adjacent links. The inverse dynamics is based on contour diagrams and D’Alembert principle.
Dan B. Marghitu, Hamid Ghaednia, Jing Zhao
##### Chapter 4. Classical Analysis of a Mechanism with Two Dyads
Abstract
A planar mechanism with a driver link and two dyads is analyzed using vectorial equations for velocities and accelerations. Newton-Euler equations of motions are developed for the force analysis. Symbolical MATLAB is applied for the manipulation of the equations.
Dan B. Marghitu, Hamid Ghaednia, Jing Zhao
##### Chapter 5. Contour Analysis of a Mechanism with Two Dyads
Abstract
A planar R-RRT-RTR mechanism with two dyads is considered. There are two independent closed contours for the velocity and acceleration fields. For dynamic analysis D’Alembert principle is employed to calculate individual joint forces.
Dan B. Marghitu, Hamid Ghaednia, Jing Zhao
##### Chapter 6. Dyad Routines for Mechanisms
Abstract
MATLAB functions are developed for position, velocity, and acceleration of dyads and kinematic links. The dynamics of mechanisms with one and two dyads are analyzed. For force analysis D’Alembert principle is employed.
Dan B. Marghitu, Hamid Ghaednia, Jing Zhao
##### Chapter 7. Epicyclic Gear Trains
Abstract
Main components of the gears are defined. The angular velocities of epicyclic gear trains are calculated using the classical method and the closed contour method.
Dan B. Marghitu, Hamid Ghaednia, Jing Zhao
##### Chapter 8. Cam and Follower Mechanism
Abstract
A cam and follower mechanism is analyzed. Same kinematic results are obtained with an equivalent mechanism. The differential method is used for velocity analysis.
Dan B. Marghitu, Hamid Ghaednia, Jing Zhao
##### Chapter 9. Direct Dynamics
Abstract
The direct dynamics of a body in planar motion is studied. The equations of motion are developed with symbolic MATLAB. At a certain moment an external elastic force acts on the body. MATLAB ODE solver is employed to integrate the equations taking into consideration different events. The impact of a free kinematic link with a surface is also studied. The results are obtained with Newton-Euler and Lagrange methods.
Dan B. Marghitu, Hamid Ghaednia, Jing Zhao
##### Backmatter
Title
Mechanical Simulation with MATLAB®
Authors
Prof. Dan B. Marghitu
Hamid Ghaednia
Jing Zhao