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Analytical Synthesis and Analysis of Mechanisms Using MATLAB and SIMULINK

Alireza Mohammadzadeh Grand Valley State University

Abstract

The approach adopted in this work is an attempt to introduce students, in kinematics and dynamics of machinery course, to a complete design and analysis of function generation mechanisms via analytical methods. Although the approach implemented in this work is for function generation type of mechanisms, the concept is indeed extendable to the other types of mechanisms as well. As a project in the kinematics and dynamics of machinery class, students designed, and analyzed a four bar quick-return mechanism using MATLAB and SIMULINK as the primary software tools. One of the aims of this project was to abandon the traditional graphical synthesis and graphical analysis, covered in all the mechanisms textbooks, and to use the powerful combination of MATLAB and SIMULINK to implement the entire design and analysis process. The project, given to an undergraduate class, serves also as a prologue to future advanced courses in mechanical engineering, such as multi-body dynamics.

In implementing the dimensional synthesis portion of the project, students employed complex number arithmetic to realize the design specifications. Once the design specifications were met, a known motor torque was applied to the crank to drive the mechanism. With the known geometric and inertial properties of each link, Lagrange’s equations for constraint motion were then utilized to arrive at the second order differential equations of motion. SIMULINK, as a user friendly graphical interface, was used to carry out the integration to obtain angular position, velocity, and acceleration of the designed mechanism.

The project, though rigorous, is an excellent way to force students to practice their knowledge of dynamics and numerical methods. The project, certainly, meets the ABET criteria for implementing design in mechanical engineering curriculum. The author received positive feedbacks from his students with regard to this project.

Problem Statement

Students in kinematics and dynamics of machinery class were, first, asked to design a four bar quick-return mechanism to meet a certain design specifications. Once the mechanism was realized, students were then asked to analyze the synthesized mechanism- using Lagrange’s equations and Lagrange’s multipliers method for

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Mohammadzadeh, A. (2007, June), Analytical Synthesis And Analysis Of Mechanisms Using Matlab And Simulink Paper presented at 2007 Annual Conference & Exposition, Honolulu, Hawaii. 10.18260/1-2--2678