EMch 112H
Kinetic Analysis of an Airfoil Cutting Mechanism

Introduction

This project is a continuation of the project in which we did the kinematic analysis of the airfoil cutting mechanism. In this project, we will use the results of the kinematic analysis performed earlier this semester to determine the loads on the mechanism designed to cut out wing or airfoil profiles.

The Mechanism

Figure 1 shows a diagram (drawn approximately to scale) of the mechanism we will analyze in this project.

Figure 1. The mechanism we will analyze in this project.

As before, the red circle at point E in the mechanism shown above is the laser cutting device. The center of the device is the point at which the cutting occurs. The motor at point D drives the link CD at a constant angular velocity w₀ (omega sub zero). The angles shown define the position of the mechanism at any given time.

Again, we will use the following for the dimensions of the links in the above mechanism: AB = 1.346 m, BC = 0.9925 m, CD = 0.5025 m, BE = 2.479, AD = 1.200 m. In addition, in Table 1, we now note the mass properties for the mechanism.

Object	Mass Property	Other Info
Laser Cutter E	20 kg	Radius = 20 cm k_G = 0.08 kg-m²
Bars AB, CD, and CE	mass/length = 33 kg/m	uniform slender rods

Table 1. The mass properties for the mechanism shown in Figure 1.

The Analysis

Assuming all motion takes place the horizontal plane and using the constant value of w₀ that you found in the kinematic analysis, please do the following:

Draw FBDs and KDs of all three links as well as the laser cutter and write all appropriate equations of motion.

Then create a Mathematica notebook that is based on the kinematic analysis you did in the previous project (I will make my solution to the kinematics part available to you if you would like it). Use that new notebook as the start of your notebook for this activity. You won't need everything from the kinematic analysis, so please remove irrelevant data (e.g., plots, velocities, etc.). Once you have derived your equations in Part 1, you will see that you have some of what you need in this new notebook (e.g., the acceleration of E, the acceleration of the mass center of CE, the angular acceleration of CE, etc.) and that you will need to determine some additional kinematic quantities (e.g., the acceleration of the mass center of AB, the acceleration of the mass center of CD, etc.).

In Mathematica, solve the equations found in Parts 1 and 2 to determine:
1. the total pin force at points A, B, C, and D as functions of theta;
2. the moment at D as a function of theta required to keep the motor rotating at a constant w₀;
3. the force and moment at E required to keep the laser cutter attached.

Please comment on the plots you obtain for each of the above quantities and comment on the ease with which one might design such a mechanism. Think about the requirements of the motor, materials issues, and anything else you think would be appropriate. Your grade will be partially determined by the thought and insight I see in your commentary.

Project Report

The project report for this one is easy -- simply turn in the Mathematica notebook you use to do the kinetic analysis and the plots. In addition, attach any handwritten work used to derive the appropriate equations. Be sure to put comments in your notebooks that clearly state exactly what you are doing each step of the way.

Important

Because this project will not be due until the end of the last week of class, I want to assure you that your grade on this project will be at least 90 as long as you have determined all required quantities correctly and your work is neat and professionally presented. The discussion is worth, at most, 10 points. Keep in mind that if you can turn these in by Tuesday during the last week of class, I can grade them Tuesday night and get them back to you on Wednesday.

[ESM] [ESM Faculty] [PSU Engineering] [Penn State]

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Prepared by Gary L. Gray.
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