Project 04:Mechanism Analysis & Design Pankaj Sharma, Department of Mechanical Engineering, University at Buffalo

10/13/2010

This project report aims to learn motion simulation and mechanism design with SolidWorks and compare it analytical with the help of MATLAB. The problem one is based on ball falling case, where we need to build a model in SolidWorks and then analysis it on MATLAB. Then, we need to compare the root mean square error (RMSE) values for both cases. In problem two, we will be discussing the case of simple pendulum and compound pendulum. The problem three is based on four bar link mechanism simulation in SolidWorks and then analyzes it on MATLAB.

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CONTENTS

1 Introduction ………………………………………….3

2 Problem 1 Ball Throwing Example…………………………………………3

3 Problem 2 Simple Pendulum Example……………………………………………10

4 Problem 3 Slider Crank Mechanism …………………………………….19

5 Reference………………………….32

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1. Introduction

The objective of this project is to learn motion simulation and mechanism design in SolidWorks and then develop an analytical method and program in MATLAB for result verification.

2. Ball Throwing Example

Problem 1) Ball Throwing Case:

The below are the images of figures plotted in SolidWorks. The following are the desired figures i.e. figure 3.17, 3.18, and 3.19.

Figure 1.CM Position –Y (inch) vs. Time (sec), SolidWorks

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Figure 2.X Velocity of Ball (inch/sec) CM vs. Time (sec), SolidWorks

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Figure 3.Y Velocity of Ball (inch/sec) CM vs. Time (sec), SolidWorks

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Problem 1 part b

The following are the images created on MATLAB. The results are shown below:

Figure 4.CM Position –Y (inch) vs. Time (sec), MATLAB

Figure5.X Velocity of Ball (inch/sec) CM vs. Time (sec), MATLAB

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Figure 6.Y Velocity of Ball (inch/sec) CM vs. Time (sec), SolidWorks

Figure 7.Animated View in MATLAB

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Problem 1 part c :

The combined plotting for the ball falling is shown below:

Figure 8.Comparision of CM position (ball) vs. time, of SolidWorks and MATLAB

Figure 9.Comparision of CM velocity vs. time, of SolidWorks and MATLAB

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Problem 1 part d: RMS error calculation:

Root mean square error (RMSE) is a measure for finding the difference between values predicted by theoretical model and the actual observed. It can be calculated by using the equation shown below [1]:

The major difference is due to the assumption of coefficient of restitution , if we decrease the coefficent of restitution the rms error reduces significantly. For the improvement of result we should know the assumption on which SolidWorks is simulating and plotting the results .

RMS Error Y position error Y-velocity error

8.715958838 86.66844682

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3 Simple Pendulum Example:

Problem 2. Simple Pendulum Part a:

In this problem we need to model and simulate the pendulum figures i.e. 4.7, 4.9 and 4.10 in SolidWorks.

Figure10: Rotation Angle of the Pendulum, SolidWorks

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Figure11: Z- Angular Velocity of the Pendulum, SolidWorks

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Figure 12: Z- Angular Acceleration of the Pendulum, SolidWorks

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Problem 2. Simple Pendulum Part b: The below are plot developed in MATLAB:

Figure 13: Rotation Angle of the Pendulum, MATLAB

Figure 14: Z- Angular Velocity of the Pendulum, MATLAB

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Figure 15: Z- Angular Acceleration of the Pendulum, MATLAB

Figure 16: Animated view of the Pendulum, MATLAB

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Problem 2. Simple Pendulum Part c:

The following are the combined plots for the case of simple pendulum for SolidWorks and MATLAB data:

Figure 17: Angular displacement vs. time comparison for SolidWorks and MATLAB data

Figure 18: Angular velocity vs. time comparison for SolidWorks and MATLAB data

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Figure 19: Angular acceleration vs. time comparison for SolidWorks and MATLAB data

Problem 2. Simple Pendulum Part d: RMS error

RMS error calculation: RMS error in the case of simple pendulum for position analysis comes out to be 0.07723. For the case of velocity it is coming 0.698, and for acceleration it is coming 7.77.The results in case of pendulum is very close to SolidWorks model.

RMS Error Position Velocity Acceleration 0.07723056 0.69828567 7.779308615

Problem 2. Part e: Compound pendulum case.

In the case of compound pendulum we are going to assume the pendulum as the rigid mass.

The equation for moment of Inertia will be:

I = 1/3*(mr)*l^2 + 2/5*mb*r^2 + mb(l+r)^2 equation (1)

We are given length of rod (l)=100 mm

Radius of rod =0.5 mm

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Radius of ball=10 mm

Density of Aluminum 2014 grade=0.0028 g/mm^3

Mass of ball(mb)=density * volume=density*4/3*pi*(r^3);

Mass of Rod(mr)=density *volume=density*pi*r^2*l

mb=0.0028*4/3*3.14*10^3=11.69;

mr=1/3*(0.0028)*0.5^2*100=0.023;

So, If we substitute these values in equation (2), we will get moment of inertia (I)= 141494.4 mm equation(2)

We know effective length of pendulum in case of compound pendulum is given by relation:

L=I/MD;

M=11.913;

D=100;

Therefore, L=0.1187 (meter)

The following are the plots for the case of compound pendulum:

Figure 20: Rotation Angle of the Pendulum, MATLAB

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Figure 21: Z- Angular Velocity of the Pendulum, MATLAB

Figure 22: Z- Angular Acceleration of the Pendulum, MATLAB

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Figure 23: Animated view of the Pendulum, MATLAB

4 Slider Crank Mechanism:

Problem3. Slider crank mechanism part a:

It is solved by hand, the document is attached.

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Problem3. Slider crank mechanism part b:

Figure 24: X position of the Piston, SolidWorks

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Figure 25: X Velocity of the Piston, SolidWorks

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Figure 26: X Acceleration of the Piston, SolidWorks

Figure 27: Angular Velocity of Concentric-2, SolidWorks

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Figure 28: CM Position of the Piston, SolidWorks

Figure 29: X Velocity of the Piston, SolidWorks

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Figure 30: X Reaction Force of Concentric 3, SolidWorks

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Problem 3 Part b:

Figure 31: Slider crank mechanism at theta 2 = 30 degree

Figure 32: Slider crank mechanism at theta 2 = 90 degree

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Figure 33: Slider crank mechanism at theta 2 = 200 degree

Figure 34: Slider crank mechanism at theta 2 = 300 degree

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Problem 3 Part c:

Figure 35: r1 vs. theta2

Figure 36: theta3 vs. theta2

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Problem 3 Part d:

Figure 37: linear velocity of the crank

Figure 38: Angular velocity of the crank

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Problem 3 Part e:

Figure 39: Angular velocity of the crank

6. References

[1] Wikipedia, October, 10, 2010,http://en.wikipedia.org/wiki/Root_mean_square_deviation

[2] October, 12, 2010, http://farside.ph.utexas.edu/teaching/301/lectures/node141.html