VPOD 3DOF Vibratory Device - Revision history

Lynch: /* Introduction */

2010-06-07T23:19:34Z

Introduction

Eric Bell: /* 399 Write-up and Raw Data */

2010-06-07T17:52:23Z

399 Write-up and Raw Data

Eric Bell: /* 399 Write-up and Raw Data */

2010-06-07T17:45:09Z

399 Write-up and Raw Data

Eric Bell: /* 399 Write-up and Raw Data */

2010-06-07T17:35:35Z

399 Write-up and Raw Data

Eric Bell: /* 399 Write-up and Raw Data */

2010-06-07T17:32:08Z

399 Write-up and Raw Data

Eric Bell: /* 399 Write-up and Raw Data */

2010-06-07T17:28:49Z

399 Write-up and Raw Data

Eric Bell: /* 399 Write-up and Raw Data */

2010-06-07T17:19:32Z

399 Write-up and Raw Data

Eric Bell: /* 399 Write-up and Raw Data */

2010-06-07T17:18:17Z

399 Write-up and Raw Data

Eric Bell: /* 399 Write-up and Raw Data */

2010-06-07T17:16:49Z

399 Write-up and Raw Data

Eric Bell: /* 399 Write-up and Raw Data */

2010-06-07T17:13:05Z

399 Write-up and Raw Data

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 The Nondimensional 3DOF Bouncing Ball Simulator is a simple Matlab program meant to mimic the behavior of a bouncing ball on a vibratory device capable of sinusoidal motion in three degrees, such as the VPOD. The simulator uses a numerical method in which the equations of motion describing the ball's flight are determined from the state variables of the previous impact. The program uses a binary search to locate the time at which the ball's position in the x,z plane is equal to that of the oscillating bar. In short, it calculates the intersection of a parabola with a sinusoid, uses a simple impact model to compute the new state variables, and repeats this computation as many times as desired.
 The equations of motion for the oscillating bar are as follows:
-: <math> x(t) = A_xsin(\omega_xt+\phi_x)\, </math>
+: <math> x(t) = A_x \sin(\omega_xt+\phi_x)\, </math>
-: <math> z(t) = A_zsin(\omega_zt+\phi_z)\, </math>
+: <math> z(t) = A_z \sin(\omega_zt+\phi_z)\, </math>
-: <math> \theta(t) = A_\theta sin(\omega_\theta t+\phi_\theta)\, </math>
+: <math> \theta(t) = A_\theta \sin(\omega_\theta t+\phi_\theta)\, </math>
 where A_x, A_z, A_theta represent the maximum x, z, and angular displacements of the bar's motion. The key input variables are the three position amplitudes, three frequencies, and three phase angles, as well as coefficients of restitution in the normal and tangential directions.

@@ Line 77: / Line 77: @@
 The following is experimental data used to create the bifurcation diagrams shown in Figure 3.8 and 3.10. This data was also used for the examples of period 1 and period 2 m=2 behavior corresponding to Figures 3.6 and 3.7 in the write-up:
 [[Media:EBell-Bifurcationsv3.zip|Data for Bifurcation Diagrams]]
+This data was collected using 3 regions of interest (XZ- raw data from real camera, YZ- raw data from "virtual" camera, bar_tracking- raw data for bar's motion using real camera). This workspace also contains the calculated 3D coordinates of the ball (XYZ_BALL) as well as the adjusted coordinates of the bar (XZ_BAR). The Matlab function used to calculate these coordinates is pasted below.
 The data for the experiment shown in Figure 3.12 can be downloaded here along with the plot.
@@ Line 82: / Line 83: @@
 In the workspace, the variable referred to as tau in the plot is saved as "ndPhase."
+Other figures included in the paper:
-This data was collected using 3 regions of interest (XZ- raw data from real camera, YZ- raw data from "virtual" camera, bar_tracking- raw data for bar's motion using real camera). This workspace also contains the calculated 3D coordinates of the ball (XYZ_BALL) as well as the adjusted coordinates of the bar (XZ_BAR). The Matlab functions used to calculate these coordinates are pasted below.
+[[Media:EBell-MiscFigures.zip|Miscellaneous Figures]]
  <nowiki>% The function "calc_coords" takes as inputs, the raw data for vision in

@@ Line 75: / Line 75: @@
 [[Media:EBell-P123v2.zip|Figures3.1-3.5 Data]]
-Finally, the following is experimental data used to create the bifurcation diagrams shown in Figure 3.8 and 3.10. This data was also used for the examples of period 1 and period 2 m=2 behavior corresponding to Figures 3.6 and 3.7 in the write-up:
+The following is experimental data used to create the bifurcation diagrams shown in Figure 3.8 and 3.10. This data was also used for the examples of period 1 and period 2 m=2 behavior corresponding to Figures 3.6 and 3.7 in the write-up:
 [[Media:EBell-Bifurcationsv3.zip|Data for Bifurcation Diagrams]]
+The data for the experiment shown in Figure 3.12 can be downloaded here along with the plot.
+[[Media:EBell-Fig3.12.zip|Data for Figure 3.12]]
+In the workspace, the variable referred to as tau in the plot is saved as "ndPhase."
 This data was collected using 3 regions of interest (XZ- raw data from real camera, YZ- raw data from "virtual" camera, bar_tracking- raw data for bar's motion using real camera). This workspace also contains the calculated 3D coordinates of the ball (XYZ_BALL) as well as the adjusted coordinates of the bar (XZ_BAR). The Matlab functions used to calculate these coordinates are pasted below.

@@ Line 76: / Line 76: @@
 Finally, the following is experimental data used to create the bifurcation diagrams shown in Figure 3.8 and 3.10. This data was also used for the examples of period 1 and period 2 m=2 behavior corresponding to Figures 3.6 and 3.7 in the write-up:
-[[Media:EBell-Bifurcationsv2.zip|Data for Bifurcation Diagrams]]
+[[Media:EBell-Bifurcationsv3.zip|Data for Bifurcation Diagrams]]
 This data was collected using 3 regions of interest (XZ- raw data from real camera, YZ- raw data from "virtual" camera, bar_tracking- raw data for bar's motion using real camera). This workspace also contains the calculated 3D coordinates of the ball (XYZ_BALL) as well as the adjusted coordinates of the bar (XZ_BAR). The Matlab functions used to calculate these coordinates are pasted below.

@@ Line 68: / Line 68: @@
 Some of the data used in the write-up are included below:
-The following contains both the raw data from the real and virtual cameras as well as the calculated a workspace containing the calculated 3D coordinates. This data was used to create Figures 2.3 and 2.4:
+The following contains both the raw data from the real and virtual cameras as well as the calculated a workspace containing the calculated 3D coordinates. This data was used to create Figures 2.3 through 2.5:
 [[Media:EBell-Fig2.3-2.5.zip|Figure2.3-2.5 Data]]
+The zipped folder also contains the Matlab Figure files corresponding to the plots used in the paper.
-The following contains the Matlab workspaces used to create Figures 3.1-3.5. The period 1 and period 2 examples were captured using 2D imaging, whereas the period 3 example uses 3D.
+The following contains the Matlab workspaces used to create Figures 3.1-3.5. The period 1 and period 2 examples were captured using 2D imaging, whereas the period 3 example uses 3D. Figure files are also included.
 [[Media:EBell-P123v2.zip|Figures3.1-3.5 Data]]
-Finally, the following is experimental data used to create the bifurcation diagrams shown in Figure 3.8 and 3.10:
+Finally, the following is experimental data used to create the bifurcation diagrams shown in Figure 3.8 and 3.10. This data was also used for the examples of period 1 and period 2 m=2 behavior corresponding to Figures 3.6 and 3.7 in the write-up:
-[[Media:EBell-Bifurcationsv2.zip|Figure3.8 Data]]
+[[Media:EBell-Bifurcationsv2.zip|Data for Bifurcation Diagrams]]
 This data was collected using 3 regions of interest (XZ- raw data from real camera, YZ- raw data from "virtual" camera, bar_tracking- raw data for bar's motion using real camera). This workspace also contains the calculated 3D coordinates of the ball (XYZ_BALL) as well as the adjusted coordinates of the bar (XZ_BAR). The Matlab functions used to calculate these coordinates are pasted below.

@@ Line 69: / Line 69: @@
 The following contains both the raw data from the real and virtual cameras as well as the calculated a workspace containing the calculated 3D coordinates. This data was used to create Figures 2.3 and 2.4:
-[[Media:EBell-Fig2.3v2.zip|Figure2.3 Data]]
+[[Media:EBell-Fig2.3.zip|Figure2.3 Data]]
 The following contains the Matlab workspaces used to create Figures 3.1-3.5. The period 1 and period 2 examples were captured using 2D imaging, whereas the period 3 example uses 3D.

@@ Line 63: / Line 63: @@
 The following is a 399 Write-up from a 2009-2010 independent study conducted by Undergraduate Eric Bell. The paper uses data from both physical experimentation as well as the simulator described above.
 [[Media:EBell-399FinalWriteup.pdf|EBell-399FinalWriteup]]
+The write-up is also available as a word document [[Media:EBell-399FinalWriteup.doc|EBell-399FinalWriteup Microsoft Word version]]
 Some of the data used in the write-up are included below: