LabAssignment < Main

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---+++++ LAB #1

Before beginning the lab, we noticed the motors were once again loose. It was decided that we to provide additional supports between the frames in order to compensate.

_Adding additional supports:_

<img width="400" alt="IMG958000.jpg" src="%PUBURL%/Main/FRCV-CISC3600S13Group10/IMG958000.jpg" height="250" />

*Measurement Set #1:*
<table cellspacing="0" id="table1" cellpadding="0" rules="all" border="1"> <tbody> <tr> <th valign="top"><a rel="nofollow" href="FRCV-CISC3600S13Group10?rev=41;sortcol=0;table=1;up=0#sorted_table" title="Sort by this column"><span style="color: #ffffff;">Object</span></a></th><th valign="top"><a rel="nofollow" href="FRCV-CISC3600S13Group10?rev=41;sortcol=1;table=1;up=0#sorted_table" title="Sort by this column"><span style="color: #ffffff;">Length (in cm)</span></a></th> </tr> <tr> <td bgcolor="#ffffff" valign="top">Outer wheel radius</td> <td bgcolor="#ffffff" valign="top">6.5</td> </tr> <tr> <td bgcolor="#edf4f9" valign="top">Innter wheel radius</td> <td bgcolor="#edf4f9" valign="top">5.1</td> </tr> <tr> <td bgcolor="#ffffff" valign="top">Chassis, side-by-side</td> <td bgcolor="#ffffff" valign="top">20.4</td> </tr> <tr> <td bgcolor="#edf4f9" valign="top">Chassis, side-to-side</td> <td bgcolor="#edf4f9" valign="top">22</td> </tr> <tr> <td bgcolor="#ffffff" valign="top">Total length, front to back</td> <td bgcolor="#ffffff" valign="top">27.3</td> </tr> <tr> <td bgcolor="#edf4f9" valign="top">Width, wheel-to-wheel</td> <td bgcolor="#edf4f9" valign="top">28</td> </tr> <tr> <td bgcolor="#ffffff" valign="top">Total width, side-to-side</td> <td bgcolor="#ffffff" valign="top">32.5</td> </tr> <tr> <td bgcolor="#edf4f9" valign="top">

Distance between points of contact (lengthwise)
</td> <td bgcolor="#edf4f9" valign="top">15.5</td> </tr> <tr> <td bgcolor="#ffffff" valign="top">Bottom of chassis to ground</td> <td bgcolor="#ffffff" valign="top">6</td> </tr> <tr> <td bgcolor="#edf4f9" valign="top">Top of chassis to ground</td> <td bgcolor="#edf4f9" valign="top">8.4</td> </tr> <tr> <td bgcolor="#ffffff" valign="top">Top of Cortex to ground</td> <td bgcolor="#ffffff" valign="top">12.7</td> </tr> </tbody> </table>

_Side-view:_

<img width="400" alt="IMG950320.jpg" src="%PUBURL%/Main/FRCV-CISC3600S13Group10/IMG950320.jpg" height="250" /> <img width="400" alt="2013-02-099515-51-5295757.jpg" src="%PUBURL%/Main/FRCV-CISC3600S13Group10/2013-02-099515-51-5295757.jpg" height="250" />

_Top-view:_

<img width="400 alt=" alt="" src="%PUBURL%/Main/FRCV-CISC3600S13Group10/IMG951826.jpg" height="250" /> <img width="400" alt="2013-02-099515-51-2395313.jpg" src="%PUBURL%/Main/FRCV-CISC3600S13Group10/2013-02-099515-51-2395313.jpg" height="250" />

_Polygon of support:_

<img width="400" alt="2013-02-099516-03-1895914.jpg" src="%PUBURL%/Main/FRCV-CISC3600S13Group10/2013-02-099516-03-1895914.jpg" height="250" />

*Measurement Set #2:*

_Centroid_: The centroid of our robot is located at the intersection of the mid-points on the Tumbler, (from the front to the back, and from side to side). Therefore, it is at the intersection of 13.65 cm from the front of the Tumbler, and 16.25 cm from either side of the it.

_Total Mass_: Based on the information given, we calculated the mass of our robot to be 1550.76 grams, or 1.55 kg. However, this figure does not account for any of the screws and bolts, (used to hold the robot together), the axels, or the wires, as the mass for these parts was not given.

_Center of Mass_: To determine the center of mass, we calculated it quantitatively. Looking at the structure, there are only two main objects (of any non-negligible mass), without an equal and opposite partner &ndash; the battery pack and the cortex. Therefore, determining the center of mass of these two objects combined would offer us a relatively accurate position for the center of mass of the entire robot. The point where the center of the battery pack contacted the chassis was the point chosen as the origin for the x and y axes.

X<sub>cm</sub> = (x<sub>1</sub>*m<sub>1</sub> + x<sub>2</sub>*m<sub>2</sub>)/m<sub>1</sub> + m<sub>2</sub> = 0.21 cm
   * X<sub>1</sub> = x position of center of mass of battery pack
   * M<sub>1</sub> = mass of battery pack
   * X<sub>2</sub> = x position of center of mass of Cortex
   * M<sub>2</sub> = mass of Coretx
Y<sub>cm</sub> = (y<sub>1</sub>*m<sub>1</sub> + y<sub>2</sub>*m<sub>2</sub>)/m<sub>1</sub> + m<sub>2</sub> = 6.26 cm
   * y<sub>1</sub> = y position of center of mass of battery pack
   * M<sub>1</sub> = mass of battery pack
   * y<sub>2</sub> = y position of center of mass of Cortex
   * M<sub>2</sub> = mass of Coretx
_Proportion of Weight on Each Wheel_:

   * d1 = 6.26 cm = distance of <a rel="nofollow" href="http://www.cis.fordham.edu/twiki/bin/edit/Main/CoM?topicparent=Main.FRCV-CISC3600S13Group10;nowysiwyg=0" title="CoM (this topic does not yet exist; you can create it)">CoM</a> from back of chassis
   * d2 = 20.4 cm = total length of chassis
   * Proportion = d1/d2 = 0.30
   * Therefore the front supports 30% (15% each)
   * Back supports 70% (35% each)
*Measurement Set #3:*

Based on our calculations, the Tumbler is capable of traveling at .67m/s
   * v = 2prw 
      * v = 2 * 3.14 * 2.5in * 100rpm
      * v = 2 * 3.14 * (2.5 * .0254)* ((100r/1min)(1min/60s)
      * v = 2 * 3.14 * .0635m * ((100r/1min)(1min/60s)
      * v = 2 * 3.14 * 2.5 * .0635 * 1.6667rps
      * v = .67m/s
<table cellspacing="0" id="table2" cellpadding="0" rules="all" border="1"> <tbody> <tr> <td bgcolor="#ffffff" valign="top"> <p align="center"> *Trial* </p> </td> <td bgcolor="#ffffff" valign="top"> <p align="center"> *Length* </p> </td> <td bgcolor="#ffffff" valign="top"> <p align="center"> *Duration* </p> </td> <td bgcolor="#ffffff" valign="top"> <p align="center"> *Speed* </p> </td> </tr> <tr> <td bgcolor="#edf4f9" valign="top"> <p align="center">1</p> </td> <td bgcolor="#edf4f9" valign="top"> <p align="center">500 cm</p> </td> <td bgcolor="#edf4f9" valign="top"> <p align="center">6.5s</p> </td> <td bgcolor="#edf4f9" valign="top"> <p align="center">.769m/s</p> </td> </tr> <tr> <td bgcolor="#ffffff" valign="top"> <p align="center">2</p> </td> <td bgcolor="#ffffff" valign="top"> <p align="center">500 cm</p> </td> <td bgcolor="#ffffff" valign="top"> <p align="center">6.7s</p> </td> <td bgcolor="#ffffff" valign="top"> <p align="center">.746m/s</p> </td> </tr> <tr> <td bgcolor="#edf4f9" valign="top"> <p align="center">3</p> </td> <td bgcolor="#edf4f9" valign="top"> <p align="center">500 cm</p> </td> <td bgcolor="#edf4f9" valign="top"> <p align="center">6.4s</p> </td> <td bgcolor="#edf4f9" valign="top"> <p align="center">.781m/s</p> </td> </tr> <tr> <td bgcolor="#ffffff" valign="top"> <p align="center">Average</p> </td> <td colspan="2" bgcolor="#ffffff" valign="top"> <p align="center">----------------------------------------------</p> </td> <td bgcolor="#ffffff" valign="top"> <p align="center">.765m/s</p> </td> </tr> </tbody> </table>
   * with speed = duration/(length * .01)
   * average speed = (.769+.746+.781)/3
There are multiple reasons that may be used to explain the discrepancies. For one, it is difficult to have both wheels rotate at the same speed, which caused the Tumbler to veer from side to side as it progressed along the test-track. Second, because humans are using the controller, it is possible that the user accelerate at different rates during each trial &ndash; it is very hard to perform each trial the same exact way. Third, the Tumbler was driving along an uneven carpet. Certain spots were flat; other areas had small bumps. Driving over these would certainly slow the robot down.

The discrepancy between our first calculation, .67m/s, and our average recorded velocity, .765m/s, can be blamed on either human error with using the stop watch, or the fact that the numbers used in obtaining the first calculation was based on approximates from the manufacture itself. It is possible that the motors we have acquired are better than average.

_Performing the speed test:_

<img width="400" alt="2013-02-12_16-10-10_691.jpg" src="%PUBURL%/Main/FRCV-CISC3600S13Group10/2013-02-12_16-10-10_691.jpg" height="250" />

*Measurement Set #4*

Theoretical Maximum Slope= (tan(x/h)^-1 x = 3.26 cm h = 7.6 cm (tan(3.26/7.6))^-1 = 55.9 degress

RMFrobot = M * (a + g * sin(angle)) * v = 1.5kg * (0.765/2) + 9.8 * sin((55.9&pi;)/180)) * .765 = 10.21

RMFmotor = t&omega; = .96Nm * ((100rpm/1min)(1min/60s)(2&pi;/1 rotation)) = 10.05

RMFrobot &lt; RMFmotor &rarr; 10.05 &lt; 10.21 Therefore, the robot should be able to drive up the maximum slope

In theory, our Tumbler should only require one motor to ascend its maximum stable slope. However, through trail and error, we found that the actual slope the Tumbler could ascend is less than half of what we calculated, and the Tumbler has four motors, not one. There are a few possibilities that could explain this discrepancy. One possibility is that our motors are not functioning at full capacity. Second, our center of mass calculation could be off, affecting our value for the maximum slope. Or third, the Tumbler is in fact capable of ascending its maximum slope, but the rigid transition from the floor to the slope negatively affects the momentum of the Tumbler, and renders it incapable of ascending the slope. Therefore, in theory, a gradual transition to its maximum slope may allow it to climb its maximum slope.

After trial and error, the actual angle that our Tumbler could ascend was discovered to be ~26°.

_Testing the Tumbler's angle of ascent:_

<img width="400" alt="2013-02-12_16-54-16_209.jpg" src="%PUBURL%/Main/FRCV-CISC3600S13Group10/2013-02-12_16-54-16_209.jpg" height="250" /> <img width="400" alt="IMG957159.jpg" src="%PUBURL%/Main/FRCV-CISC3600S13Group10/IMG957159.jpg" height="250" />

_The Tumbler successfully climbing the ramp:_

<img width="400" alt="2013-02-12_16-55-34_989.jpg" src="%PUBURL%/Main/FRCV-CISC3600S13Group10/2013-02-12_16-55-34_989.jpg" height="250" />

*Measurement Set #5:*

The Tumbler, as intended, can successfully flip on a wall and can then continue driving upside down. Also, the Tumbler has no problem flipping against one of the storage boxes. There is no difference between the two actions.

_The Tumbler driving up the box:_

<img width="400" alt="IMG959714.jpg" src="%PUBURL%/Main/FRCV-CISC3600S13Group10/IMG959714.jpg" height="250" />

*Measurement Set #6:*

In order to determine the center of rotation for the robot, we created a coordinate plane on the floor using tape. We began by lining up the robot&rsquo;s front right wheel with the center of the plane (0,0). Next, we attempted to make a perfect 180° turn, by only moving the left wheels of the Tumbler. After the turn, we measured the distance of the wheel to the center. In centimeters, the new coordinates were (10, 9.3). We then ran a second trial. This time the robot&rsquo;s ending coordinates were (7.6, 6.4). The results from these trials were averaged, and it was concluded that the chassis center of rotation was approximately 5.90cm away from the right front wheel, at an angle of 48°.

_Set up on coordinate plane:_

<img width="400" alt="2013-02-12_16-32-58_376.jpg" src="%PUBURL%/Main/FRCV-CISC3600S13Group10/2013-02-12_16-32-58_376.jpg" height="250" /> <img width="400" alt="2013-02-12_16-33-42_451.jpg" src="%PUBURL%/Main/FRCV-CISC3600S13Group10/2013-02-12_16-33-42_451.jpg" height="250" />

_Post spin & measurements:_

<img width="400" alt="2013-02-12_16-33-48_993.jpg" src="%PUBURL%/Main/FRCV-CISC3600S13Group10/2013-02-12_16-33-48_993.jpg" height="250" /> <img width="400" alt="2013-02-12_16-34-29_910.jpg" src="%PUBURL%/Main/FRCV-CISC3600S13Group10/2013-02-12_16-34-29_910.jpg" height="250" />

These numbers more closely resembles the centriod, rather than the center of mass, due to the fact that the centriod has the true influence over the moment of the robot rather than the center of mass. In an optimal situation, they would be the same; however, when they are not, the location of the centriod is important in directing the vehicle&rsquo;s movement. All the weight rotates around this point.

(10,9.3)

   * c<sup>2</sup> = &radic;(a<sup>2</sup>+b<sup>2</sup>) 
      * c<sup>2</sup> = &radic;(10<sup>2</sup>+9.3<sup>2</sup>)
      * c<sup>2</sup> = &radic;(186.49)
      * c = 13.66
      * 13.66/2 = 6.83cm (to represent the radius instead of diameter)
   * angle = tan<sup>-1</sup>(opposite/adjacent) 
      * angle = tan<sup>-1</sup>(10/9.3)
      * angle = tan<sup>-1</sup>(1.0752688)
      * angle = 47°
(7.6, 6.4)

   * c<sup>2</sup> = &radic;(a<sup>2</sup>+b<sup>2</sup>) 
      * c<sup>2</sup> = &radic;(7.6<sup>2</sup>+6.4<sup>2</sup>)
      * c<sup>2</sup> = &radic;(98.72)
      * c = 9.94
      * 9.94/2 = 4.96cm (to represent the radius instead of diameter)
   * angle = tan<sup>-1</sup>(opposite/adjacent) 
      * angle = tan<sup>-1</sup>(7.6/6.4)
      * angle = tan<sup>-1</sup>(1.1875)
      * angle = 49°
Calculating the average

   * average distance 
      * (6.83+4.96)/2
      * =5.90cm
   * average angle 
      * (47+49)/2
      * =48°
Through experimentation, it was easily discovered that the Tumbler&rsquo;s skidding was unpredictable. Some spins caused little variation from a full circle, while other&rsquo;s misplaced the robot greatly. This could be in part to human error; however, it is most likely due to engineering fault. As already discussed, the center of mass and the centriod are not located in the same spot. This inequality would cause the vehicle to sway back and forth with moment. This swaying would throw off the degree to which the robot skids.
Topic revision: r1 - 2013-03-26 - JosephTaliercio