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:

Measurement Set #1:

Object	Length (in cm)
Outer wheel radius	6.5
Innter wheel radius	5.1
Chassis, side-by-side	20.4
Chassis, side-to-side	22
Total length, front to back	27.3
Width, wheel-to-wheel	28
Total width, side-to-side	32.5
Distance between points of contact (lengthwise)	15.5
Bottom of chassis to ground	6
Top of chassis to ground	8.4
Top of Cortex to ground	12.7

Side-view:

Top-view:

Polygon of support:

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 – 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_cm = (x₁*m₁ + x₂*m₂)/m₁ + m₂ = 0.21 cm

• X₁ = x position of center of mass of battery pack
• M₁ = mass of battery pack
• X₂ = x position of center of mass of Cortex
• M₂ = mass of Coretx

Y_cm = (y₁*m₁ + y₂*m₂)/m₁ + m₂ = 6.26 cm

• y₁ = y position of center of mass of battery pack
• M₁ = mass of battery pack
• y₂ = y position of center of mass of Cortex
• M₂ = mass of Coretx

Proportion of Weight on Each Wheel:

• d1 = 6.26 cm = distance of CoM 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

Trial	Length	Duration	Speed
1	500 cm	6.5s	.769m/s
2	500 cm	6.7s	.746m/s
3	500 cm	6.4s	.781m/s
Average	----------------------------------------------		.765m/s

• 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 – 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:

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((55.9π)/180)) * .765 = 10.21

RMFmotor = tω = .96Nm * ((100rpm/1min)(1min/60s)(2π/1 rotation)) = 10.05

RMFrobot < RMFmotor → 10.05 < 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:

The Tumbler successfully climbing the ramp:

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:

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’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’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:

Post spin & measurements:

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’s movement. All the weight rotates around this point.

(10,9.3)

• c² = √(a²+b²)
  • c² = √(10²+9.3²)
  • c² = √(186.49)
  • c = 13.66
  • 13.66/2 = 6.83cm (to represent the radius instead of diameter)
• angle = tan^-1(opposite/adjacent)
  • angle = tan^-1(10/9.3)
  • angle = tan^-1(1.0752688)
  • angle = 47°

(7.6, 6.4)

• c² = √(a²+b²)
  • c² = √(7.6²+6.4²)
  • c² = √(98.72)
  • c = 9.94
  • 9.94/2 = 4.96cm (to represent the radius instead of diameter)
• angle = tan^-1(opposite/adjacent)
  • angle = tan^-1(7.6/6.4)
  • angle = tan^-1(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’s skidding was unpredictable. Some spins caused little variation from a full circle, while other’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.