Double Pendulum -Estimating Tilt Angle of the Second Link Using Multiple Accelerometers

MECH496 Lab 3: Double Pendulum -Estimating Tilt Angle of the Second Link

Using Multiple Accelerometers

November.7/2017

Meghan Lea

10130156

Results, Discussion and Conclusion

Below are the calculated values for gain and bias for both potentiometers and accelerometers in the x and y directions. These values were used to calculate the accelerations and tilt angles.

Table 1: Values of gain and bias for potentiometer 1 and 2 and both accelerometers in x and y

The following plot shows tilt angle of the lower pendulum estimated from  the  accelerometer using equations 7-10 from the lab manual and the potentiometer measured angle (Eq.13).

[pic 1]

Figure 1: Section of Potentiometer vs Accelerometer reading

[pic 2]

Figure 2 Potentiometer vs Accelerometer reading

The following plot is the tilt angle of the lower pendulum estimated from the accelerometers (Eqs.11-12) and the potentiometer measured angle (Eq. 13)

[pic 3]

Figure 3:  Section of Potentiometer vs Accelerometer readings for the second method

[pic 4]

Figure 4 Potentiometer vs Accelerometer reading for method 2

The following plot shows the error propagation of the length measurement with adding 10% to the original length. The error is measured by taking the difference of the 2 measurements and comparing. For L; we saw a minimum error of -8.8°,  a maximum value of 2.9° and a average error of -0.43°. There for the range of this plot is ±5.9°.

[pic 5]

Figure 5 Error propagation for adding 10% to length L

[pic 6]

Figure 6: Section of Error propagation with 10% added to length

The following plot shows the error propagation of the length measurement with adding 10% to the length L1. The error is measured by taking the difference of the 2 measurements and comparing. For L1; we saw a minimum error of -11°, a maximum value of 0.29° and a average error of -0.98°. There for the range of this plot is  ±5.6°.

[pic 7]

Figure 7 Error propagation with 10% added to length L1

[pic 8]

Figure 8: Section of Error propagation with 10% added to length L1

...