Double Pendulum -Estimating Tilt Angle of the Second Link Using Multiple Accelerometers
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MECH496 Lab 3: Double Pendulum -Estimating Tilt Angle of the Second LinkUsing Multiple AccelerometersNovember.7/2017Meghan Lea10130156Results, 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 GainBiasPot 171.428571432.55 VPot 267.16417912.09 Vacc1x28.852941181.6 Vacc1y29.727272731.6 Vacc2x28.852941181.64 Vacc2y28.028571431.6 VThe 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 readingThe 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 2The 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 lengthThe 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