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Whole-Body Vibration Sensor Calibration Using a Six-Degree of Freedom Robot

Whole-Body Vibration Sensor Calibration Using a Six-Degree of Freedom Robot Hindawi Publishing Corporation Advances in Acoustics and Vibration Volume 2011, Article ID 276898, 7 pages doi:10.1155/2011/276898 Research Article Whole-Body Vibration Sensor Calibration Using a Six-Degree of Freedom Robot 1 1, 2 1, 2, 3 Sarah Cation, Michele Oliver, Robert Joel Jack, 2, 4 2 James P. Dickey, and Natasha Lee Shee School of Engineering, University of Guelph, Guelph, ON, Canada N1G 2W1 Biophysics Interdepartmental Group Graduate Program, University of Guelph, Guelph, ON, Canada N1G 2W1 School of Human Kinetics, Laurentian University, Sudbury, ON, Canada P3E 2C6 School of Kinesiology, University of Western Ontario, London, ON, Canada N6A 3K7 Correspondence should be addressed to Michele Oliver, moliver@uoguelph.ca Received 23 September 2010; Revised 7 February 2011; Accepted 8 March 2011 Academic Editor: Gurvinder Virk Copyright © 2011 Sarah Cation et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Exposure to whole-body vibration (WBV) is associated with a wide variety of health disorders and as a result WBV levels are frequently assessed. Literature outlining WBV accelerations rarely address the calibration techniques and procedures used for WBV sensors to any depth, nor are any detailed information provided regarding such procedures or sensor calibration ranges. The purpose of this paper is to describe a calibration method for a 6 DOF transducer using a hexapod robot. Also described is a separate motion capture technique used to verify the calibration for acceleration values obtained which were outside the robot calibration range in order to include an acceptable calibration range for WBV environments. The sensor calibrated in this study used linear (Y = mX) calibration equations resulting in r values greater than 0.97 for maximum and minimum acceleration amplitudes of 2 ◦ up to ±8m/s and maximum and minimum velocity amplitudes up to ±100 /s. The motion capture technique verified that the translational calibrations held for accelerations up to ±4 g. Thus, the calibration procedures were shown to calibrate the sensor through the expected range for 6-DOF WBV field measurements for off-road vehicles even when subjected to shocks as a result of high speed travel over rough terrain. 1. Introduction vibration [5]. Compliance with the ISO and BS standards is recommended for reducing the risk of workplace injury. With technological advancements, the detail and complexity In contrast, the European Directive mandates that health of the measurements researchers are able to undertake has in- surveillance is compulsory for workers exposed to vibration creased. This is exemplified in the field of whole-body vibra- levels that exceed the daily exposure action values. This tion (WBV). The most recent publication of the ISO 2631-1 progression from assessment to compulsory surveillance has standard outlines the measurement of WBV in 6 degrees-of- motivated increased vibration measurements in the work- freedom (DOF), and some researchers have suggested that place. The movement to 6-DOF and 12-DOF measurements 12 DOF measurements should be performed [1]. Thus, has increased the complexity of the sensors used to measure measurements in translational axes X-, Y -, and Z-aswell WBV. as rotational axes roll, pitch, and yaw (about X-, Y -, and In some WBV environments, there may be transients (or Z-axes, resp.) are required. Exposure to excessive levels of shocks), which by definition are sudden changes in accel- whole-body vibration is associated with decreased worker erations [2]. Off-road vehicles are likely often subjected to performance and injury [2]; the vibration limits described in shocks as a result of high speeds over rough terrain [6, 7]. the International and British standards ([3] and BS 6841 [4], Based on forestry skidder WBV literature, the WBV trans- resp.) and European Directive 2002/44/EC, are important ducer is required to record peak accelerations of no less than 2 2 benchmarks for assessing human exposure to whole-body 7.08 ± 3.48 m/s [6]or noless than 3.32 ± 1.42 m/s [8]at 2 Advances in Acoustics and Vibration the operator seat interface (OSI) in the translational axes. The reported dominant frequency band was 2.5 Hz at the SPT chassis [9]. In contrast, accelerations at the OSI of up to 11.73 m/s have been reported for heavy haul dump trucks [10]. These published values have been weighted according to various versions of the ISO 2631-1 standard. Accordingly, since the ISO 2631 frequency weightings attenuate the PRSCO acceleration signals according to the sensitivity to vibration 6-DOF at various frequencies, it is therefore important to calibrate robot the WBV sensors for a larger amplitude range than reported in these papers. This should be done to ensure that there has been no underestimation of the actual recorded field accelerations which may be attenuated at certain frequencies during the weighting process. In the field of WBV, the literature outlining WBV accel- Figure 1: Experiment Setup for the low g (LG) calibration using erations rarely address the calibration technique/procedures a Parallel Robotics System Corporation (PRSCO) six-degree-of- used for WBV sensors to any depth, nor is any detailed freedom (6-DOF) robot shown here with the seat-pad transducer (SPT). information provided regarding such procedures or sensor calibration ranges. Therefore, the purpose of this paper was to describe a simple calibration method for a 6 DOF OSI transducer used for WBV measurements. Also described is a equations using a 6-DOF robot. The second phase was used separate technique used to verify the calibration for accelera- to assess the sensor calibration previously determined in the tion values obtained which were outside the robot calibration LG calibration using an expanded range of WBV values in range in order to include an acceptable calibration range for order to validate the calibration values determined in the WBV environments. LG calibration. The range consisted of the expected field range for WBV measurements of forestry skidders. The high g (HG) calibration used a vibration table and an optical 2. Methodology motion capture system. The sensor was zeroed before each axis was tested in order to eliminate orientation bias. A seat-pad transducer (SPT) used for WBV measurements at the OSI was calibrated in two phases. The first calibration phase used a 6-DOF robot to generate the calibration equa- 2.1.1. Low g (LG) Calibration. The LG calibration was com- tions for each DOF. The second phase was used to confirm pleted using a Parallel Robotics System Corporation that the robot determined calibration equations would hold (PRSCO) R2000 6-DOF robot (Parallel Robotic Systems outside of their calibrated range. This larger acceleration Corporation, Hampton, New Hampshire, USA). The PRSCO range was designed to represent the range of vibrations was calibrated by PRSCO for repeatability and accuracy observed in forestry skidders. The SPT was designed to be (within 24 µm), and accuracy (within +24/−38 µm) for compact and flat to remove pressure points as it was to be travel in the X, Y,and Z axes. Sinusoidal acceleration and used at the OSI in the field to measure WBV. The sensor was velocity profiles were created as inputs to the PRSCO. The built at the University of Guelph (Guelph, Ontario, Canada) acceleration profiles were developed to achieve acceleration using two Analog Devices (Analog Devices Inc., Norwood, amplitudes between ±1and ±8m/s for the translational Massachusetts, USA) ADXL320EB biaxial accelerometers axes (X, Y , Z) at known frequencies (Table 1)and were measuring the X, Y,and Z axes and three Analog Devices double integrated using the trapezoid rule prior to imple- ADXRS150EB rate gyroscopes to measure roll, pitch, and mentation on the robot. The profiles were integrated into yaw. The ADXL320EB accelerometers were rated for ±5g displacement form as the robot requires displacement inputs. (±10%) and the ADXRS150EB gyroscopes were capable For pitch, roll, and yaw, a single integration was required, of recording ±150 /s velocities. The accelerometers and since the sensors for these axes monitor angular velocity. gyroscopes were mounted to evaluation boards to simplify Angular velocity profiles ranged between ±10 and ±100 /s mechanical attachment, relative alignment and wiring. The at frequencies between 0.5 and 5 Hz as shown in Table 2. accelerometers and rate gyroscopes were orthogonally placed The sensors were placed in the centre of the PRSCO 6DOF in a Delrin plastic casing to monitor the roll, pitch, and yaw robot platform which reproduced the known displacement axes. For both calibration phases, a 12-bit SOMAT Series profiles. The sensors were oriented such that the axis of 2001 Field computer (nCode International Inc., Southfield, interest was aligned such that the PRSCO robot would Michigan, USA) collected raw device voltages at a sampling have the largest movement displacement allowing higher rate of 500 Hz. accelerations and angular velocities to be produced. The experimental Setup is shown in Figure 1. 2.1. Experiment Setup. The first phase was the low g (LG) cal- ibration (maximum and minimum amplitude values of: ±1 2.1.2. High g (HG) Calibration. The LG calibration cali- 2 ◦ ◦ to ±8m/s and ±10 to ±100 /s) to determine the calibration brated up to ±100 /s, which exceeded the expected field Advances in Acoustics and Vibration 3 Table 1: The sinusoidal minimum and maximum linear acceleration amplitudes and corresponding frequencies used to calibrate the translational (X, Y , Z) accelerometers using displacement profiles on a Parallel Robotics System Corporation Robot six-degree-of-freedom robot. Acceleration (m/s ) ±1 ±2 ±3 ±4 ±5 ±6 ±7 ±8 Frequency (Hz) 1,2,5 1, 2, 5 2,5 2, 5 2,5 2, 5 2,5 2, 5 Table 2: The sinusoidal minimum and maximum angular velocity amplitudes and corresponding frequencies used to calibrate the gyroscopes (roll, pitch, yaw) using displacement profiles on a Parallel Robotics System Corporation Robot six-degree-of-freedom robot. Velocity ( /s) ±10 ±20 ±30 ±40 ±60 ±80 ±100 Frequency (Hz) 0.5, 1, 2, 5 0.5, 1, 2, 5 0.5, 1, 2, 5 0.5, 1, 2, 5 0.5, 1, 2, 5 0.5, 1, 2, 5 0.5, 1, 2 Frequency Sensor axis indicator being tested Vibration table movement Reflective markers used for motion Z-axis Sensor Analog Motor frequency setting dial Displacement Figure 2: Sensor axis orientation and vibration direction for the setting high g calibration verification. requirements for the gyroscopes, but did not encompass Figure 3: The experimental Setup for the high g (HG) calibration the entire expected field requirements for the accelerome- verification. ters. Thus, a second stage was completed to calibrate the accelerometers up to and including approximately ±4g min- imum and maximum acceleration amplitudes at frequencies Table 3: The peak-to-peak displacements and frequency settings between 10 and 35 Hz. used for the high g calibration verification and resulting ± approxi- An All American vibration fatigue testing machine mate peak acceleration amplitude values. (VTM) (All American Tool & Mfg. Co., Illinois, USA) was used to calibrate at HGs. This vibration machine is only able Peak-to-peak displacement Frequency Approximate (mm) (Hz) acceleration (g) to move in the Z-axis, thus the axis being tested was oriented with respect to the Z axis for each of the accelerometer 5.08 10 1.02 axes as shown in Figure 2. The SPT movement on the 1.27 20 1.01 VTM was recorded using three VICON M m cameras from 3.81 15 1.72 a VICON 460 Motion Capture System (VICON Motion 2.54 20 2.03 Systems, Centennial, CO, USA) and simultaneous data 3.81 20 3.04 were recorded from the SPT. The experimental Setup is 2.54 25 3.17 shown in Figure 3. The various accelerations were tested by 1.27 35 3.08 changing the VTM using an analog frequency setting dial (between approximately 10 Hz and 35 Hz) and peak-to- 5.08 20 4.06 peak displacements (between approximately 1.27 mm to 5.08 mm) outlined in Table 3. The accelerations tested for HG calibration verification included and exceeded the accelerations determined at the LG accelerations which were tape such that all M m cameras had full view of the markers. used to generate the calibration equations. The VICON 460 The cameras were oriented in an umbrella fashion (Figure 4) M m cameras were previously validated for vibration mea- oftenused ingait analysis [12]. The cameras recorded the surements of displacements greater than 1 mm to contain X, Y,and Z lab coordinates of the reflective markers for less than 5% error for frequencies between 3 and 30 Hz each trial and were sampled at 500 Hz for 10 seconds. The [11]. VICON system was calibrated statically and dynamically Four, 14 mm diameter spherical reflective markers were in the measurement volume to minimize error due to the adhered to the sensor/vibration table using double-sided optical distortion phenomena [13]. The calibration residuals 4 Advances in Acoustics and Vibration Table 4: Calibration equations for the seat-pad transducer devel- Camera no. 1 oped using a low g acceleration values where Y = mX + b;slope values m are tabulated, Y refers to the calibrated output and X refers to the recorded voltage. Camera no. 2 Axis Calibration equation Unit of measurement XY =−52.02X m/s VTM table YY =−52.18X m/s ZY = 51.13X m/s Roll Y = 81.47X /s Pitch Y =−84.34X /s Camera no. 3 Yaw Y = 79.22X /s Figure 4: The umbrella camera orientation. (error) were less than 1 mm during the calibration of the VICON motion capture system. 2.2. Data Analysis −5 2.2.1. Calibration at Low g Values. The raw dynamic cal- −10 ibration data from the SPT were then second-order low pass Butterworth filtered at a cut-off frequency of 10 Hz −15 (two times the highest expected signal frequency of 5 Hz −20 as shown in Tables 1 and 2) such that the Nyquist rate 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 was exceeded. The acceleration and velocity known input Time (seconds) profiles were then aligned with the sensor voltage output for the translational and rotational axes, respectively. The SPT calibration equations were determined for each sensor and VICON VTM each axis independently. The calibration equations were determined to be of the form Y = mX for all 6-DOF for the Figure 5: The expected acceleration profile is shown (VTM) along- SPT, where Y refers to the calibrated output and X refers to side the accelerations determined using the seat-pad transducer the recorded voltage. The zero offset values are not presented, (SPT) and VICON for a high g test with a peak-to-peak displace- since they are easily identified and calculated from the resting ment of 3.81 mm and frequency setting of 15 Hz. transducer voltages. 2.2.2. Translational Acceleration Data Validation at High g 3. Results (HG) Values. The sensor voltages and raw digitized VICON 3D coordinates were second-order zero lag low pass But- The SPT calibration equations are shown in Table 4.The cal- terworth filtered at a cut-off frequency of two times the ibration equations fit the LG calibration data with r values frequency set on the VTM. The calibrations determined from of greater than 0.997 in all 6-DOF. When the LG calibration the LG calibration were applied to the filtered sensor voltages equations were applied to HG data and compared to VICON and then compared to the double-differentiated, filtered determined accelerations, the accuracy of the sensor was VICON displacement data for the three translational axes (X, shown to generally produce less than 10% error. The largest Y , Z). Five individual cycles of double-differentiated VICON error between the VICON and the system gold standard displacement data and sensor data were manually aligned SPT data was approximately 12% (under 6 m/s ). This error using peak acceleration values. Maximum and minimum was less than 12% at both the maximum and minimum acceleration amplitudes as well as r values were determined peaks. For the largest acceleration values, the SPT recorded from the VICON and SPT data for five individual cycles acceleration amplitudes of approximately ±45.63 m/s and 2 2 at each VTM setting outlined in Table 3. In addition, VICON predicted accelerations of±51.58 m/s .The r values the corresponding percent error was determined for the exceeded 0.9 in all translational axes at all acceleration levels difference between the sensor maximum and minimum tested at the HG levels as shown in Table 5. acceleration amplitude and VICON maximum and mini- The effects of using VICON in addition to the known mum acceleration amplitude, where the VICON data were VTM settings were visually assessed, an example of which is taken to be the gold standard. The overall average (n = 5) showninFigure 5. As can be seen in the figure, there is a shift was reported using the five single cycle values. This was between the VTM and the SPT which is not constant over completed for each of the VTM settings listed in Table 3. time. In contrast, the SPT and VICON data are well aligned. Acceleration (m/s ) Advances in Acoustics and Vibration 5 Table 5: Results of high g acceleration data verification for the seat-operator interface (SPT) transducer for the X, Y,and Z axes at various displacement and frequency settings. The reported accelerations are maximum and minimum amplitudes while the displacements are peak- to-peak values. Displacement (mm) 1.27 5.08 2.54 3.81 1.27 2.54 3.81 5.08 Frequency(Hz) 20 10 201535252020 r 0.97 0.98 0.95 0.96 0.92 0.97 0.95 0.98 Maximum camera acceleration (m/s ) 11.48 8.40 17.65 15.74 28.80 25.23 25.82 39.79 Maximum sensor acceleration (m/s ) 10.37 8.74 16.93 15.93 28.96 25.09 26.75 39.17 Maximum acceleration percent error (%) 9.61 4.01 4.01 3.21 3.81 2.62 3.62 2.95 Minimum camera acceleration (m/s ) −11.48 −8.40 −17.65 −16.44 −28.80 −25.23 −25.82 −40.73 Minimum sensor acceleration (m/s ) −10.37 −9.05 −16.93 −16.02 −28.96 −25.09 −26.50 −39.17 Minimum acceleration percent error (%) 9.61 7.77 4.01 2.54 3.81 2.62 3.30 3.77 Displacement (mm) 1.27 5.08 2.54 3.81 1.27 2.54 3.81 5.08 Frequency(Hz) 20 10 201535252020 r 0.98 0.99 0.92 0.96 0.95 0.96 0.98 0.99 Maximum camera acceleration (m/s ) 10.42 9.90 20.33 15.38 29.49 32.30 27.88 40.40 Maximum sensor acceleration (m/s ) 10.54 9.47 18.76 17.00 29.00 29.06 28.21 36.69 Maximum acceleration percent error (%) 4.53 4.42 7.72 10.55 1.61 9.99 2.13 9.16 Minimum camera acceleration (m/s ) −10.42 −9.90 −20.33 −15.48 −29.49 −32.30 −27.88 −40.40 Minimum sensor acceleration (m/s ) −10.54 −9.58 −18.76 −17.18 −29.00 −29.06 −28.21 −36.69 Minimum acceleration percent error (%) 4.53 3.28 7.72 10.97 1.61 9.99 2.13 9.16 Displacement (mm) 1.27 5.08 2.54 3.81 1.27 2.54 3.81 5.08 Frequency(Hz) 20 10 201535252020 r 0.92 1.00 0.99 0.99 0.98 0.94 0.99 0.98 Maximum camera acceleration (m/s ) 12.07 8.28 20.10 17.90 51.58 29.18 27.35 36.05 Maximum sensor acceleration (m/s ) 11.54 8.15 19.08 16.36 45.63 30.48 26.51 33.23 Maximum acceleration percent error (%) 4.37 4.20 5.07 7.09 11.46 4.77 3.07 7.82 Minimum camera acceleration (m/s ) −12.07 −8.29 −20.10 −18.24 −51.58 −29.18 −27.35 −36.05 Minimum sensor acceleration (m/s ) −11.54 −8.32 −19.08 −16.85 −45.63 −30.48 −26.51 −33.23 Minimum acceleration percent error (%) 4.37 5.01 5.07 7.62 11.46 4.77 3.07 7.82 There was minimal cross-talk encountered in the SPT of keeping the required calibration time minimal, the VTM (Figure 6). Cross-talk was determined by expressing the rms was not calibrated. The calibration method being devel- of theindividual axesasapercentofthe rmsofthe vibration oped is more widely applicable when using any vibration axis (mean ± SD). For the representative data presented in table alongside a calibrated optical measurement system. Figure 6, cross-talk for the translational vibration axes was Because the VTM was not calibrated, the accuracy of analog 7.7 ± 2.5%, while for the rotational vibration axes, cross-talk frequency settings and displacements were not validated. was 1.7 ± 0.6%. This is likely the reason for part of the shift between the VTM and SPT data shown in Figure 5.The VTM data (Figure 5) were determined using the manual settings 4. Discussion (peak-to-peak displacement and frequency) to determine the expected acceleration of the VTM. This is also why the The LG calibration method produced near perfect calibra- VTM data were not included in the calibration verification tions which held throughout the expected field range as process and why the VICON Motion Capture System was shown through the HG data verification (Table 5). The errors used. encountered in the LG and HG acceleration values showed The VICON motion capture system is not without issues. no apparent trends based on frequency or displacement It has been noted that any measurement error in 3-D (Table 5). The errors shown in Table 5 were based on the marker coordinates may propagate unpredictably [13]. For VICON double-differentiated accelerations as it appeared example, thedoubledifferentiation may have also introduced that the true acceleration was different than the dial settings high frequency errors which result from small errors in of the VTM (Figure 5) to introduce a phase lag between the displacement data [14]. Thedata werelow pass filteredso it VTM and the VICON and SPT accelerations. In the interest is believed any error resulting from the double differentiation 6 Advances in Acoustics and Vibration 0.1 0.1 0.1 0.08 X-axis 0.08 0.08 Y-axis Z-axis 0.06 0.06 0.06 0.04 0.04 0.04 0.02 0.02 0.02 0 0 0 −0.02 −0.02 −0.02 −0.04 −0.04 −0.04 −0.06 −0.06 −0.06 −0.08 −0.08 −0.08 −0.1 −0.1 −0.1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Time (seconds) Time (seconds) Time (seconds) (a) (b) (c) 0.6 0.6 0.6 0.4 0.4 0.4 Roll Yaw Pitch 0.2 0.2 0.2 0 0 0 −0.2 −0.2 −0.2 −0.4 −0.4 −0.4 −0.6 −0.6 −0.6 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Time (seconds) Time (seconds) Time (seconds) Pitch Pitch Pitch X-axis X-axis X-axis Roll Roll Roll Y-axis Y-axis Y-axis Z-axis Yaw Z-axis Yaw Z-axis Yaw (d) (e) (f) Figure 6: A sample of raw voltages recorded for single axis excitement with maximum and minimum translational acceleration amplitudes 2 ◦ of ±4m/s at 5 Hz or maximum and minimum angular velocity amplitudes of ±40 /s at 2 Hz; minimal cross-talk is apparent. was minimized. The calibration data determined at LGs sensors were used to quantify 6-DOF movements in the field were applied to the SPT data, and compared to the VICON of biomechanics kinematic measurements. The calibration of data with good results. It was shown in Figure 5 that the these sensors requires the use of more complex mathematics VICON and SPT accelerations are aligned, and the results than those required by the sensor and calibration procedure in Table 5 indicate that the calibration determined at the LGs presented in this paper. The method outlined in the current was successfully applied to HG accelerations. paper can be used for WBV transducer calibration, as well as The findings of this study in the HG portion compare for almost any sensor measuring translational or rotational with previous literature which found the difference between displacements, velocities, accelerations, or jerk. The method the VICON measurements and accelerometer data was less has been used successfully by our research group to quantify than 5% absolute error for displacements greater than 1 mm 6-DOF OSI and chassis accelerations in forestry skidders for frequencies between 3 and 30 Hz [11]. This error value [19, 20]. does not seem unreasonable, as they are extremely small and In addition to the ease with which this calibration can fast motions (i.e., 1 mm at 30 Hz). It is also possible that the be completed, the incorporation of the VTM for verification errors reported by Jack et al. [11] may have resulted from the allows for comparisons between the sensor and VICON double differentiation process [14]. at various frequencies and displacements that exceed the The purpose of the work was to provide a simple and PRSCO robot’s capabilities. The inclusion of a dynamic reasonably fast calibration procedure and the procedure calibration allows for more data points to be added to presented satisfied both constraints. In the future, a multiple the data set. The increased number of data points likely resolution cross-correlation technique [15] could be used to increased the accuracy of the calibration equation compared automate data alignment which would streamline the align- to a simple static calibration procedure alone. In this case, ment portion of the procedure. Other studies which have the calibration verification was quick with more emphasis utilized a robot to calibrate accelerometers have relied on placed on the relationship between the VICON double dif- complex mathematical analyses. Renk et al. [16] developed a ferentiated displacements and the SPT accelerations. The HG kinematic model which could be used by a 6-DOF robot arm data verification was included to confirm that the calibration to calibrate accelerometers. Kinematic model development determined easily at LG values did hold throughout the required detailed math, whereas the PRSCO 6-DOF robot expected field testing range. utilized in the current study requires simple sinusoidal The methods outlined in this paper required little time, equations and integration techniques. Others have reported approximately three hours for the LG and five for the HG cal- instances where 6 [17]or 9 [17, 18] linear accelerometer ibrations, including VICON Setup and calibration. The data Raw voltage (Volts) Raw voltage (Volts) Raw voltage (Volts) Raw voltage (Volts) Raw voltage (Volts) Raw voltage (Volts) Advances in Acoustics and Vibration 7 processing took approximately 15 hours. Thus, a compre- [13] L. Chiari, U. Della Croce, A. Leardini, and A. 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Whole-Body Vibration Sensor Calibration Using a Six-Degree of Freedom Robot

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Copyright © 2011 Sarah Cation et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Hindawi Publishing Corporation Advances in Acoustics and Vibration Volume 2011, Article ID 276898, 7 pages doi:10.1155/2011/276898 Research Article Whole-Body Vibration Sensor Calibration Using a Six-Degree of Freedom Robot 1 1, 2 1, 2, 3 Sarah Cation, Michele Oliver, Robert Joel Jack, 2, 4 2 James P. Dickey, and Natasha Lee Shee School of Engineering, University of Guelph, Guelph, ON, Canada N1G 2W1 Biophysics Interdepartmental Group Graduate Program, University of Guelph, Guelph, ON, Canada N1G 2W1 School of Human Kinetics, Laurentian University, Sudbury, ON, Canada P3E 2C6 School of Kinesiology, University of Western Ontario, London, ON, Canada N6A 3K7 Correspondence should be addressed to Michele Oliver, moliver@uoguelph.ca Received 23 September 2010; Revised 7 February 2011; Accepted 8 March 2011 Academic Editor: Gurvinder Virk Copyright © 2011 Sarah Cation et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Exposure to whole-body vibration (WBV) is associated with a wide variety of health disorders and as a result WBV levels are frequently assessed. Literature outlining WBV accelerations rarely address the calibration techniques and procedures used for WBV sensors to any depth, nor are any detailed information provided regarding such procedures or sensor calibration ranges. The purpose of this paper is to describe a calibration method for a 6 DOF transducer using a hexapod robot. Also described is a separate motion capture technique used to verify the calibration for acceleration values obtained which were outside the robot calibration range in order to include an acceptable calibration range for WBV environments. The sensor calibrated in this study used linear (Y = mX) calibration equations resulting in r values greater than 0.97 for maximum and minimum acceleration amplitudes of 2 ◦ up to ±8m/s and maximum and minimum velocity amplitudes up to ±100 /s. The motion capture technique verified that the translational calibrations held for accelerations up to ±4 g. Thus, the calibration procedures were shown to calibrate the sensor through the expected range for 6-DOF WBV field measurements for off-road vehicles even when subjected to shocks as a result of high speed travel over rough terrain. 1. Introduction vibration [5]. Compliance with the ISO and BS standards is recommended for reducing the risk of workplace injury. With technological advancements, the detail and complexity In contrast, the European Directive mandates that health of the measurements researchers are able to undertake has in- surveillance is compulsory for workers exposed to vibration creased. This is exemplified in the field of whole-body vibra- levels that exceed the daily exposure action values. This tion (WBV). The most recent publication of the ISO 2631-1 progression from assessment to compulsory surveillance has standard outlines the measurement of WBV in 6 degrees-of- motivated increased vibration measurements in the work- freedom (DOF), and some researchers have suggested that place. The movement to 6-DOF and 12-DOF measurements 12 DOF measurements should be performed [1]. Thus, has increased the complexity of the sensors used to measure measurements in translational axes X-, Y -, and Z-aswell WBV. as rotational axes roll, pitch, and yaw (about X-, Y -, and In some WBV environments, there may be transients (or Z-axes, resp.) are required. Exposure to excessive levels of shocks), which by definition are sudden changes in accel- whole-body vibration is associated with decreased worker erations [2]. Off-road vehicles are likely often subjected to performance and injury [2]; the vibration limits described in shocks as a result of high speeds over rough terrain [6, 7]. the International and British standards ([3] and BS 6841 [4], Based on forestry skidder WBV literature, the WBV trans- resp.) and European Directive 2002/44/EC, are important ducer is required to record peak accelerations of no less than 2 2 benchmarks for assessing human exposure to whole-body 7.08 ± 3.48 m/s [6]or noless than 3.32 ± 1.42 m/s [8]at 2 Advances in Acoustics and Vibration the operator seat interface (OSI) in the translational axes. The reported dominant frequency band was 2.5 Hz at the SPT chassis [9]. In contrast, accelerations at the OSI of up to 11.73 m/s have been reported for heavy haul dump trucks [10]. These published values have been weighted according to various versions of the ISO 2631-1 standard. Accordingly, since the ISO 2631 frequency weightings attenuate the PRSCO acceleration signals according to the sensitivity to vibration 6-DOF at various frequencies, it is therefore important to calibrate robot the WBV sensors for a larger amplitude range than reported in these papers. This should be done to ensure that there has been no underestimation of the actual recorded field accelerations which may be attenuated at certain frequencies during the weighting process. In the field of WBV, the literature outlining WBV accel- Figure 1: Experiment Setup for the low g (LG) calibration using erations rarely address the calibration technique/procedures a Parallel Robotics System Corporation (PRSCO) six-degree-of- used for WBV sensors to any depth, nor is any detailed freedom (6-DOF) robot shown here with the seat-pad transducer (SPT). information provided regarding such procedures or sensor calibration ranges. Therefore, the purpose of this paper was to describe a simple calibration method for a 6 DOF OSI transducer used for WBV measurements. Also described is a equations using a 6-DOF robot. The second phase was used separate technique used to verify the calibration for accelera- to assess the sensor calibration previously determined in the tion values obtained which were outside the robot calibration LG calibration using an expanded range of WBV values in range in order to include an acceptable calibration range for order to validate the calibration values determined in the WBV environments. LG calibration. The range consisted of the expected field range for WBV measurements of forestry skidders. The high g (HG) calibration used a vibration table and an optical 2. Methodology motion capture system. The sensor was zeroed before each axis was tested in order to eliminate orientation bias. A seat-pad transducer (SPT) used for WBV measurements at the OSI was calibrated in two phases. The first calibration phase used a 6-DOF robot to generate the calibration equa- 2.1.1. Low g (LG) Calibration. The LG calibration was com- tions for each DOF. The second phase was used to confirm pleted using a Parallel Robotics System Corporation that the robot determined calibration equations would hold (PRSCO) R2000 6-DOF robot (Parallel Robotic Systems outside of their calibrated range. This larger acceleration Corporation, Hampton, New Hampshire, USA). The PRSCO range was designed to represent the range of vibrations was calibrated by PRSCO for repeatability and accuracy observed in forestry skidders. The SPT was designed to be (within 24 µm), and accuracy (within +24/−38 µm) for compact and flat to remove pressure points as it was to be travel in the X, Y,and Z axes. Sinusoidal acceleration and used at the OSI in the field to measure WBV. The sensor was velocity profiles were created as inputs to the PRSCO. The built at the University of Guelph (Guelph, Ontario, Canada) acceleration profiles were developed to achieve acceleration using two Analog Devices (Analog Devices Inc., Norwood, amplitudes between ±1and ±8m/s for the translational Massachusetts, USA) ADXL320EB biaxial accelerometers axes (X, Y , Z) at known frequencies (Table 1)and were measuring the X, Y,and Z axes and three Analog Devices double integrated using the trapezoid rule prior to imple- ADXRS150EB rate gyroscopes to measure roll, pitch, and mentation on the robot. The profiles were integrated into yaw. The ADXL320EB accelerometers were rated for ±5g displacement form as the robot requires displacement inputs. (±10%) and the ADXRS150EB gyroscopes were capable For pitch, roll, and yaw, a single integration was required, of recording ±150 /s velocities. The accelerometers and since the sensors for these axes monitor angular velocity. gyroscopes were mounted to evaluation boards to simplify Angular velocity profiles ranged between ±10 and ±100 /s mechanical attachment, relative alignment and wiring. The at frequencies between 0.5 and 5 Hz as shown in Table 2. accelerometers and rate gyroscopes were orthogonally placed The sensors were placed in the centre of the PRSCO 6DOF in a Delrin plastic casing to monitor the roll, pitch, and yaw robot platform which reproduced the known displacement axes. For both calibration phases, a 12-bit SOMAT Series profiles. The sensors were oriented such that the axis of 2001 Field computer (nCode International Inc., Southfield, interest was aligned such that the PRSCO robot would Michigan, USA) collected raw device voltages at a sampling have the largest movement displacement allowing higher rate of 500 Hz. accelerations and angular velocities to be produced. The experimental Setup is shown in Figure 1. 2.1. Experiment Setup. The first phase was the low g (LG) cal- ibration (maximum and minimum amplitude values of: ±1 2.1.2. High g (HG) Calibration. The LG calibration cali- 2 ◦ ◦ to ±8m/s and ±10 to ±100 /s) to determine the calibration brated up to ±100 /s, which exceeded the expected field Advances in Acoustics and Vibration 3 Table 1: The sinusoidal minimum and maximum linear acceleration amplitudes and corresponding frequencies used to calibrate the translational (X, Y , Z) accelerometers using displacement profiles on a Parallel Robotics System Corporation Robot six-degree-of-freedom robot. Acceleration (m/s ) ±1 ±2 ±3 ±4 ±5 ±6 ±7 ±8 Frequency (Hz) 1,2,5 1, 2, 5 2,5 2, 5 2,5 2, 5 2,5 2, 5 Table 2: The sinusoidal minimum and maximum angular velocity amplitudes and corresponding frequencies used to calibrate the gyroscopes (roll, pitch, yaw) using displacement profiles on a Parallel Robotics System Corporation Robot six-degree-of-freedom robot. Velocity ( /s) ±10 ±20 ±30 ±40 ±60 ±80 ±100 Frequency (Hz) 0.5, 1, 2, 5 0.5, 1, 2, 5 0.5, 1, 2, 5 0.5, 1, 2, 5 0.5, 1, 2, 5 0.5, 1, 2, 5 0.5, 1, 2 Frequency Sensor axis indicator being tested Vibration table movement Reflective markers used for motion Z-axis Sensor Analog Motor frequency setting dial Displacement Figure 2: Sensor axis orientation and vibration direction for the setting high g calibration verification. requirements for the gyroscopes, but did not encompass Figure 3: The experimental Setup for the high g (HG) calibration the entire expected field requirements for the accelerome- verification. ters. Thus, a second stage was completed to calibrate the accelerometers up to and including approximately ±4g min- imum and maximum acceleration amplitudes at frequencies Table 3: The peak-to-peak displacements and frequency settings between 10 and 35 Hz. used for the high g calibration verification and resulting ± approxi- An All American vibration fatigue testing machine mate peak acceleration amplitude values. (VTM) (All American Tool & Mfg. Co., Illinois, USA) was used to calibrate at HGs. This vibration machine is only able Peak-to-peak displacement Frequency Approximate (mm) (Hz) acceleration (g) to move in the Z-axis, thus the axis being tested was oriented with respect to the Z axis for each of the accelerometer 5.08 10 1.02 axes as shown in Figure 2. The SPT movement on the 1.27 20 1.01 VTM was recorded using three VICON M m cameras from 3.81 15 1.72 a VICON 460 Motion Capture System (VICON Motion 2.54 20 2.03 Systems, Centennial, CO, USA) and simultaneous data 3.81 20 3.04 were recorded from the SPT. The experimental Setup is 2.54 25 3.17 shown in Figure 3. The various accelerations were tested by 1.27 35 3.08 changing the VTM using an analog frequency setting dial (between approximately 10 Hz and 35 Hz) and peak-to- 5.08 20 4.06 peak displacements (between approximately 1.27 mm to 5.08 mm) outlined in Table 3. The accelerations tested for HG calibration verification included and exceeded the accelerations determined at the LG accelerations which were tape such that all M m cameras had full view of the markers. used to generate the calibration equations. The VICON 460 The cameras were oriented in an umbrella fashion (Figure 4) M m cameras were previously validated for vibration mea- oftenused ingait analysis [12]. The cameras recorded the surements of displacements greater than 1 mm to contain X, Y,and Z lab coordinates of the reflective markers for less than 5% error for frequencies between 3 and 30 Hz each trial and were sampled at 500 Hz for 10 seconds. The [11]. VICON system was calibrated statically and dynamically Four, 14 mm diameter spherical reflective markers were in the measurement volume to minimize error due to the adhered to the sensor/vibration table using double-sided optical distortion phenomena [13]. The calibration residuals 4 Advances in Acoustics and Vibration Table 4: Calibration equations for the seat-pad transducer devel- Camera no. 1 oped using a low g acceleration values where Y = mX + b;slope values m are tabulated, Y refers to the calibrated output and X refers to the recorded voltage. Camera no. 2 Axis Calibration equation Unit of measurement XY =−52.02X m/s VTM table YY =−52.18X m/s ZY = 51.13X m/s Roll Y = 81.47X /s Pitch Y =−84.34X /s Camera no. 3 Yaw Y = 79.22X /s Figure 4: The umbrella camera orientation. (error) were less than 1 mm during the calibration of the VICON motion capture system. 2.2. Data Analysis −5 2.2.1. Calibration at Low g Values. The raw dynamic cal- −10 ibration data from the SPT were then second-order low pass Butterworth filtered at a cut-off frequency of 10 Hz −15 (two times the highest expected signal frequency of 5 Hz −20 as shown in Tables 1 and 2) such that the Nyquist rate 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 was exceeded. The acceleration and velocity known input Time (seconds) profiles were then aligned with the sensor voltage output for the translational and rotational axes, respectively. The SPT calibration equations were determined for each sensor and VICON VTM each axis independently. The calibration equations were determined to be of the form Y = mX for all 6-DOF for the Figure 5: The expected acceleration profile is shown (VTM) along- SPT, where Y refers to the calibrated output and X refers to side the accelerations determined using the seat-pad transducer the recorded voltage. The zero offset values are not presented, (SPT) and VICON for a high g test with a peak-to-peak displace- since they are easily identified and calculated from the resting ment of 3.81 mm and frequency setting of 15 Hz. transducer voltages. 2.2.2. Translational Acceleration Data Validation at High g 3. Results (HG) Values. The sensor voltages and raw digitized VICON 3D coordinates were second-order zero lag low pass But- The SPT calibration equations are shown in Table 4.The cal- terworth filtered at a cut-off frequency of two times the ibration equations fit the LG calibration data with r values frequency set on the VTM. The calibrations determined from of greater than 0.997 in all 6-DOF. When the LG calibration the LG calibration were applied to the filtered sensor voltages equations were applied to HG data and compared to VICON and then compared to the double-differentiated, filtered determined accelerations, the accuracy of the sensor was VICON displacement data for the three translational axes (X, shown to generally produce less than 10% error. The largest Y , Z). Five individual cycles of double-differentiated VICON error between the VICON and the system gold standard displacement data and sensor data were manually aligned SPT data was approximately 12% (under 6 m/s ). This error using peak acceleration values. Maximum and minimum was less than 12% at both the maximum and minimum acceleration amplitudes as well as r values were determined peaks. For the largest acceleration values, the SPT recorded from the VICON and SPT data for five individual cycles acceleration amplitudes of approximately ±45.63 m/s and 2 2 at each VTM setting outlined in Table 3. In addition, VICON predicted accelerations of±51.58 m/s .The r values the corresponding percent error was determined for the exceeded 0.9 in all translational axes at all acceleration levels difference between the sensor maximum and minimum tested at the HG levels as shown in Table 5. acceleration amplitude and VICON maximum and mini- The effects of using VICON in addition to the known mum acceleration amplitude, where the VICON data were VTM settings were visually assessed, an example of which is taken to be the gold standard. The overall average (n = 5) showninFigure 5. As can be seen in the figure, there is a shift was reported using the five single cycle values. This was between the VTM and the SPT which is not constant over completed for each of the VTM settings listed in Table 3. time. In contrast, the SPT and VICON data are well aligned. Acceleration (m/s ) Advances in Acoustics and Vibration 5 Table 5: Results of high g acceleration data verification for the seat-operator interface (SPT) transducer for the X, Y,and Z axes at various displacement and frequency settings. The reported accelerations are maximum and minimum amplitudes while the displacements are peak- to-peak values. Displacement (mm) 1.27 5.08 2.54 3.81 1.27 2.54 3.81 5.08 Frequency(Hz) 20 10 201535252020 r 0.97 0.98 0.95 0.96 0.92 0.97 0.95 0.98 Maximum camera acceleration (m/s ) 11.48 8.40 17.65 15.74 28.80 25.23 25.82 39.79 Maximum sensor acceleration (m/s ) 10.37 8.74 16.93 15.93 28.96 25.09 26.75 39.17 Maximum acceleration percent error (%) 9.61 4.01 4.01 3.21 3.81 2.62 3.62 2.95 Minimum camera acceleration (m/s ) −11.48 −8.40 −17.65 −16.44 −28.80 −25.23 −25.82 −40.73 Minimum sensor acceleration (m/s ) −10.37 −9.05 −16.93 −16.02 −28.96 −25.09 −26.50 −39.17 Minimum acceleration percent error (%) 9.61 7.77 4.01 2.54 3.81 2.62 3.30 3.77 Displacement (mm) 1.27 5.08 2.54 3.81 1.27 2.54 3.81 5.08 Frequency(Hz) 20 10 201535252020 r 0.98 0.99 0.92 0.96 0.95 0.96 0.98 0.99 Maximum camera acceleration (m/s ) 10.42 9.90 20.33 15.38 29.49 32.30 27.88 40.40 Maximum sensor acceleration (m/s ) 10.54 9.47 18.76 17.00 29.00 29.06 28.21 36.69 Maximum acceleration percent error (%) 4.53 4.42 7.72 10.55 1.61 9.99 2.13 9.16 Minimum camera acceleration (m/s ) −10.42 −9.90 −20.33 −15.48 −29.49 −32.30 −27.88 −40.40 Minimum sensor acceleration (m/s ) −10.54 −9.58 −18.76 −17.18 −29.00 −29.06 −28.21 −36.69 Minimum acceleration percent error (%) 4.53 3.28 7.72 10.97 1.61 9.99 2.13 9.16 Displacement (mm) 1.27 5.08 2.54 3.81 1.27 2.54 3.81 5.08 Frequency(Hz) 20 10 201535252020 r 0.92 1.00 0.99 0.99 0.98 0.94 0.99 0.98 Maximum camera acceleration (m/s ) 12.07 8.28 20.10 17.90 51.58 29.18 27.35 36.05 Maximum sensor acceleration (m/s ) 11.54 8.15 19.08 16.36 45.63 30.48 26.51 33.23 Maximum acceleration percent error (%) 4.37 4.20 5.07 7.09 11.46 4.77 3.07 7.82 Minimum camera acceleration (m/s ) −12.07 −8.29 −20.10 −18.24 −51.58 −29.18 −27.35 −36.05 Minimum sensor acceleration (m/s ) −11.54 −8.32 −19.08 −16.85 −45.63 −30.48 −26.51 −33.23 Minimum acceleration percent error (%) 4.37 5.01 5.07 7.62 11.46 4.77 3.07 7.82 There was minimal cross-talk encountered in the SPT of keeping the required calibration time minimal, the VTM (Figure 6). Cross-talk was determined by expressing the rms was not calibrated. The calibration method being devel- of theindividual axesasapercentofthe rmsofthe vibration oped is more widely applicable when using any vibration axis (mean ± SD). For the representative data presented in table alongside a calibrated optical measurement system. Figure 6, cross-talk for the translational vibration axes was Because the VTM was not calibrated, the accuracy of analog 7.7 ± 2.5%, while for the rotational vibration axes, cross-talk frequency settings and displacements were not validated. was 1.7 ± 0.6%. This is likely the reason for part of the shift between the VTM and SPT data shown in Figure 5.The VTM data (Figure 5) were determined using the manual settings 4. Discussion (peak-to-peak displacement and frequency) to determine the expected acceleration of the VTM. This is also why the The LG calibration method produced near perfect calibra- VTM data were not included in the calibration verification tions which held throughout the expected field range as process and why the VICON Motion Capture System was shown through the HG data verification (Table 5). The errors used. encountered in the LG and HG acceleration values showed The VICON motion capture system is not without issues. no apparent trends based on frequency or displacement It has been noted that any measurement error in 3-D (Table 5). The errors shown in Table 5 were based on the marker coordinates may propagate unpredictably [13]. For VICON double-differentiated accelerations as it appeared example, thedoubledifferentiation may have also introduced that the true acceleration was different than the dial settings high frequency errors which result from small errors in of the VTM (Figure 5) to introduce a phase lag between the displacement data [14]. Thedata werelow pass filteredso it VTM and the VICON and SPT accelerations. In the interest is believed any error resulting from the double differentiation 6 Advances in Acoustics and Vibration 0.1 0.1 0.1 0.08 X-axis 0.08 0.08 Y-axis Z-axis 0.06 0.06 0.06 0.04 0.04 0.04 0.02 0.02 0.02 0 0 0 −0.02 −0.02 −0.02 −0.04 −0.04 −0.04 −0.06 −0.06 −0.06 −0.08 −0.08 −0.08 −0.1 −0.1 −0.1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Time (seconds) Time (seconds) Time (seconds) (a) (b) (c) 0.6 0.6 0.6 0.4 0.4 0.4 Roll Yaw Pitch 0.2 0.2 0.2 0 0 0 −0.2 −0.2 −0.2 −0.4 −0.4 −0.4 −0.6 −0.6 −0.6 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Time (seconds) Time (seconds) Time (seconds) Pitch Pitch Pitch X-axis X-axis X-axis Roll Roll Roll Y-axis Y-axis Y-axis Z-axis Yaw Z-axis Yaw Z-axis Yaw (d) (e) (f) Figure 6: A sample of raw voltages recorded for single axis excitement with maximum and minimum translational acceleration amplitudes 2 ◦ of ±4m/s at 5 Hz or maximum and minimum angular velocity amplitudes of ±40 /s at 2 Hz; minimal cross-talk is apparent. was minimized. The calibration data determined at LGs sensors were used to quantify 6-DOF movements in the field were applied to the SPT data, and compared to the VICON of biomechanics kinematic measurements. The calibration of data with good results. It was shown in Figure 5 that the these sensors requires the use of more complex mathematics VICON and SPT accelerations are aligned, and the results than those required by the sensor and calibration procedure in Table 5 indicate that the calibration determined at the LGs presented in this paper. The method outlined in the current was successfully applied to HG accelerations. paper can be used for WBV transducer calibration, as well as The findings of this study in the HG portion compare for almost any sensor measuring translational or rotational with previous literature which found the difference between displacements, velocities, accelerations, or jerk. The method the VICON measurements and accelerometer data was less has been used successfully by our research group to quantify than 5% absolute error for displacements greater than 1 mm 6-DOF OSI and chassis accelerations in forestry skidders for frequencies between 3 and 30 Hz [11]. This error value [19, 20]. does not seem unreasonable, as they are extremely small and In addition to the ease with which this calibration can fast motions (i.e., 1 mm at 30 Hz). It is also possible that the be completed, the incorporation of the VTM for verification errors reported by Jack et al. [11] may have resulted from the allows for comparisons between the sensor and VICON double differentiation process [14]. at various frequencies and displacements that exceed the The purpose of the work was to provide a simple and PRSCO robot’s capabilities. The inclusion of a dynamic reasonably fast calibration procedure and the procedure calibration allows for more data points to be added to presented satisfied both constraints. In the future, a multiple the data set. The increased number of data points likely resolution cross-correlation technique [15] could be used to increased the accuracy of the calibration equation compared automate data alignment which would streamline the align- to a simple static calibration procedure alone. In this case, ment portion of the procedure. Other studies which have the calibration verification was quick with more emphasis utilized a robot to calibrate accelerometers have relied on placed on the relationship between the VICON double dif- complex mathematical analyses. Renk et al. [16] developed a ferentiated displacements and the SPT accelerations. The HG kinematic model which could be used by a 6-DOF robot arm data verification was included to confirm that the calibration to calibrate accelerometers. Kinematic model development determined easily at LG values did hold throughout the required detailed math, whereas the PRSCO 6-DOF robot expected field testing range. utilized in the current study requires simple sinusoidal The methods outlined in this paper required little time, equations and integration techniques. Others have reported approximately three hours for the LG and five for the HG cal- instances where 6 [17]or 9 [17, 18] linear accelerometer ibrations, including VICON Setup and calibration. The data Raw voltage (Volts) Raw voltage (Volts) Raw voltage (Volts) Raw voltage (Volts) Raw voltage (Volts) Raw voltage (Volts) Advances in Acoustics and Vibration 7 processing took approximately 15 hours. Thus, a compre- [13] L. Chiari, U. Della Croce, A. Leardini, and A. Cappozzo, “Human movement analysis using stereophotogrammetry— hensive calibration using a wide range of accelerations and part 2: instrumental errors,” Gait and Posture, vol. 21, no. 2, angular rotations for a 6-DOF motion sensor may be per- pp. 197–211, 2005. formed in a reasonable amount of time by using the methods [14] G. E. Robertson and G. E. Caldwell, “Planar kinematics,” in outlined in this paper. Research Methods in Biomechanics,G.E. Robertson,G. E. Caldwell, J. Hamill, G. Kamen, and S. N. Whittlesey, Eds., 5. Conclusions Human Kinetics, Windsor, Canada, 2004. [15] R. J. Jack,M.Oliver, R. Dony, and J. P. Dickey, “The use This study described a method for calibrating multi-DOF of multiple resolution cross-correlations to align simultane- sensors. 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