Mine Countermeasures Technology (1993)

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10. By adjusting the gain on the Strain Analyzer, the pen on the Brush Recorder linear acceleration channel, was set to a convenient deflection equivalent to 6.) ft. per second’, completing the static calibration of the linear accelerometer. Static Calibration — Angular Accelerometer: = A similar procedure was followed to calibrate the angular accelerometer (composed of the two type AP linear accelerometers) except that the wiring was connected so that the outputs were additive. (The basic circuit for this case is shown in Fig. 2<a and the actual bridge in Fig. 3<b). Upon invert- ing, the bridge was thrown out of balance by an amount corresponding to hg or 128.8 ft./second’ linear acceleration. For a distance between the sensitive axes of 10 in. this combined linear acceleration is equivalent tos: 128.8 £t./second = 151.6 rad/second” angular acceleration. 10 Once the pen deflection on the Brush Recorder angular acceleration channel was set to a convenient value equivalent to 15),.6 rad/second“, the angular accelerometer static calibration was complete. Dynamic Calibration: =- Supplementary tests were made to test the reliability of the static calibration procedure. A short, stiff beam with one end secured in a fixed pivot and the other end connected with @ pivot to the vibrating table was designed to transfer the linear vertical acceleration of the table top to an angular acceleration, the magnitude of which could be easily calculated for a particular table frequency and displacernient. The type AP accelerometers were bolted to this oscillating beam. Details of this arrangement are shown in Fig. h. Inasmich as resonance effects of the rotating beam might contaminate the record, it was necessary to again establish the upper limiting frequency of the flat response range when the beam was included in the system. For this purpose the accelerometers were wired to subtract outputs. A table displacement equal to 0.123 in. was used and the table frequency varied between 10 cps and approximately 36 cps. The resulting plot of system output vs frequency squared is shown in Fig. 5=b.

It can be seen that in this case, flat response was realized up to a frequency of approximately 1,00 = 20 cps. This was lower than in the case where the accelerometers were mounted directly on the table because above a frequency of 20 cps the forced vibration of the beam increased the linear acceleration imposed by the table motion on the points of the beam at which the accelerometers were mounted. This caused peak pen deflections higher than those that would occur if the beam were rigid. Therefore, the dynamic calibrations runs were made at frequencies not far in excess of 20 cps. Iwo dynamic calibrations runs were made, one at a table frequency of 10.2 cps and one at 21.); cps. For each run the frequency was maintained at a constant value and the total table displacement varied from approximately 0.01 in. to approximately 0.125 ine At each displacement setting a test run was made and the record obtained on the Brush Recorder. The amplitude of the sinusoidal record was plotted against the corresponding value of angular acceleration, a plot being made for each of the two frequencies. Each point on the plot represented a run at a particular table displacement, and hence at a particular angular acceleration. These plots are shown in Fige 6—a and 6<b. The angular calibration constant in radians per second per mm pen deflection was given by the slope of the best straight line drawn through the test points. The "best" straight line was determined by the method of least squares. Table I below shows the value of the calibration constants obtained from Fig. 6. Also shown is the constant obtained by static calibration procedure explained earlier in this report. The. variation in the average dynamic calibration constant and the static calibration constant was less than 1 percent.

TABLE I COMPARISON OF STATIC AND DYNAMIC CALIBRATION Angular Acceleration | Calibration Procedure Calibration Constant Rad/Sec“/mm Dynamic Calibration-f=#10.22cps 2203 Dynamic Calibration-f=21.licps 21h Average Dynamic Calibration 21.8 One Point Static Calibration 217 Although the above comparison was made for angular acceleration only, it was considered valid for linear acceleration inasmuch as the measured quantities involved were actually differences of the outputs of two linear accelerometers, In view of the agreement obtained in this comparison, the static calibration procedure was judged to be entirely satisfactory for both the angular and linear accelero- meters provided that no changes in the measuring and recording system are made subsequent to an initial dynamic calibration check. Accuracy An exact determination of the accuracy of the measuring and recording system is difficult for two reasons. The first is that the accuracy may vary depending on the instantaneous magnitude and frequency of the phenomenon being measured and the second is that it is difficult to establish some standard against which to check. For these reasons the following estimate of errors can only be considered approximate e

136 The quantitative use of the system output depends upon the value of an experimental calibration constant. Any error present in this calibration constant will be reflected as a systematic error in the final result. Accidental errors due to non-uniformity in system response and to the human error in reading the record may also be presente As previously explained, the difference in the calibration constants obtained by two independent methods (static calibration and average dynamic calibration) was less than one percent. Therefore the maximum systematic error was estimated as one percent of the required amplitude. A good estimate of the accidental errors present can be made by examining the agreement between the actual measured output at various values of input and the most probable correct output determined by the "best" straight line through the test points. The test run considered in making this comparison was the angular accelerometer dynamic calibration at a frequency of 21.) cps (Fig. 6—b). This run was used because the maximum angular acceleration (80.1 radians per second’) was near the maximum required amplitude of + 100 radians per second”. The most probable true output for an input of 100 radians per second’ was determined on Fig. 6—b by the intersection of the "best" straight line and an abscissa of 100 radians per second’. The percent error of each test point was determined by the difference in the ordinates of the test point and the best straight line compared to the most probable true output for an input of 100 radians per second’. Each percentage was considered the probable accidental error of the test point. On this basis, the maximum accidental error in the angular acceleration record was )\.28 percent of the required amplitude and the average accidental error was 1.79 percent. The estimated value of the total error possible in the angular acceleration record was }.28 percent (accidental) +1.00 percent (systematic) = 5.28, or not over 6 percent of the required amplitude. This figure was also considered indicative of the error to be expected in the linear acceleration record.

Use of Equipment to Obtain Shank Accelerations The foregoing laboratory tests were conducted to determine the characteristic properties of the equipment as a distinct méasuring and recording "unit" to insure that initially specified requirements were met. Test runs were then made to test the adaptability of the Nunit" to the particular application at hand. This section of the report deals with the manner in which the equipment was used, the salient features of the runs, the significance of the information obtained, and the time required for data reduction. Attachment of Accelerometers to Shank The angular accelerometer (consisting of two type AP linear accelerometers ) and the model C linear accelerometer were rigidly bolted to a mounting bracket constructed of thin aluminum sheet metal. This assembly is shown in Fig. 7-ae The position of the model C accelerometer along the length of the bracket and its inclination with respect to the front face of the bracket was adjustable, as shown. Following the calibration procedure (outlined earlier in the report), the entire assembly was securely fastened to the shank with adhesive tape. Where needed to secure a proper seating, felt padding was placed between the mounting bracket and the shank. The assembly was seated so that the linear accelerometer sensitive axis intersected the center of gravity of the combined shank, foot, and shoe, and was normal to a line through the knee joint and the center of gravity. The assembly in place is shown in Fige 7—b. The total weight of the mounting assembly was 12 ouncese The effect of this additional weight on the shank motion pattern was believed to be negligible. During the test runs, the shielded cables from the accelerometers to the Strain Analyzers were carefully tended by an assistant and the disturbance to the normal walking pattern caused by these cables was believed to be small. Probably a more serious disturbing effect was that due to the possible difference in system frequency response when the accelerometers were mounted on the shank from that determined when the accelerometers

15. were mounted on the vibrating ‘able. Since system frequency response partially depends upon the manner in which the accelerometers are mounted, it should ideally be determined with the accelerometers mounted on the considered body exactly as they are to be mounted later. In this case, however, the possible error due to variation of frequency response with the manner of mounting had to be accepted as there was no feasible way to make the ideal frequency response determination. The error is difficult to evaluate and no attempt was made to do so. The opinion of the investigators was that, although this error may have been present, the effect on major conclusions drawn from the test records was small and for the purpose of this investigation could be discarded. Typical Test Run Procedure The static calibration described earlier was made just prior to the test runs and repeated at the conclusion of the runs to insure a consistant calibration. When the mounting system had been secured in place, the shank was positioned until the sensitive axis of the model C accelerometer was horizontal. The linear acceleration circuit was then balanced to zero output. The leads on the angular acceleration circuit were arranged so that the type AP accelerometers subtracted and this circuit was then balanced to zero output. The subject took a position at one end of the walkway and commenced to walk. The recorder was then switched on and continuous records of angular and linear acceleration obtained. The shielded cables were carefully tended during the test run. In this mamner a record of three of four steps was usually obtained depending upon the distance the subject travelled and the points where the recorder was switched on and then off. Figure 8 shows a typical test run. interpretation of Test Records A typical record for swing phase of one step is shown in Fig. 9. The prosthetic shank angular acceleration and the shank center of gravity apparent linear acceleration are shown for a right AK subject

walking level at normal cadencee The advantage of the Brush Recorder can be demonstrated by noting on Fig. 9 the ease and speed of reading and interpreting the test record. for instance, the peak values of angular acceleration and apparent linear acceleration are -110 and +170 radians per second’ and -2h and +2 ft. per second- » respectively. Also, the general shape of the curve is immediately seen as well as the sharp breaks in the curve corresponding to the points where the prosthesis heel struck the walkway. Another advantage to this type of record is that comparison between several steps of one run can be immediately made and irregular- ities noted. The most representative step can then be singled out for further study and can at the same time be compared with other steps of the rune The possibility of incorrectly generalizing the behavior of the entire run on the basis of one non-standard step is therefore slight. It mst be pointed out that the accelerometer records in themselves provide no way to make the + g sin 9 correction to the apparent linear accelerations If the true linear acceleration is required, simultan— eous motion pictures must be taken and synchronized by a timing device to the accelerometer record in order to obtain the instantaneous value of the inclination angle, 9. ‘this procedure also allows the toe off and heel contact points to be checked against the motion picture record. In one instaice of the shank acceleration study, however, the linear acceleration quantity desired was not the true linear acceleration but the quantity (a, + g sin 6). In this case the linear acceleration record provided the desired quantity directly, and motion pictures to obtain shank inclination were unnecessary. #* It is theoretically possible to make this correction if the output of each of the three accelerometers is recorded separately. There are pratical difficulties involved, however, and at the present time this system has not been attempted.

lie Time Required for Data Reduction The angular acceleration record requires no reduction except possibly to transfer the curve to a standard sheet of graph paper. This operation requires a negligible expenditure of time. If apparent linear acceleration only is desired, the linear acceleration record can be handled in the same manner as the angular acceleration record. If true linear accelerations are required, the linear acceleration record reduction requires two man hours once the developed motion picture film is available.

18. Comparison of Accelerometer and Grapho-Numerical Differentiation Methods General Comparison As a result of a separate study, a method for determining angular and linear accelerations from motion picture time-displace- ment data has been developed which is more reliable than other differentiation procedures. This procedure has been named the "Grapho=Numerical® method. } A general comparison between the grapho-numerical and accelerometer methods of determining acceleration is presented in Table II. This comparison was made on the basis of the grapho-mumerical procedure applied to motion picture time-displacement data. As the grapho- mumerical "method" is a differentiation procedure, its use is not confined to determination of acceleration. The method may be applied to any experimental curve, irregardless of how the basic data is obtained, in order to obtain derivitives. Also, when motion picture data is used, useful information other than desired accelerations is providede These advantages of the grapho=numerical method are not shown in Table II because they are aside from the acceleration determination problem. The following examples are presented to illustrate situations in which each of the two methods may be used to advantage. Ener gy Studies in Human locomotion The Prosthetic Devices Research Project has conducted experimental studies of the energy transfers occuring in the lover extremity during locomotion. In addition to force plate data, these studies involve angular and linear displacements, angular and linear accelerations, % E. 0. Felkel, "Determination of Accelerations from Displacement- Time Data," Prosthetic Devices Research Project, I.li.Rk., University of California, Report Series 11, Issue 16, September 1951.

19. and angular velocity, all as functions of time. ‘furthermore, these quantities are required for the foot, shank, and thigh. Extreme accuracy in the kinematic data is unnecessary because other errors of considerable magnitude are present. On the other hand, the locations in the walking cycle of the heel contact and toe-off points are desired, Accelerometers could be used to provide angular accelerations and true linear accelerations if the ¢ g sin 6 correction is made. Because these quantities must be obtained for the foot, shank and thigh the required number of accelerometers is too great to make the method practical. Motion picture data and grapho=numerical differentiation, however, provide all the necessary kinematic quantities with sufficient accuracy as well as the heel contact and toe-off points. Therefore, this method is used for this type of analysis e Performance Evaluation of Prosthetic Knee Joint Mechanisms During owing Phase Suggested methods for evaluating the performance of a knee joint mechanism during swing phase include correlation of the mechanism operation to the knee moment or, possibly, to the shank angular acceleration pattern. During swing phase, the knee moment depends on the shank angular acceleration and the apparent linear acceleration of the center of gravity of the combined shank, foot and shoe in a direction perpendicular to a line betweeen the knee joint and the center of gravity. The accelerometer assembly described in Part II of this report provides these quantities directly. The £ g sin 0 correction is unnecessary and no data reduction aside from the knee moment computation is required. If the shank angular acceleration pattern is accepted as one evaluation criteria, the knee moment computation is eliminated. In either case the effect of adjustments in the mechanism may be immediately observed on the Brush record. For purposes of evaluation the toe-off and heel contact points can probably be estimated with fair accuracy or they may be accurately determined by a foot contact device feeding an event marker on the pen and ink record.