Linear Pendulum Rangefinder for Education By
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1. 5 56 instruction cycles goto TTT on last instruction additional cycle here so 16 89 56 cycles Output2 movf TimerC1 W movwf WL move counter 1 value to WL registar movf TimerC2 W movwf WH move counter 2 value to WH registar call Bin2BCD movlw 5 call BCD2TCL movlw n call TxByte ready for new data goto Timer loop to timer end of mode two END return for ending purposes 1 3 User Manual 1 load the program into the Picboard 2 Select a mode of operation Switch 2 selects mode 2 any other button selects mode 1 3 If mode one is selected press the reset button when the desired amount of trials are conducted and or before the upper limit of trials is reached 4 If mode 2 selected hold down button 2 until desired time period is achieved then release button 2 5 Press button 2 again and repeat instruction 4 to conduct another trial Press the reset button when the desired amount of trials have been conducted Device best operated within 30 degrees operational range 2 400cm For best performance an object of area at least 0 5m not made of an acoustically absorbent material should be used for detection Taken from Cytron Technologies HC SRO4 User s_ Manual 12 1 4 Device Properties and Limitations When tested on a reasonably sized object a picboard the operational range of the rangefinder is greatly reduced An object of similar size to a picboard should surpass no more than 50cm from the rang2. Figure 1 4 2 PlCLab Output Data at 30cm eos Son Sew sa The time resolution of the device in the distance measuring mode is variable and may be approximated by 38 75ms 5 8us distance The constant term is due to the wait function applied at the beginning of the program The variable term is the time required to count to a specific distance This gives a minimum time resolution of about 38 9ms and a maximum of 0 419s 14 It should be noted that the maximum distance time and trial values which may be obtained is 2 1 However for the applicational purposes of the device these values would never be obtained In practice the distance values should never surpass 4m and 9999 trials is sufficient for any sized pendulum or oscillator The accuracy and precision of mode 2 the timing mode is not determinable due to the dependance of a human input pressing and releasing the button Thus it is not viable to use the measurements obtained for qualitative purposes The feature was included only to show the independance of period from amplitude for the linear pendulum i e to be able to change the amplitude in the same data set To calculate the actual period it is advised that one uses mode 1 to acquire distance data and utilize a graphing program capable of fitting functions to data e g Physica 1 5 Pendulum Demo The equation of a linear pendulum x t A sin wt C is only applied for linear pendulums For the purpo
3. Introduction 2 5 1 2 The Program 6 12 1 3 User s Manual wl2 1 4 Device Propoties and Limitations 13 15 1 5 Pendulum Demo 15 16 1 6 References 16 1 1 Introduction The sensor used in the project is a HC SR04 Ultrasonic rangefinder The device operates by emitting a bundle of ultrasonic pulses from an emitting device This is done by setting the trigger high for a certain amount of time 20us was used in this project Then upon receiving the bundle of pulses in the receiving device the sensor outputs a high signal on the echo output The duration of the signal is equal to the time between the emission of the bundle and the reception of said bundle From this one can determine the distance by using a calibrated counter In this project the counter is calibrated to cycle ever 5 8us This gives the distance in millimeters A timing diagram is shown below in figure 1 1 0 Figure 1 1 0 HC SR04 Timing Diagram Initiate Echo back 10uS TTL to signal pin pulse width corresponds to distance about 150uS 25ms 38ms if no obstacle Signal Formula pulse width uS 58 distance cm puise width uS 148 distance inch Internal Ultrasonic Transducer will issue 8 40kHz pulse Taken from Cytron Technologies HC SR04 User s_Manual The purpose of the device constructed in this project is to model the SHM of a linear pendulum The device produced can model the position x t of a pendulum or spring oscillator by provid
4. incf ECount1 increment LSD counter btfsc STATUS Z if LSD 0 increment MSD counter incf ECount2 MSD counter movf ECount1 W iorwf ECount2 W Test for 0 state btfsc STATUS Z goto END end if 0 state decfsz EHold goto EWait for delay nop btfss PORTE ECHO Test if Echo is high skip if yes goto Output go to output if ECHO is low goto Echo go to counter function Echo if Echo input is high Output movf ECount1 W movwf WL move counter 1 value to WL register movf ECount2 W movwf WH move counter 2 value to WH register call Bin2BCD movlw 5 call BCD2TCL movlw n call TxByte new line output ready for new trial goto Trigger loop to trial counter end of mode 1 mode 2 Timer call Getkey test to see if 2 is pressed sublw 2 btfss STATUS Z goto Timer clrf TimerC1 clearing counters of data clrf TimerC2 This is a repeat of the above distance counter bsf PORTE TRIG Set trigger output high movliw 32 Delay device movwf THold TWW decfsz THold to delay signal deactivation goto clrf clrf bcf TWW ECount1 clear counters ECount2 PORTE TRIG Set trigger output low total execution time between bsf and bcf is 10us so x 10000 5 200 200 3 15 For Echo we want distance to be in reasonable units As distance 340 2 t if we want dist in mm then t 5 8823us therefore we want Echo clock to take 5880ns per cycle but cycles only in intervals of 200ns
5. so 5800ns DLAY moviw 3 movwf EHold DELAY 1 decfsz EHold goto DELAY1 btfss PPORTE ECHO Test if high goto DLAY Echo1 movlw 5 For delay movwf EHold to store delay value nop incf ECount1 incriment LSD counter btfsc STATUS Z if LSD 0 incriment incf ECount2 MSD counter movf ECount1 W 10 EWait1 iorwf ECount2 W Test for 0 state btfsc STATUS Z goto END error if 0 state decfsz EHold goto EWait1 for delay nop btfss PORTE ECHO Test if Echo is high skip if yes goto Output1 go to output if ECHO is set goto Echo1 go to counter function Echo if ECHO is low 14 Output1 movf ECount1 W TTT movwf WL move counter 1 value to WL register movf ECount2 W movwf WH move counter 2 value to WH register call Bin2BCD movlw 5 call BCD2TCL movlw 0x20 call TxByte move amplitude to graphing output goto TIT call Getkey test to see if 2 is released stop counter if 2 released sublw 7 btfsc STATUS Z goto Output2 if yes output time incf TimerC1 incriment LSD counter 6 btfsc STATUS Z if LSD 0 incriment incf TimerC2 MSD counter movf TimerC1 W iorwf TimerC2 W Test for 0 state btfsc STATUS Z goto END error if 0 state nop for time delay movlw 89 movwf THold 15 instruction cycles We want nice time units 1ms 16 89 56 200ns 5 200 us 1ms TW TWT movlw 17 movwf EHold decfsz EHold goto TWT 11 nop for missing goto cycle decfsz THold goto TW one TW loop is 17 3
6. G73rE e dit pli 1 Georgia State University HyperPhysics Mechanics Periodic Motion http hyperphysics phy astr gsu edu hbase permot html permot 16
7. Linear Pendulum Rangefinder for Education By Mathew Pula April 22 2014 Physics 2P32 Brock University Abstract The apparatus produced in this project can measure physical quantities of a pendulum bound by small amplitudes This device is intended as an educational model for SHM specifically that of a linear pendulum The device produced can measure distances and periods of an oscillating pendulum The data collected by the device can then be graphed e g by physica The device utilizes a rangefinder The rangefinder emits ultrasonic pulses which are received again by the rangefinder Then the rangefinder creates a high on its output proportional to the time between the emission and detection of the ultrasonic pulse By measuring the time the output stays high one can determine the distance the pulse had to travel and thus the distance of an object To measure the period a simple stopwatch was implemented The stopwatch initially records the distance of a given object then records the time until the stop button is pushed This creates data of amplitude vs time This device was created as an educational model for SHM A linear pendulum was chosen because basic physical properties are observable in the model e g the amplitude should never increase due to conservation of energy as well as some properties specific to a pendulum However the device will also operate on other apparatus such as a spring oscillator Contents Page 1 1
8. ed by pressing switch 2 and is manual An example of the data collected via this mode of operation is shown in figure 1 1 2 Figure 1 1 2 Example Data Mode 2 left column distance mm right column time ms Read PIC Open Clear Save 87 1143 121 497 448 479 109 465 159 555 311 400 2636 426 454 453 337 529 Zoe 530 139 433 105 2579 88 610 90 a i Bs 86 109 90 96 86 95 86 101 90 3115 202 852 336 544 453 529 162 1296 57 464 50 393 170 4769 In terms of the oscillation of a pendulum this distance will be the amplitude of oscillation plus some constant distance see figure 1 2 3 For the intended purposes of this mode of operation it is not necessary to find the actual amplitude It is only necessary to show that the amplitude may have changes between data points Figure 1 2 3 Constant Value Explanation Pendulum Distance measured ement Taaa A Sensor j se i 1 i Constant value P eee eee o Rest position N B Angle in this diagram is exaggerated The device can model the equation x t A sin wt C i e the position equation for SHM which is an important model in physics The data has a small error but not negligibly small It also shows how much a simple measurement such as the position can do i e show conservation of energy calculate amplitude determine v t a t etc This is important to those just introduced to physics as it has a stigma o
9. efinder and should not come closer than 2cm From the manufacturer the performance vs angle measurement is shown in figure 1 4 1 It can be said that the device operates most effectively within 15 from the axis of measurement Figure 1 4 1 Performance vs Angle Practical test of performance Best in 30 degree angie Taken from Cytron Technologies HC SR04 User s_Manual The precision and accuracy of distance measurements is quite high typically varying 1mm as shown in figure 1 4 2 The measurement listed in figure 1 4 2 is of a distance 30cm Due to disciples in the origin i e it is difficult to determine the actual location of the sensor all that may be said of the accuracy of the device is that it is accurate to within 5mm w r t the picboard When analysing the accuracy of the device the resolution of the counter should be considered The test for the echo output to go high has an associated resolution of 13 instruction cycles Also the counter itself has an associated resolution of 29 instruction cycles This creates an error of about 1 428mm 13 29 200 10 340 2 In addition the device has associated errors with the speed of sound in air as this is variable and dependant on environment Additionally there is a rounding error associated with the counter cycle The actual period of the cycle should be 5 8823us d v 2 t t 2 10 340 This implies that the counter has an overestimation of about 1 42 5 8823 5 8 13
10. f being difficult in reality most things are fundamentally simple The data output of the rangefinder synergies well with Physica The device is also simple to use having only a few operation buttons For these reasons this device makes an ideal educational tool for introductory mechanical physics 1 2 The Program The program can be explained with the flowchart figure 1 2 1 This device operates Figure 1 2 1 Program Flowchart Preliminary Operations eua Mode 1 ress No Measure ee Distance Yes Operation Mode id Button 2 ee Increment Measure Trial counter Time Operation Set trig high for 20 ps Button 2 Path N B some checking and clearing steps are omitted for compactness The entire program appears as Rangefinder Effective angle 30 degrees Distance between 2cm 4m First create a pulse TRIG equ 1 Define Trigger and ECHO equ 2 Echo channels incase they change on board Selector1 equ 0x26 THold equ 0x20 EHold equ 0x21 ECount1 equ 0x22 ECount2 equ 0x23 Graph1 equ 0x24 Graph2 equ 0x25 TimerC1 equ 0x27 TimerC2 equ 0x28 Bank1 Setting the Trigger bcf TRISE TRIG set channel trigger to an output bsf TRISE ECHO set channel Echo to input BankO end of preliminary operations Selector call Getkey to select timer or distance movwf Selector1 movf Selector1 W sublw 7 btfsc STATUS Z goto Selector movf Selector1 W sublw 2 pushing 2 selects timer btfsc STATUS Z goto Timer cl
11. ing data points which can then be graphed In addition a stopwatch function has been included This is to measure the period of oscillation however it requires manual control This device measures distance fairly precise and accurately and could be used for quantitative analysis However the period measurements hence relying on the judgment of the user should not be used quantitatively Instead the period should be determined graphically The device produced in this project is a distance measuring device The device measures distance in millimeters and outputs the data along with a trial number to the PICLab output The trial number is added for graphing purposes An example of this is shown below in figure 1 1 1 This process is automated This mode is selected by pressing any button excluding reset and switch 2 on the Picboard Figure 1 1 1 Example Data Mode 1 left column trial number right column distance mm Read PIC Open Clear save 269 292 5 270 302 271 308 272 321 273 331 274 350 275 350 276 330 277 SLB 278 oud 279 299 280 307 281 264 282 246 283 232 284 223 285 199 286 200 287 180 In addition to the distance measuring technique mentioned above this device can also measure the period of an oscillation The program first measures the distance between the object in question and the Picboard Then a counter is run until a button switch 2 is released The countermeasures in milliseconds This mode is select
12. rf Grapn1 clearing trial counters clrf Graph2 mode 1 Triggermovlw 250 This is for points per seconds It is just to delay between data points TWait call Wait incf Graph increment LSD counter btfsc STATUS Z if LSD 0 increment incf Graph2 MSD counter movf Graphi W iorwf Graph2 W Test for 0 state omitted from flowchart btfsc STATUS Z goto END end operation if 0 state movf Graphi W movwf WL move counter 1 value to WL register movf Graph2W movwf WH move counter 2 value to WH register call Bin2BCD movlw 4 this selects the amount of trials possible call BCD2TCL movlw 0x20 call TxByte at this point the output is ready for a distance measurement bsf PORTE TRIG Need to set Trigger high for 20us movliw 32 Delay device movwf THold decfsz THold to delay signal deactivation goto TWait clrf ECount1 clear counters clrf ECount2 bcf PORTE TRIG Set trigger output low For Echo we want distance to be in reasonable units As distance 340 2 t if we want dist in mm then t 5 8823us therefore we want Echo clock to take 5880ns per cycle but cycles only in intervals of 200ns so 5800ns TIH movlw 3 this is to test if the echo input is high from the sensor movwf EHold DELAYdecfsz EHold goto DELAY nop btfss PORTE ECHO Test if high goto TIH Distance counter begins now Echo EWait movlw 5 For delay to make 5800ns movwf EHold to store delay value nop for delay
13. se of a demonstration of mode one small angle approximation will be used so that the data will approximate a linear pendulum well In addition if the amplitude of the pendulum is too large the rangefinder will not be able to detect it as it will pass the optimal angle threshold The period of a linear pendulum can be found with the following equation T 21r I mgL in the case of a simple pendulum this reduces to T 2tr L g The period of a non linear simple pendulum is T 21r L g sin 6 Period equation taken from Georgia State University HyperPhysics This implies the period should remain constant within experimental error until a sufficient amplitude is exceeded This will be tested by the second mode of operation Note that the amplitude values obtained in mode two will not reflect actual amplitude values This is especially true once the amplitude begins to affect the period as this is when the small angle approximation is no longer valid This is shown in figure 1 5 1 As the sum of the vectors in not zero the amplitude measurements would be off if the constant value method was used hence the data the rangefinder gives is a magnitude only 15 Figure 1 5 1 The Effect of Exceeding Small Angles on Amplitude Pendulum Distance measured T h d x t Amplitude Constant value 1 6 References Cytron Technologies HC SR04 User s_ Manual httos docs google com document d 1 Y vyZnNhMYy7rwhAgyL_pfa39RsB x2qR4vP8sa
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