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[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Generated by Four-Bar"]
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{"sheet":"4DV_Chen (2)","index":2,"n_rows":98,"n_cols":29,"rows_kept":98,"cut":false,"hidden":false,"merged":[[34,5,34,6],[63,5,63,6]]}
["Synthesize",null,null,null,null,null,null,null,{"$f":"PI()/180","v":1.7453292519943295E-2}]
["y=log x",null,"1<x<10",null,null,null,null,null,null,null,null,"Optimal Synthesis of Function Generators Without the Branch Defect"]
[null,null,null,null,null,null,null,null,null,null,null,"Tinunu&Gupta"]
[null,"qin",140,{"$f":"C4*D_R","v":2.4434609527920612},null,null,null,null,null,null,null,"Transactions of the ASME",null,"Vol. 106, SEPTEMBER 1984"]
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[null,null,{"$f":"O24","v":-0.57246568239116769},{"$f":"-N24","v":-4.4999999999999991},{"$f":"K24","v":2.7755575615628914E-16},null,{"$f":"P24","v":0.52904149907978337},null,null,null,75,{"$f":"K27*D_R","v":1.3089969389957472},{"$f":"FourBar(ABS(F31),F32,ABS(F33),F30,-1,L27+PI())","v":5.619197241321241}]
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[null,null,null,null,null,null,null,null,null,null,"4 Design Parameter"]
[null,"K1",{"$f":"MMULT(MINVERSE(C26:E28),G26:G28)","v":0.24846870598912221},null,"a1",1,null,null,"d1",{"$f":"S24","v":5.7364841720217892E-3},null,"fin, "]
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[null,"K3",-0.15714509433265564,null,"a3",{"$f":"SQRT(F30^2+F31^2+F33^2-2*C32*F31*F33)","v":7.3250671439053239},null,null,"d",{"$f":"SQRT(J30^2+J31^2)","v":5.7364842405112464E-3}]
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[]
[null,null,null,null,null,"Generated by Four-Bar"]
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[null,null,300,5.2359877559829888,3.5159342499631738,381.44819356838445,null,-0.57010182084036387,160]
[null,null,340,5.9341194567807207,4.2749102199563884,424.93431340084351,null,{"$f":"F42-E17","v":1.9160180116186893},200]
[null,null,380,6.6322511575784526,-1.0893112348438163,{"$f":"E43/D_R+180+360","v":477.58706366726528},null,{"$f":"F43-E18","v":-0.4312317219595343},240]
[null,null,420,7.3303828583761845,-0.19099100982908235,{"$f":"E44/D_R+180","v":169.05702121185195},null,{"$f":"F44-E19+360","v":2.038725822627157},280]
[null,null,460,8.0285145591739155,0.57662270358762768,{"$f":"E45/D_R+180","v":213.03804728699413},null,{"$f":"F45-E20+360","v":-1.9802481022306893},320]
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[null,null,null,null,null,"Generated by Four-Bar"]
[null,"x","y(required)","q","fg","freqired","y (generated)","e"]
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[null,1.1000000000000001,9.5310179804324935E-2,39.000000000000007,38.000787264398923,38.250211424996102,9.2428718909633847E-2,2.8814608946910875E-3]
[null,1.2,0.18232155679395459,48,44.863686229607481,45.782064350027625,0.17171203671300181,1.0609520080952783E-2]
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[null,1.4,0.33647223662121289,66,58.556713840775842,59.125609630214498,0.32990009474651566,6.5721418746972349E-3]
[null,1.5,0.40546510810816438,75,65.20142847992463,65.097750043269372,0.40666284837570527,-1.197740267540881E-3]
[null,1.6,0.47000362924573563,84,71.555001966575929,70.684314306758267,0.48006220752158479,-1.0058578275849162E-2]
[null,1.7,0.53062825106217038,93,77.429359080930283,75.932084781778627,0.54792544204520099,-1.7297190983030619E-2]
[null,1.8,0.58778666490211906,102,82.485294410779147,80.879814393297011,0.60633389736150367,-1.8547232459384611E-2]
[null,1.9,0.64185388617239469,110.99999999999999,85.931758825388897,85.55996511337338,0.64614901555961912,-4.2951293872244278E-3]
[null,2,0.69314718055994529,120,83.942436164667583,90,0.62316745900123605,6.997972155870924E-2]
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[]
[]
[]
[null,"qin",28]
[null,"fin",14]
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[null,"x","y(required)","q","fg","freqired","y (generated)","e"]
[null,1,0,28,13.848874116863897,14,-1.7458746634236965E-3,1.7458746634236965E-3]
[null,1.1000000000000001,9.5310179804324935E-2,37.000000000000014,22.442574499594087,22.250211424996102,9.7532445184348879E-2,-2.2222653800239439E-3]
[null,1.2,0.18232155679395459,46,29.74673752556896,29.782064350027625,0.18191344531442691,4.0811147952768412E-4]
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[null,1.4,0.33647223662121289,63.999999999999986,42.937478956762732,43.125609630214498,0.33429886585654722,2.1733707646656719E-3]
[null,1.5,0.40546510810816438,73,49.031151548963237,49.097750043269372,0.40469573213220045,7.6937597596393736E-4]
[null,1.6,0.47000362924573563,82,54.795424298057327,54.684314306758267,0.47128722219908531,-1.283592953349677E-3]
[null,1.7,0.53062825106217038,91,60.194967796254758,59.93208478177862,0.53366519473385754,-3.0369436716871645E-3]
[null,1.8,0.58778666490211906,100,65.17450983988013,64.879814393297011,0.59119112020083475,-3.4044552987156917E-3]
[null,1.9,0.64185388617239469,109,69.660971353235141,69.55996511337338,0.643020756012047,-1.166869839652307E-3]
[null,2,0.69314718055994529,118,73.564124321091668,74,0.68811174726144586,5.0354332984994254E-3]

{"sheet":"4DV_Chen (1)","index":3,"n_rows":98,"n_cols":29,"rows_kept":98,"cut":false,"hidden":false,"merged":[[34,5,34,6],[63,5,63,6]]}
["Synthesize",null,null,null,null,null,null,null,{"$f":"PI()/180","v":1.7453292519943295E-2}]
["y=log x",null,"1<x<10",null,null,null,null,null,null,null,null,"Optimal Synthesis of Function Generators Without the Branch Defect"]
[null,null,null,null,null,null,null,null,null,null,null,"Tinunu&Gupta"]
[null,"qin",172.5316293183177,{"$f":"C4*D_R","v":3.0112449954350238},null,null,null,null,null,null,null,"Transactions of the ASME",null,"Vol. 106, SEPTEMBER 1984"]
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[null,"y=sin(X)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"fin",132.61951932673611]
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[null,null,null,null,null,null,null,null,null,null,"4 Design Parameter"]
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[null,null,null,null,null,"Generated by Four-Bar"]
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[null,null,null,null,null,"Generated by Four-Bar"]
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{"sheet":"5DV_Chen","index":4,"n_rows":98,"n_cols":29,"rows_kept":98,"cut":false,"hidden":false,"merged":[[34,5,34,6],[63,5,63,6]]}
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["y=log x",null,"1<x<10",null,null,null,null,null,null,null,null,"Optimal Synthesis of Function Generators Without the Branch Defect"]
[null,null,null,null,null,null,null,null,null,null,null,"Tinunu&Gupta"]
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[null,null,null,null,null,null,null,null,null,null,"4 Design Parameter"]
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[null,null,null,null,null,"Generated by Four-Bar"]
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[null,null,{"$f":"D13","v":45.653239648381472},3.9383919996560683,{"$f":"FourBar($G$31,$F$32,$F$33,$F$30,1,D38)","v":2.5122798757432303},143.94303383573796,null,{"$f":"F38-E13","v":1.9370800951689944}]
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[null,null,125.65323964838147,5.3346554012515313,3.5870746210241973,205.52423658317574,null,-4.4817171573932342]
[null,null,165.65323964838149,6.032787102049264,4.2778410786123411,245.10223923217896,null,2.09628549160999]
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[null,null,285.65323964838149,8.1271822044424589,0.60683765697229175,34.76923659411991,null,{"$f":"F44-E19+360","v":6.7632828535508906}]
[null,null,325.65323964838149,8.8253139052401899,1.3355912179671083,76.523739944252512,null,{"$f":"F45-E20+360","v":0.51778620368349948}]
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[null,null,null,null,null,"Generated by Four-Bar"]
[null,"x","y(required)","q","fg","freqired","y (generated)","e"]
[null,1,0,30,31.2500212393048,30,1.4440811627736182E-2,-1.4440811627736182E-2]
[null,1.1000000000000001,9.5310179804324935E-2,39.000000000000007,38.000787264398923,38.250211424996102,9.2428718909633847E-2,2.8814608946910875E-3]
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[null,2,0.69314718055994529,120,83.942436164667583,90,0.62316745900123605,6.997972155870924E-2]
[]
[]
[]
[]
[]
[]
[null,"qin",28]
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[]
[]
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[null,1.9,0.64185388617239469,109,69.660971353235141,69.55996511337338,0.643020756012047,-1.166869839652307E-3]
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{"sheet":"LwSR5dvlogx","index":5,"n_rows":98,"n_cols":29,"rows_kept":98,"cut":false,"hidden":false,"merged":[[34,5,34,6],[63,5,63,6]]}
["Synthesize",null,null,null,null,null,null,null,{"$f":"PI()/180","v":1.7453292519943295E-2}]
["y=log x",null,"1<x<10",null,null,null,null,null,null,null,null,"Optimal Synthesis of Function Generators Without the Branch Defect"]
[null,null,null,null,null,null,null,null,null,null,null,"Tinunu&Gupta"]
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[]
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[null,null,null,null,null,null,null,null,null,null,"4 Design Parameter"]
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[null,null,null,null,null,"Generated by Four-Bar",null,null,{"$f":"MAX(J37:J55)","v":0.10579488997206543},{"$f":"MAX(-I34,I35)","v":0.22500756084319751},{"$f":"SQRT(SUM(K37:K55))","v":0.41466122003094708}]
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[null,3.5,158.47370027047955,2.7658878475384965,{"$f":"FourBar($F$31,$F$32,$G$33,$F$30,-1,D42)","v":4.2930517542018762},65.973746747001996,null,0.45110179387752158,0.54406804435027567,9.2966250472754086E-2,8.642723726962849E-3]
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[null,8,203.47370027047955,3.5512860109359448,{"$f":"FourBar($F$31,$F$32,$G$33,$F$30,-1,D51)","v":4.7800739351572687},93.878062245002639,null,0.91617371884419896,0.90308998699194354,-1.308373185225542E-2,1.7118403918172306E-4]
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[null,9,213.47370027047955,3.725818936135378,{"$f":"FourBar($F$31,$F$32,$G$33,$F$30,-1,D53)","v":4.9011691161682815},100.8163050363064,null,1.0318110986992617,0.95424250943932487,-7.7568589259936815E-2,6.0168860397767851E-3]
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[null,10,223.47370027047955,3.9003518613348107,{"$f":"FourBar($F$31,$F$32,$G$33,$F$30,-1,D55)","v":5.0277549849644618},108.06914106432436,null,1.1526916991662275,1,-0.15269169916622749,2.3314754994269715E-2]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,"Generated by Four-Bar"]
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[null,1,0,30,31.2500212393048,30,1.4440811627736182E-2,-1.4440811627736182E-2]
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[null,1.5,0.40546510810816438,75,65.20142847992463,65.097750043269372,0.40666284837570527,-1.197740267540881E-3]
[null,1.6,0.47000362924573563,84,71.555001966575929,70.684314306758267,0.48006220752158479,-1.0058578275849162E-2]
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[null,1.9,0.64185388617239469,110.99999999999999,85.931758825388897,85.55996511337338,0.64614901555961912,-4.2951293872244278E-3]
[null,2,0.69314718055994529,120,83.942436164667583,90,0.62316745900123605,6.997972155870924E-2]
[]
[]
[]
[]
[]
[]
[null,"qin",28]
[null,"fin",14]
[]
[]
[null,"x","y(required)","q","fg","freqired","y (generated)","e"]
[null,1,0,28,13.848874116863897,14,-1.7458746634236965E-3,1.7458746634236965E-3]
[null,1.1000000000000001,9.5310179804324935E-2,37.000000000000014,22.442574499594087,22.250211424996102,9.7532445184348879E-2,-2.2222653800239439E-3]
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[null,1.6,0.47000362924573563,82,54.795424298057327,54.684314306758267,0.47128722219908531,-1.283592953349677E-3]
[null,1.7,0.53062825106217038,91,60.194967796254758,59.93208478177862,0.53366519473385754,-3.0369436716871645E-3]
[null,1.8,0.58778666490211906,100,65.17450983988013,64.879814393297011,0.59119112020083475,-3.4044552987156917E-3]
[null,1.9,0.64185388617239469,109,69.660971353235141,69.55996511337338,0.643020756012047,-1.166869839652307E-3]
[null,2,0.69314718055994529,118,73.564124321091668,74,0.68811174726144586,5.0354332984994254E-3]

{"sheet":"Least_4DV_1 LOGX","index":6,"n_rows":98,"n_cols":30,"rows_kept":98,"cut":false,"hidden":false,"merged":[[34,5,34,6],[63,5,63,6]]}
["Synthesize",null,null,null,null,null,null,null,{"$f":"PI()/180","v":1.7453292519943295E-2}]
["y=log x",null,"1<x<10",null,null,null,null,null,null,null,null,"Optimal Synthesis of Function Generators Without the Branch Defect"]
[null,null,null,null,null,null,null,null,null,null,null,"Tinunu&Gupta"]
[null,"qin",275.90506242682409,{"$f":"C4*D_R","v":4.8154517622685766},null,null,null,null,null,null,null,"Transactions of the ASME",null,"Vol. 106, SEPTEMBER 1984"]
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[null,"Dq",90,{"$f":"C7/9","v":10},{"$f":"D7*D_R","v":0.17453292519943295},null,null,"qin",294.90972816636673,300340,"qin",129.56318637371035,160,"qin",233.10995467869367,220]
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[]
[]
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[]
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[null,null,{"$f":"O24","v":0.29147278804165822},{"$f":"-N24","v":-5.580367863929264},{"$f":"K24","v":6.8214520780177139},null,{"$f":"P24","v":-2.7174352598347089},null,null,null,75,{"$f":"K27*D_R","v":1.3089969389957472},{"$f":"FourBar(ABS(F31),F32,ABS(F33),F30,-1,L27+PI())","v":6.4615140790495573}]
[null,null,{"$f":"J24","v":1.7120762787698534},{"$f":"-K24","v":-6.8214520780177139},10,null,{"$f":"L24","v":-4.6572664451263304}]
[null,null,null,null,null,null,null,null,null,null,"4 Design Parameter"]
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[null,"K2",-0.34399905184710633,null,"a2",{"$f":"F30/C30","v":-6.2351869499314025},{"$f":"-F31","v":6.2351869499314025},null,"d2",{"$f":"T24","v":-6.0784468453177171E-2}]
[null,"K3",-0.67292565017277184,null,"a3",{"$f":"SQRT(F30^2+F31^2+F33^2-2*C32*F31*F33)","v":8.527747073328964},null,null,"d",{"$f":"SQRT(J30^2+J31^2)","v":6.0784468453438129E-2}]
[null,null,null,null,"a4",{"$f":"F30/C31","v":-2.9069847565872351},{"$f":"-F33","v":2.9069847565872351}]
[null,null,null,null,null,null,null,null,{"$f":"MIN(J37:J55)","v":-0.21852311137200076},null,{"$f":"SQRT(SUM(L37:L47))","v":0}]
[null,null,null,null,null,"Generated by Four-Bar",null,null,{"$f":"MAX(J37:J55)","v":0.13799833998838673},{"$f":"MAX(-I34,I35)","v":0.21852311137200076},{"$f":"SQRT(SUM(K37:K55))","v":0.49534717888691643}]
[null,"x","q",null,null,"f ",null,"ygen","yactual","e"]
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[null,1.5,{"$f":"(B38-$B$37)*$D$7+$C$4","v":280.90506242682409},1.7611255712784999,{"$f":"FourBar($G$31,$F$32,$G$33,$F$30,-1,D38)","v":4.1062258668238822},55.269411896456489,null,{"$f":"(F38-$C$5)/$D$8","v":0.25449019827427483},{"$f":"LOG(B38)","v":0.17609125905568124},{"$f":"I38-H38","v":-7.8398939218593588E-2},{"$f":"J38^2","v":6.1463936706007321E-3}]
[null,2,285.90506242682409,1.8483920338782163,4.1462520562745171,57.562743621968934,null,0.29271239369948227,0.3010299956639812,8.317601964498933E-3,6.9182502439836511E-5]
[null,2.5,290.90506242682409,1.9356584964779335,4.1885307083722667,59.985131950671899,null,0.33308553251119832,0.3979400086720376,6.4854476160839281E-2,4.2061030780968702E-3]
[null,3,295.90506242682409,2.0229249590776499,4.2329951573422413,62.532757215026265,null,0.37554595358377107,0.47712125471966244,0.10157530113589136,1.0317541800847013E-2]
[null,3.5,300.90506242682409,2.1101914216773663,4.2796096728789284,65.203572219325451,null,0.42005953698875753,0.54406804435027567,0.12400850736151814,1.5378109898031699E-2]
[null,4,305.90506242682409,2.1974578842770827,4.3283615333981489,67.996848070487232,null,0.46661413450812056,0.6020599913279624,0.13544585681984184,1.8345580129661095E-2]
[null,4.5,310.90506242682409,2.284724346876799,4.3792553755190049,70.912850427217421,null,0.515214173786957,0.65321251377534373,0.13799833998838673,1.9043541839550378E-2]
[null,5,315.90506242682409,2.3719908094765154,4.4323090510987306,73.952602125591994,null,0.56587670209319996,0.69897000433601886,0.1330933022428189,1.7713827101898342E-2]
[null,5.5,320.90506242682409,2.4592572720762318,4.4875505146327983,77.117704840219915,null,0.61862841400366519,0.74036268949424389,0.12173427549057869,1.4819233829216108E-2]
[null,6,325.90506242682409,2.5465237346759482,4.5450154376876784,80.410202401308538,null,0.67350337335514232,0.77815125038364363,0.10464787702850131,1.0951178166572333E-2]
[null,6.5,330.90506242682409,2.6337901972756645,4.6047453543424215,83.832474536293489,null,0.73054124227155814,0.81291335664285558,8.2372114371297434E-2,6.7851652259981049E-3]
[null,7,335.90506242682409,2.7210566598753818,4.6667862097847728,87.387153710521488,null,0.78978589517535813,0.84509804001425681,5.531214483889868E-2,3.0594333666793057E-3]
[null,7.5,340.90506242682409,2.8083231224750982,4.7311872285028436,91.077060279409977,null,0.85128433799016634,0.87506126339170009,2.3776925401533755E-2,5.6534218155010116E-4]
[null,8,345.90506242682409,2.8955895850748146,4.7980000477281424,94.905152838390109,null,0.91508588063983509,0.90308998699194354,-1.1995893647891553E-2,1.4390146441152493E-4]
[null,8.5,350.90506242682409,2.9828560476745309,4.8672780811537875,98.874491766645804,null,0.98124152944409671,0.92941892571429274,-5.1822603729803962E-2,2.6855822573362913E-3]
[null,9,355.90506242682409,3.0701225102742473,4.9390760907021454,102.98821469120668,null,1.0498035781867781,0.95424250943932487,-9.5561068747453182E-2,9.1319178601554727E-3]
[null,9.5,360.90506242682409,3.1573889728739637,5.0134499523328913,107.24952306873843,null,1.1208253844789737,0.97772360528884772,-0.14310177919012601,2.0478119207379582E-2]
[null,10,365.90506242682409,3.2446554354736801,5.0904566069929809,111.66167937518298,null,1.1943613229197163,1,-0.19436132291971631,3.7776323847102236E-2]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,"Generated by Four-Bar"]
[null,"x","y(required)","q","fg","freqired","y (generated)","e"]
[null,1,0,30,31.2500212393048,30,1.4440811627736182E-2,-1.4440811627736182E-2]
[null,1.1000000000000001,9.5310179804324935E-2,39.000000000000007,38.000787264398923,38.250211424996102,9.2428718909633847E-2,2.8814608946910875E-3]
[null,1.2,0.18232155679395459,48,44.863686229607481,45.782064350027625,0.17171203671300181,1.0609520080952783E-2]
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[null,1.4,0.33647223662121289,66,58.556713840775842,59.125609630214498,0.32990009474651566,6.5721418746972349E-3]
[null,1.5,0.40546510810816438,75,65.20142847992463,65.097750043269372,0.40666284837570527,-1.197740267540881E-3]
[null,1.6,0.47000362924573563,84,71.555001966575929,70.684314306758267,0.48006220752158479,-1.0058578275849162E-2]
[null,1.7,0.53062825106217038,93,77.429359080930283,75.932084781778627,0.54792544204520099,-1.7297190983030619E-2]
[null,1.8,0.58778666490211906,102,82.485294410779147,80.879814393297011,0.60633389736150367,-1.8547232459384611E-2]
[null,1.9,0.64185388617239469,110.99999999999999,85.931758825388897,85.55996511337338,0.64614901555961912,-4.2951293872244278E-3]
[null,2,0.69314718055994529,120,83.942436164667583,90,0.62316745900123605,6.997972155870924E-2]
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[]
[]
[null,"qin",28]
[null,"fin",14]
[]
[]
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[null,1,0,28,13.848874116863897,14,-1.7458746634236965E-3,1.7458746634236965E-3]
[null,1.1000000000000001,9.5310179804324935E-2,37.000000000000014,22.442574499594087,22.250211424996102,9.7532445184348879E-2,-2.2222653800239439E-3]
[null,1.2,0.18232155679395459,46,29.74673752556896,29.782064350027625,0.18191344531442691,4.0811147952768412E-4]
[null,1.3,0.26236426446749106,55,36.522767305865727,36.710697395223789,0.26019321094114239,2.1710535263486652E-3]
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[null,1.5,0.40546510810816438,73,49.031151548963237,49.097750043269372,0.40469573213220045,7.6937597596393736E-4]
[null,1.6,0.47000362924573563,82,54.795424298057327,54.684314306758267,0.47128722219908531,-1.283592953349677E-3]
[null,1.7,0.53062825106217038,91,60.194967796254758,59.93208478177862,0.53366519473385754,-3.0369436716871645E-3]
[null,1.8,0.58778666490211906,100,65.17450983988013,64.879814393297011,0.59119112020083475,-3.4044552987156917E-3]
[null,1.9,0.64185388617239469,109,69.660971353235141,69.55996511337338,0.643020756012047,-1.166869839652307E-3]
[null,2,0.69314718055994529,118,73.564124321091668,74,0.68811174726144586,5.0354332984994254E-3]

{"sheet":"Sheet1","index":7,"n_rows":98,"n_cols":17,"rows_kept":98,"cut":false,"hidden":false,"merged":[[34,5,34,6],[63,5,63,6]]}
["Synthesize y=sinx",null,null,null,null,null,null,null,{"$f":"PI()/180","v":1.7453292519943295E-2}]
["0<x<90",null,null,null,null,null,null,null,null,null,null,"Optimal Synthesis of Function Generators Without the Branch Defec"]
[null,null,null,null,null,null,null,null,null,null,null,"Tinunu&Gupta"]
[null,"qin",73.304239129471483,{"$f":"C4*D_R","v":1.2794003284785394},null,null,null,null,null,null,null,"Transactions of the ASME",null,"Vol. 106, SEPTEMBER 1984"]
[null,"fin",60.417659470803343,{"$f":"C5*D_R","v":1.0544870841142533},null,null,null,null,null,null,null,"assuming initial crank angles Least squares formulation with 3 design variables is performed."]
[null,null,null,null,null,null,null,null,null,null,null,"In the resulting error curve max error is tried to be minized uzing the initial crank angles as the two design variables."]
[null,"Dq",120,{"$f":"C7/90","v":1.3333333333333333}]
[null,"Df",60,{"$f":"C8*D_R","v":1.0471975511965976}]
[]
[null,"y=sin(X)"]
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[null,null,null,null,null,null,null,null,null,{"$f":"SUM(J12:J22)","v":-0.29646571755841356},{"$f":"SUM(K12:K22)","v":-4.424783268884962},8.7101651030910858,{"$f":"SUM(M12:M22)","v":2.3273982657270151},5.9067053587658389,3.2098718873188088,-2.4399426315349215,0.59577804916149513]
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[null,null,{"$f":"J24","v":-0.29646571755841356},{"$f":"-K24","v":4.424783268884962},11,null,{"$f":"L24","v":8.7101651030910858}]
[]
[null,"K1",{"$f":"MMULT(MINVERSE(C26:E28),G26:G28)","v":7.0366466794271787},null,"a1",1]
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[null,null,null,null,"a4",{"$f":"F30/C31","v":0.1995192158105964},{"$f":"-F33","v":-0.1995192158105964}]
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[null,null,null,null,null,"Generated by Four-Bar",null,null,{"$f":"MAX(J37:J55)","v":3.7033710040971224E-3},{"$f":"MAX(-I34,I35)","v":3.7033710040971224E-3}]
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[null,5,{"$f":"B38*$D$7+$C$4","v":79.970905796138155},4.5373482655346216,{"$f":"FourBar($G$31,$F$32,$G$33,$F$30,-1,D38)","v":4.2911362562277295},{"$f":"E38-PI()-$D$5","v":9.5056518523683131E-2},null,{"$f":"F38/$D$8","v":9.077228877690291E-2},8.7155742747658166E-2,{"$f":"I38-H38","v":-3.6165460292447438E-3}]
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[null,20,99.97090579613814,4.8864141159334871,4.5536991770444439,0.35761943934039753,null,0.34150140910065896,0.34202014332566871,5.1873422500975375E-4]
[null,25,106.63757246280481,5.0027693993997753,4.6365304023835403,0.4404506646794939,null,0.42059940283111402,0.42261826174069944,2.0188589095854192E-3]
[null,30,113.30423912947148,5.1191246828660644,4.7163976359783568,0.52031789827431041,null,0.49686699293725484,0.49999999999999994,3.1330070627451079E-3]
[null,35,119.97090579613814,5.2354799663323526,4.79284941622827,0.59676967852422358,null,0.56987306534694893,0.57357643635104605,3.7033710040971224E-3]
[null,40,126.63757246280481,5.3518352497986417,4.8653760411486919,0.66929630344464552,null,0.63913089051809091,0.64278760968653925,3.6567191684483413E-3]
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[null,55,146.63757246280483,5.7009011001975072,5.0534753893178284,0.85739565161378195,null,{"$f":"F48/$D$8","v":0.81875253683897997},0.8191520442889918,3.9950745001182675E-4]
[null,60,153.30423912947148,5.8172563836637963,5.1041660153847488,0.90808627768070238,null,0.86715851908081965,0.8660254037844386,-1.1331152963810487E-3]
[null,65,159.97090579613814,5.9336116671300845,5.1477337059099852,0.95165396820593884,null,0.90876259891795552,0.90630778703664994,-2.4548118813055853E-3]
[null,70,166.63757246280483,6.0499669505963736,5.183562269516635,0.9874825318125886,null,0.94297635692923965,0.93969262078590832,-3.2837361433313283E-3]
[null,75,173.30423912947148,6.1663222340626618,5.2111313134689423,1.0150515757648959,null,0.96930285465720423,0.96592582628906831,-3.3770283681359148E-3]
[null,80,179.97090579613814,6.2826775175289509,5.2300571006195611,1.0339773629155147,null,0.98737565011876061,0.98480775301220802,-2.5678971065525857E-3]
[null,85,186.63757246280483,6.39903280099524,5.2401217262954152,1.0440419885913688,null,0.99698665967885136,0.99619469809174555,-7.919615871058161E-4]
[null,90,193.30423912947148,6.5153880844615273,5.2412834816139462,1.0452037439098998,null,0.99809605428849635,1,1.9039457115036518E-3]
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[]
[]
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[]
[null,null,null,null,null,"Generated by Four-Bar"]
[null,"x","y(required)","q","fg","freqired","y (generated)","e"]
[null,1,0,30,31.2500212393048,30,1.4440811627736182E-2,-1.4440811627736182E-2]
[null,1.1000000000000001,9.5310179804324935E-2,39.000000000000007,38.000787264398923,38.250211424996102,9.2428718909633847E-2,2.8814608946910875E-3]
[null,1.2,0.18232155679395459,48,44.863686229607481,45.782064350027625,0.17171203671300181,1.0609520080952783E-2]
[null,1.3,0.26236426446749106,57,51.745210659907912,52.710697395223789,0.25121052432662061,1.115374014087045E-2]
[null,1.4,0.33647223662121289,66,58.556713840775842,59.125609630214498,0.32990009474651566,6.5721418746972349E-3]
[null,1.5,0.40546510810816438,75,65.20142847992463,65.097750043269372,0.40666284837570527,-1.197740267540881E-3]
[null,1.6,0.47000362924573563,84,71.555001966575929,70.684314306758267,0.48006220752158479,-1.0058578275849162E-2]
[null,1.7,0.53062825106217038,93,77.429359080930283,75.932084781778627,0.54792544204520099,-1.7297190983030619E-2]
[null,1.8,0.58778666490211906,102,82.485294410779147,80.879814393297011,0.60633389736150367,-1.8547232459384611E-2]
[null,1.9,0.64185388617239469,110.99999999999999,85.931758825388897,85.55996511337338,0.64614901555961912,-4.2951293872244278E-3]
[null,2,0.69314718055994529,120,83.942436164667583,90,0.62316745900123605,6.997972155870924E-2]
[]
[]
[]
[]
[]
[]
[null,"qin",28]
[null,"fin",14]
[]
[]
[null,"x","y(required)","q","fg","freqired","y (generated)","e"]
[null,1,0,28,13.848874116863897,14,-1.7458746634236965E-3,1.7458746634236965E-3]
[null,1.1000000000000001,9.5310179804324935E-2,37.000000000000014,22.442574499594087,22.250211424996102,9.7532445184348879E-2,-2.2222653800239439E-3]
[null,1.2,0.18232155679395459,46,29.74673752556896,29.782064350027625,0.18191344531442691,4.0811147952768412E-4]
[null,1.3,0.26236426446749106,55,36.522767305865727,36.710697395223789,0.26019321094114239,2.1710535263486652E-3]
[null,1.4,0.33647223662121289,63.999999999999986,42.937478956762732,43.125609630214498,0.33429886585654722,2.1733707646656719E-3]
[null,1.5,0.40546510810816438,73,49.031151548963237,49.097750043269372,0.40469573213220045,7.6937597596393736E-4]
[null,1.6,0.47000362924573563,82,54.795424298057327,54.684314306758267,0.47128722219908531,-1.283592953349677E-3]
[null,1.7,0.53062825106217038,91,60.194967796254758,59.93208478177862,0.53366519473385754,-3.0369436716871645E-3]
[null,1.8,0.58778666490211906,100,65.17450983988013,64.879814393297011,0.59119112020083475,-3.4044552987156917E-3]
[null,1.9,0.64185388617239469,109,69.660971353235141,69.55996511337338,0.643020756012047,-1.166869839652307E-3]
[null,2,0.69314718055994529,118,73.564124321091668,74,0.68811174726144586,5.0354332984994254E-3]

{"sheet":"Sheet1 (2)","index":8,"n_rows":98,"n_cols":20,"rows_kept":98,"cut":false,"hidden":false,"merged":[[34,5,34,6],[63,5,63,6]]}
["Synthesize y=sinx",null,null,null,null,null,null,null,{"$f":"PI()/180","v":1.7453292519943295E-2}]
["0<x<90",null,null,null,null,null,null,null,null,null,null,"Optimal Synthesis of Function Generators Without the Branch Defect"]
[null,null,null,null,null,null,null,null,null,null,null,"Tinunu&Gupta"]
[null,"qin",85.426869382590041,{"$f":"C4*D_R","v":1.4909801403973317},null,null,null,null,null,null,null,"Transactions of the ASME",null,"Vol. 106, SEPTEMBER 1984"]
[null,"fin",72.952442617739564,{"$f":"C5*D_R","v":1.2732603210517863}]
[]
[null,"Dq",120,{"$f":"C7/90","v":1.3333333333333333}]
[null,"Df",60,{"$f":"C8*D_R","v":1.0471975511965976}]
[]
[null,"y=sin(X)"]
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[]
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[]
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[]
[]
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[null,null,null,null,null,"Generated by Four-Bar"]
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[null,2,0.69314718055994529,120,83.942436164667583,90,0.62316745900123605,6.997972155870924E-2]
[]
[]
[]
[]
[]
[]
[null,"qin",28]
[null,"fin",14]
[]
[]
[null,"x","y(required)","q","fg","freqired","y (generated)","e"]
[null,1,0,28,13.848874116863897,14,-1.7458746634236965E-3,1.7458746634236965E-3]
[null,1.1000000000000001,9.5310179804324935E-2,37.000000000000014,22.442574499594087,22.250211424996102,9.7532445184348879E-2,-2.2222653800239439E-3]
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[null,1.6,0.47000362924573563,82,54.795424298057327,54.684314306758267,0.47128722219908531,-1.283592953349677E-3]
[null,1.7,0.53062825106217038,91,60.194967796254758,59.93208478177862,0.53366519473385754,-3.0369436716871645E-3]
[null,1.8,0.58778666490211906,100,65.17450983988013,64.879814393297011,0.59119112020083475,-3.4044552987156917E-3]
[null,1.9,0.64185388617239469,109,69.660971353235141,69.55996511337338,0.643020756012047,-1.166869839652307E-3]
[null,2,0.69314718055994529,118,73.564124321091668,74,0.68811174726144586,5.0354332984994254E-3]

{"sheet":"Sheet1 (3)","index":9,"n_rows":98,"n_cols":20,"rows_kept":98,"cut":false,"hidden":false,"merged":[[34,5,34,6],[63,5,63,6]]}
["Synthesize y=sinx",null,null,null,null,null,null,null,{"$f":"PI()/180","v":1.7453292519943295E-2}]
["0<x<90",null,null,null,null,null,null,null,null,null,null,"Optimal Synthesis of Function Generators Without the Branch Defect"]
[null,null,null,null,null,null,null,null,null,null,null,"Tinunu&Gupta"]
[null,"qin",82.690003143939606,{"$f":"C4*D_R","v":1.4432128133462088},null,null,null,null,null,null,null,"Transactions of the ASME",null,"Vol. 106, SEPTEMBER 1984"]
[null,"fin",70,{"$f":"C5*D_R","v":1.2217304763960306}]
[]
[null,"Dq",120,{"$f":"C7/90","v":1.3333333333333333}]
[null,"Df",60,{"$f":"C8*D_R","v":1.0471975511965976}]
[]
[null,"y=sin(X)"]
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[]
[null,null,null,null,null,null,null,null,null,{"$f":"SUM(J12:J22)","v":-1.8263006956222418},{"$f":"SUM(K12:K22)","v":-5.2908186307023009},8.7288962385485078,{"$f":"SUM(M12:M22)","v":2.9107439541212998},6.4182578582416827,4.0409224214280481,-3.2791613044368439,-0.61211775472712326,null,{"$f":"SUM(S12:S22)","v":-2.1872652905541301E-7},{"$f":"SUM(T12:T22)","v":-3.083959783198937E-3}]
[]
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[null,null,{"$f":"O24","v":4.0409224214280481},{"$f":"-N24","v":-6.4182578582416827},{"$f":"K24","v":-5.2908186307023009},null,{"$f":"P24","v":-3.2791613044368439},null,null,null,75,{"$f":"K27*D_R","v":1.3089969389957472},{"$f":"FourBar(ABS(F31),F32,ABS(F33),F30,-1,L27+PI())","v":4.7591348573953081}]
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[null,null,null,null,null,null,null,null,null,null,"Design Parameter"]
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[null,null,null,null,"a4",{"$f":"F30/C31","v":0.3944884877453928},{"$f":"-F33","v":-0.3944884877453928}]
[null,null,null,null,null,null,null,null,{"$f":"MIN(J37:J55)","v":-1.593709736043003E-3},null,{"$f":"SQRT(SUM(L37:L47))","v":0}]
[null,null,null,null,null,"Generated by Four-Bar",null,null,{"$f":"MAX(J37:J55)","v":1.661874054423973E-3},{"$f":"MAX(-I34,I35)","v":1.661874054423973E-3}]
[null,"x","q",null,null,"f ",null,"ygen","yactual","e"]
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[null,5,{"$f":"B38*$D$7+$C$4","v":89.356669810606277},4.7011607504022903,{"$f":"FourBar($G$31,$F$32,$G$33,$F$30,-1,D38)","v":4.4561475062295361},{"$f":"E38-PI()-$D$5","v":9.2824376243712425E-2},null,{"$f":"F38/$D$8","v":8.8640749911652397E-2},8.7155742747658166E-2,{"$f":"I38-H38","v":-1.4850071639942314E-3}]
[null,10,96.023336477272935,4.8175160338685785,4.5468360053412873,0.18351287535546357,null,0.17524188740297333,0.17364817766693033,-1.593709736043003E-3]
[null,15,102.69000314393961,4.9338713173348676,4.6354690683377786,0.27214593835195489,null,0.25988022798657506,0.25881904510252074,-1.0611828840543236E-3]
[null,20,109.35666981060626,5.0502266008011567,4.7217225238199392,0.35839939383411545,null,0.34224621077903061,0.34202014332566871,-2.2606745336190004E-4]
[null,25,116.02333647727293,5.1665818842674449,4.8052248825863444,0.44190175260052067,null,0.42198508972406812,0.42261826174069944,6.3317201663132261E-4]
[null,30,122.69000314393961,5.2829371677337331,4.8855531680201345,0.52223003803431078,null,0.49869295190537449,0.49999999999999994,1.3070480946254515E-3]
[null,35,129.35666981060626,5.3992924512000222,4.9622306591165204,0.59890752913069667,null,0.57191456229662208,0.57357643635104605,1.661874054423973E-3]
[null,40,136.02333647727295,5.5156477346663113,5.0347280075115908,0.67140487752576705,null,0.64114443044540659,0.64278760968653925,1.643179241132664E-3]
[null,45,142.69000314393961,5.6320030181325995,5.1024695594783172,0.73914642949249343,null,0.70583284753473263,0.70710678118654746,1.2739336518148292E-3]
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[null,55,156.02333647727295,5.8647135850651768,5.2212406312213098,0.85791750123548605,null,{"$f":"F48/$D$8","v":0.81925086652004908},0.8191520442889918,-9.8822231057282828E-5]
[null,60,162.69000314393961,5.9810688685314659,5.2710520014459252,0.90772887146010151,null,0.86681722128061711,0.8660254037844386,-7.9181749617851516E-4]
[null,65,169.35666981060626,6.0974241519977541,5.3137397546271234,0.95041662464129972,null,0.90758102285026399,0.90630778703664994,-1.2732358136140487E-3]
[null,70,176.02333647727295,6.2137794354640423,5.3488594997649024,0.98553636977907866,null,0.94111790908309445,0.93969262078590832,-1.4252882971861336E-3]
[null,75,182.69000314393961,6.3301347189303314,5.376096612375961,1.0127734823901373,null,0.96712743572869786,0.96592582628906831,-1.2016094396295474E-3]
[null,80,189.35666981060626,6.4464900023966196,5.395285256233489,1.0319621262476653,null,0.98545124085563096,0.98480775301220802,-6.4348784342294074E-4]
[null,85,196.02333647727295,6.5628452858629087,5.4064080890179911,1.0430849590321674,null,0.9960727637686595,0.99619469809174555,1.2193432308604812E-4]
[null,90,202.69000314393961,6.6792005693291969,5.4095760932787833,1.0462529632929596,null,0.99909798499570712,1,9.0201500429287762E-4]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,"Generated by Four-Bar"]
[null,"x","y(required)","q","fg","freqired","y (generated)","e"]
[null,1,0,30,31.2500212393048,30,1.4440811627736182E-2,-1.4440811627736182E-2]
[null,1.1000000000000001,9.5310179804324935E-2,39.000000000000007,38.000787264398923,38.250211424996102,9.2428718909633847E-2,2.8814608946910875E-3]
[null,1.2,0.18232155679395459,48,44.863686229607481,45.782064350027625,0.17171203671300181,1.0609520080952783E-2]
[null,1.3,0.26236426446749106,57,51.745210659907912,52.710697395223789,0.25121052432662061,1.115374014087045E-2]
[null,1.4,0.33647223662121289,66,58.556713840775842,59.125609630214498,0.32990009474651566,6.5721418746972349E-3]
[null,1.5,0.40546510810816438,75,65.20142847992463,65.097750043269372,0.40666284837570527,-1.197740267540881E-3]
[null,1.6,0.47000362924573563,84,71.555001966575929,70.684314306758267,0.48006220752158479,-1.0058578275849162E-2]
[null,1.7,0.53062825106217038,93,77.429359080930283,75.932084781778627,0.54792544204520099,-1.7297190983030619E-2]
[null,1.8,0.58778666490211906,102,82.485294410779147,80.879814393297011,0.60633389736150367,-1.8547232459384611E-2]
[null,1.9,0.64185388617239469,110.99999999999999,85.931758825388897,85.55996511337338,0.64614901555961912,-4.2951293872244278E-3]
[null,2,0.69314718055994529,120,83.942436164667583,90,0.62316745900123605,6.997972155870924E-2]
[]
[]
[]
[]
[]
[]
[null,"qin",28]
[null,"fin",14]
[]
[]
[null,"x","y(required)","q","fg","freqired","y (generated)","e"]
[null,1,0,28,13.848874116863897,14,-1.7458746634236965E-3,1.7458746634236965E-3]
[null,1.1000000000000001,9.5310179804324935E-2,37.000000000000014,22.442574499594087,22.250211424996102,9.7532445184348879E-2,-2.2222653800239439E-3]
[null,1.2,0.18232155679395459,46,29.74673752556896,29.782064350027625,0.18191344531442691,4.0811147952768412E-4]
[null,1.3,0.26236426446749106,55,36.522767305865727,36.710697395223789,0.26019321094114239,2.1710535263486652E-3]
[null,1.4,0.33647223662121289,63.999999999999986,42.937478956762732,43.125609630214498,0.33429886585654722,2.1733707646656719E-3]
[null,1.5,0.40546510810816438,73,49.031151548963237,49.097750043269372,0.40469573213220045,7.6937597596393736E-4]
[null,1.6,0.47000362924573563,82,54.795424298057327,54.684314306758267,0.47128722219908531,-1.283592953349677E-3]
[null,1.7,0.53062825106217038,91,60.194967796254758,59.93208478177862,0.53366519473385754,-3.0369436716871645E-3]
[null,1.8,0.58778666490211906,100,65.17450983988013,64.879814393297011,0.59119112020083475,-3.4044552987156917E-3]
[null,1.9,0.64185388617239469,109,69.660971353235141,69.55996511337338,0.643020756012047,-1.166869839652307E-3]
[null,2,0.69314718055994529,118,73.564124321091668,74,0.68811174726144586,5.0354332984994254E-3]

{"sheet":"Least_4DV_2LOGX","index":10,"n_rows":98,"n_cols":29,"rows_kept":98,"cut":false,"hidden":false,"merged":[[34,5,34,6],[63,5,63,6]]}
["Synthesize",null,null,null,null,null,null,null,{"$f":"PI()/180","v":1.7453292519943295E-2}]
["y=log x",null,"1<x<10",null,null,null,null,null,null,null,null,"Optimal Synthesis of Function Generators Without the Branch Defect"]
[null,null,null,null,null,null,null,null,null,null,null,"Tinunu&Gupta"]
[null,"qin",30,{"$f":"C4*D_R","v":0.52359877559829882},null,null,null,null,null,null,null,"Transactions of the ASME",null,"Vol. 106, SEPTEMBER 1984"]
[null,"fin",348.8419872565525,{"$f":"C5*D_R","v":6.0884412468269424},null,null,null,null,null,null,null,null,null,"qin",30]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"fin",348.50014212505567,310]
[null,"Dq",90,{"$f":"C7/9","v":10},{"$f":"D7*D_R","v":0.17453292519943295},null,null,null,null,null,null,null,null,"qin",30]
[null,"Df",60,{"$f":"C8/LOG(10)","v":60},{"$f":"D8*D_R","v":1.0471975511965976},null,null,null,null,null,null,null,null,"fin",177.56645228426663,100,null,null,null,null,null,null,null,null,null,null,null,"f is variable"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"qin",80]
[null,"y=log(X)",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"fin",132.61951932673611]
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[]
[]
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[null,null,null,null,null,null,null,null,null,null,"4 Design Parameter"]
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[null,null,null,null,null,"Generated by Four-Bar",null,null,{"$f":"MAX(J37:J55)","v":7.7442005124532032E-2},{"$f":"MAX(-I34,I35)","v":0.23612575885207623},{"$f":"SQRT(SUM(K37:K55))","v":0.34315155397521013}]
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[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,"Generated by Four-Bar"]
[null,"x","y(required)","q","fg","freqired","y (generated)","e"]
[null,1,0,30,31.2500212393048,30,1.4440811627736182E-2,-1.4440811627736182E-2]
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[null,1.6,0.47000362924573563,84,71.555001966575929,70.684314306758267,0.48006220752158479,-1.0058578275849162E-2]
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[null,2,0.69314718055994529,120,83.942436164667583,90,0.62316745900123605,6.997972155870924E-2]
[]
[]
[]
[]
[]
[]
[null,"qin",28]
[null,"fin",14]
[]
[]
[null,"x","y(required)","q","fg","freqired","y (generated)","e"]
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[null,1.5,0.40546510810816438,73,49.031151548963237,49.097750043269372,0.40469573213220045,7.6937597596393736E-4]
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