{"text_format":"1","workbook":"xlsx","n_sheets":3,"sheets":["Geometric Loci","Determine Link Lengths","Optimum"],"not_rendered":{"charts":3,"images":6,"macros":1,"external_links":0,"defined_names":5,"comments":3,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Geometric Loci","index":0,"n_rows":196,"n_cols":10,"rows_kept":196,"cut":false,"hidden":false,"merged":[[1,9,3,16],[11,1,13,5]]}
["In order to draw the circles, you must seperate the real and imaginary parts of the vectors. ",null,null,null,null,null,null,null,null,"1.If more accuracy is required use 0.2 degree steps instead of 1 degreee"]
[null,"s",100,null,null,null,null,null,null,"2. Try different  corresponding crank rotations In some cases you will have some problems. Be sure to change the scale of your drawings (otherwise the circles will look like an ellips). "]
[null,"f",160]
[]
[null,null,"f"]
[null,null,{"$f":"y*PI()/180","v":2.7925268031909272}]
[null,"cos",{"$f":"+COS(C6)","v":-0.93969262078590832},{"$f":"+COS(C6/2)","v":0.17364817766693041},null,0,0]
[null,"sin",{"$f":"+SIN(C6)","v":0.34202014332566888},{"$f":"+SIN(C6/2)","v":0.98480775301220802},null,{"$f":"4*COS(15*PI()/18)","v":-3.4641016151377539},{"$f":"4*SIN(15*PI()/183)","v":1.0186844809649147}]
[null,"1-cos",{"$f":"1-C7","v":1.9396926207859084}]
[null,"1+cos",{"$f":"1+C7","v":6.0307379214091683E-2}]
[null,"t",{"$f":"+TAN(C6/2)","v":5.6712818196177066}]
[null,"In this sheet the loci for A0 and A are drawn for any given corresponding crank rotation f between dead centers. Stroke=1"]
[]
[]
[null,"l","Real","Im","Denom","Zreal","Zim","Z2real","Z2im"]
[-90,{"$f":"+TAN(A16*PI()/180)","v":-1.6324552277619072E+16},{"$f":"+B16*$C$9+$C$10","v":-3.1664613590531508E+16},{"$f":"+$C$8*(1-B16)","v":5583325709718649},{"$f":"(C16^2+D16^2)","v":1.0338212798184779E+33},{"$f":"-C16/E16","v":3.06287113727155E-17},{"$f":"D16/E16","v":5.4006681993419502E-18},{"$f":"+F16*(1+B16)","v":-0.5},{"$f":"+G16*(1+B16)","v":-8.8163490354232529E-2}]
[-89,{"$f":"+TAN(A17*PI()/180)","v":-57.289961630759876},{"$f":"+B17*$C$9+$C$10","v":-111.06460844107866},{"$f":"+$C$8*(1-B17)","v":19.936341031400232},{"$f":"(C17^2+D17^2)","v":12732.804941890414},{"$f":"-C17/E17","v":8.722713412162672E-3},{"$f":"D17/E17","v":1.5657462061490061E-3},{"$f":"+F17*(1+B17)","v":-0.49100120328675134},{"$f":"+G17*(1+B17)","v":-8.8135793867635398E-2}]
[-88,-28.636253282915515,-55.485221800613374,10.13619559545859,3181.3522994126561,1.7440766246120273E-2,3.1861279863063083E-3,-0.48199743342590351,-8.8052640021346718E-2]
[-87,-19.081136687728161,-36.951232650179492,6.8681532480791336,1412.5651234067909,2.6158958647556997E-2,4.8621852077974891E-3,-0.47298370691510666,-8.7913835343236352E-2]
[-86,-14.300666256711896,-27.678589431252014,5.2331360660988278,793.4900259901201,3.4882088652235493E-2,6.5950873920171829E-3,-0.46395501950042156,-8.7719056335069004E-2]
[-85,-11.430052302761348,-22.110480727649076,4.2513282701359971,506.94715006819877,4.3614962081697448E-2,8.386137035318323E-3,-0.45490633569505734,-8.7467847896494103E-2]
[-84,-9.5143644542225871,-18.394635144109209,3.5961244376115276,351.29471305568444,5.2362402451509249E-2,1.0236773580596126E-2,-0.445832578170828,-8.7159621100552531E-2]
[-83,-8.1443464279745932,-15.7372212882523,3.1275506759154386,257.44170710584052,6.1129260931222569E-2,1.2148578064818482E-2,-0.4367286169787068,-8.6793650302356418E-2]
[-82,-7.1153697223841954,-13.74132276545801,2.775619915590636,196.52801726031797,6.9920426395267937E-2,1.4123278473389842E-2,-0.42758925855381424,-8.6369069556968728E-2]
[-81,-6.3137515146750411,-12.186429843276938,2.5014503412974856,154.76632613508809,7.8740835604251463E-2,1.6162755838205332E-2,-0.41840923445886963,-8.5884868316586455E-2]
[-80,-5.6712818196177066,-10.940236116695655,2.2817127641115773,124.89497942696171,8.7595483556594675E-2,1.8269051122634737E-2,-0.40918318981854246,-8.5339886370830106E-2]
[-79,-5.1445540159703071,-9.9185460827980236,2.1015612452144787,102.79411606397545,9.6489434051118927E-2,2.0444372943550004E-2,-0.39990567139526706,-8.4732807987184855E-2]
[-78,-4.7046301094784511,-9.0652289276684606,1.9510984076637461,85.985160507425064,0.10542783050205101,2.2691106187971391E-2,-0.3905711152548888,-8.4062155201331618E-2]
[-77,-4.3314758742841573,-8.341424411247079,1.8234721426600133,72.904411863605773,0.11441590704898283,2.5011821590049742E-2,-0.38117383396802496,-8.3326280199150324E-2]
[-76,-4.010780933535842,-7.7193748011541974,1.7137880130614576,62.525816674407544,0.12345900000557396,2.7409286343043137E-2,-0.3717080032901835,-8.2523356723458619E-2]
[-75,-3.7320508075688776,-7.1787240326253503,1.6184566954290547,54.153480811571903,0.13256255969221742,2.9886475830805899E-2,-0.36216764826052017,-8.1651370428940995E-2]
[-74,-3.4874144438409087,-6.7042046831263118,1.5347861312441442,47.301928901912142,0.14173216269950673,3.2446586574233799E-2,-0.35254662865556269,-8.0708108098083667E-2]
[-73,-3.2708526184841404,-6.284141308537861,1.4607176246967537,41.624127964771667,0.15097352463110836,3.5093050500253686E-2,-0.3428386237303323,-7.9691145619097264E-2]
[-72,-3.0776835371752527,-5.9094526669590186,1.3946499078214003,36.866679188415297,0.16029251337657663,3.7829550654501165E-2,-0.33303711617495724,-7.8597834613594375E-2]
[-71,-2.9042108776758222,-5.572969029419867,1.3353187639563202,32.841060004246849,0.16969516296670076,4.0660038493996332E-2,-0.32313537521016295,-7.742528758698547E-2]
[-70,-2.7474774194546216,-5.2689542970779479,1.2817127641115775,29.404666994382712,0.17918768806613239,4.3588752913149065E-2,-0.31312643873984475,-7.6170361457914851E-2]
[-69,-2.6050890646938005,-4.9927646560625369,1.2330130786083753,26.448020162846568,0.18877649916027484,4.6620241175574922E-2,-0.30300309447333557,-7.4829639304302961E-2]
[-68,-2.4750868534162964,-4.7406003261617116,1.1885497036745893,23.885941850509482,0.19846821849566695,4.9759381945796613E-2,-0.29275785992391135,-7.3399410142364799E-2]
[-67,-2.3558523658237518,-4.5093220704352639,1.1477691071388245,21.651359458216831,0.20826969683531568,5.3011410639309246E-2,-0.28238296118355832,-7.1875646530961845E-2]
[-66,-2.2460367739042164,-4.2963135771417047,1.1102099626511119,19.690876514301934,0.21818803109253129,5.6381947337120368E-2,-0.27187031036705056,-7.0253979766382882E-2]
[-65,-2.1445069205095586,-4.0993768697226116,1.0754847076412368,17.961558076386915,0.22823058290871992,5.9877027542232994E-2,-0.26121148161096053,-6.8529672401627106E-2]
[-64,-2.050303841579296,-3.916651852666269,1.0432653570837893,16.428564340285284,0.23840499824212003,6.3503136091176721E-2,-0.25039768550540398,-6.6697587788895743E-2]
[-63,-1.9626105055051504,-3.7465537357911503,1.0132724697110038,15.063385993044861,0.24871922803551785,6.7267244574284749E-2,-0.23941974182812062,-6.4752156303590824E-2]
[-62,-1.8807264653463318,-3.5877238673349527,0.98526647855979987,13.842512582018498,0.25918155003127297,7.1176852664715407E-2,-0.2282680504420265,-6.2687337861871445E-2]
[-61,-1.8040477552714236,-3.4389907392312713,0.95904081514995243,12.74641658964193,0.26980059180129767,7.5240033809132995E-2,-0.21693256020873505,-6.0496580290779402E-2]
[-60,-1.7320508075688767,-3.2993387910535321,0.93441640877771659,11.758770483143627,0.2805853550575873,7.9465485793537391E-2,-0.20540273576190679,-5.8172773049012153E-2]
[-59,-1.6642794823505174,-3.1678832516265985,0.91123725041316284,10.865837622476851,0.29154524130505866,8.3862586767190037E-2,-0.19366752197588105,-5.5708195726284347E-2]
[-58,-1.6003345290410507,-3.0438496975557263,0.88936678831730587,10.055994265471927,0.30269007889225152,8.8441457387363365E-2,-0.1817153059571783,-5.3094460668346936E-2]
[-57,-1.5398649638145827,-2.9265573281038142,0.86868497895170826,9.319351387334466,0.31403015150616315,9.3213029839426489E-2,-0.16953387637956269,-5.0322448981309602E-2]
[-56,-1.4825609685127403,-2.8154051912752802,0.84908585826543892,8.6474531857661532,0.32557622814419884,9.8189124592550317E-2,-0.15711037997798949,-4.7382239060799212E-2]
[-55,-1.4281480067421144,-2.7098607708536915,0.83047552928187529,8.0330350021477734,0.33733959457778567,0.10338253587340687,-0.14443127501367192,-4.4263026666144289E-2]
[-54,-1.3763819204711734,-2.6094504753069803,0.81277048503607896,7.4698276444256084,0.34933208629710405,0.10880712698138524,-0.13148228152270569,-4.09530354142046E-2]
[-53,-1.3270448216204098,-2.5137516687351695,0.79589620341586809,6.9523982186806421,0.3615661228928001,0.11447793673229861,-0.11824832816545898,-3.7439416398087164E-2]
[-52,-1.2799416321930788,-2.4223859597874946,0.77978596381683629,6.4760198875413337,0.37405474378602788,0.12041129850712788,-0.10471349550502454,-3.3708135438573407E-2]
[-51,-1.2348971565350511,-2.3350135227464479,0.76437984579624796,6.0365647000682721,0.38681164515971134,0.12662497360255295,-9.0860955562661341E-2,-2.974384624556559E-2]
[-50,-1.19175359259421,-2.2513282701359936,0.74962387787362139,5.6304149381918114,0.39985121786761241,0.13313830083620098,-7.6672907529284851E-2,-2.5529747497230252E-2]
[-49,-1.1503684072210094,-2.1710537314577394,0.73546931084071987,5.2543894120650982,0.41318858599870395,0.13997236465800184,-6.2130509558526184E-2,-2.1047421528582046E-2]
[-48,-1.1106125148291928,-2.0939395203525741,0.72187199482683095,4.9056818918096372,0.42683964564611204,0.14715018436724248,-4.721380663371795E-2,-1.6276651950440056E-2]
[-47,-1.0723687100246826,-2.019758294382489,0.70879184322627342,4.5818094447509594,0.44082110326442686,0.15469692744168659,-3.1901654594903968E-2,-1.119521708373678E-2]
[-46,-1.0355303137905694,-1.9483031290455921,0.6961923696663942,4.2805688982305545,0.45515051278603552,0.16264015046088315,-1.6171640541226398E-2,-5.7786555808205936E-3]
[-45,-0.99999999999999989,-1.8793852415718164,0.68404028665133776,3.9999999999999991,0.46984631039295421,0.17101007166283447,5.2163419183343575E-17,1.8985931900287686E-17]
[-44,-0.96568877480707394,-1.8128320112549745,0.67230515649317391,3.7383541244780667,0.48492784548817308,0.17983987982600186,1.6638468508865162E-2,6.1705266153787106E-3]
[-43,-0.93251508613766154,-1.748485252138666,0.66095908673982029,3.4940675912903516,0.50041540595754597,0.18916608493418685,3.3770490566432124E-2,1.27658569474594E-2]
[-42,-0.90040404429783993,-1.6861997012362164,0.649976463607428,3.2657388356927237,0.51633023523099397,0.19902891697999359,5.142440323575196E-2,1.9822475198988335E-2]
[-41,-0.86928673781622645,-1.6258416914750975,0.63933371798467786,3.052108808690718,0.53269453790297372,0.20947278031641894,6.9630240796775503E-2,2.7380870453864069E-2]
[-40,-0.83909963117727993,-1.5672879834846554,0.62900911944543803,2.852044095520923,0.54953146970835731,0.22054677220218438,8.8419816155766121E-2,3.5486056989991896E-2]
[-39,-0.80978403319500702,-1.5104247344045145,0.61898259442186343,2.6645223304981691,0.56686510640806675,0.2323052756349526,0.10782679426342563,4.4188172598802887E-2]
[-38,-0.78128562650671729,-1.4551465852470833,0.60923556528178124,2.4886195585604582,0.58472038453672392,0.24480863826136345,0.12788675257270093,5.3543167943077785E-2]
[-37,-0.75355405010279419,-1.401355851133633,0.59975080754546484,2.3234992526579061,0.60312300489470294,0.25812395113077641,0.14863722184613218,6.3613602327644125E-2]
[-36,-0.7265425280053609,-1.3489618010450459,0.59051232288625621,2.1684027441592164,0.62209928698835737,0.27232594335939353,0.17011769834950369,7.4469564029615035E-2]
[-35,-0.70020753820970971,-1.2978800156699495,0.5815052259018676,2.0226408628266102,0.64167595914985209,0.28749801143106679,0.19236961546517992,8.6189736606732528E-2]
[-34,-0.67450851684242674,-1.2480318135624109,0.57271564293050004,1.8855866153211764,0.66187986455866454,0.30373340491332879,0.21543625878733344,9.8862636449739139E-2]
[-33,-0.64940759319751062,-1.1993437371934568,0.56413062142785919,1.75666875797775,0.6827375575200203,0.32113659383188303,0.23936260350539695,0.11258805134387334]
[-32,-0.62486935190932746,-1.1517470916397037,0.55573804862551479,1.6353661417906109,0.70427475670899098,0.3398248468181081,0.26419504591814452,0.12747871502419042]
[-31,-0.60086061902756038,-1.1051775296345201,0.54752657836422514,1.5212027260242966,0.72651561210577809,0.35993005336980971,0.2899809916827133,0.143662258695403]
[-30,-0.57735026918962573,-1.0595746775417831,0.53948556514301815,1.4137431722854554,0.74948172929378398,0.38160082801382267,0.31676825113331158,0.16128348723705807]
[-29,-0.55430905145276899,-1.0148817975236808,0.5316050045502605,1.3125889438077798,0.77319087770123995,0.40500493856674646,0.34460417569073171,0.18050703523612627]
[-28,-0.53170943166147877,-0.97104548178194794,0.52387547935013778,1.2173748455534721,0.7976552869715885,0.43033210458029547,0.37353444767415145,0.20152046582821853]
[-27,-0.50952544949442879,-0.92801537527287492,0.51628811058982926,1.1277659498792707,0.82287940629190004,0.45779721461274725,0.40360140692131097,0.22453788305988973]
[-26,-0.48773258856586144,-0.8857439237439193,0.50883451317156425,1.0434548602438167,0.8488569630476912,0.48764401083212022,0.43484175913828499,0.24980413513033126]
[-25,{"$f":"+TAN(A81*PI()/180)","v":-0.46630765815499858},{"$f":"+B81*$C$9+$C$10","v":-0.84418614432511696},{"$f":"+$C$8*(1-B81)","v":0.50150675540169853},{"$f":"(C81^2+D81^2)","v":0.96415927198404627},{"$f":"-C81/E81","v":0.87556710686186867},{"$f":"D81/E81","v":0.52014928443274555},{"$f":"+F81*(1+B81)","v":0.46728345970356333},{"$f":"+G81*(1+B81)","v":0.27759968971791377}]
[-24,-0.4452286853085361,-0.80329941624108714,0.49429732208759353,0.88961979475623754,0.90296935946799295,0.55562761193171817,0.50094149867816751,0.30824626075023781]
[-23,-0.4244748162096047,-0.76304328949713329,0.48719908080381485,0.81959800598268817,0.93099700576046862,0.59443663509121036,0.53581222284860142,0.34211325366261297]
[-22,-0.40402622583515679,-0.72337930964234287,0.48020525099313827,0.75387470870001549,0.95954845187702476,0.63698283740172967,0.57186571235918282,0.37962506568453946]
[-21,-0.38386403503541577,-0.68427085692920775,0.47330937560605141,0.69224837067922251,0.98847593712327941,0.68372768453271793,0.60903557536372344,0.421269216682567]
[-20,-0.36397023426620234,-0.64568299837777943,0.46650529501567267,0.63453372467177926,1.0175708134532444,0.73519385475843468,0.6472053260982169,0.46760517521093486]
[-19,-0.34432761328966521,-0.60758235141669581,0.45978712297398561,0.58056051220573623,1.046544397427746,0.79197105780947163,0.68619026285977935,0.51927355367944483]
[-18,-0.32491969623290629,-0.5699369579168756,0.45314922440058031,0.53017235557438991,1.0750031606219916,0.85472058215792379,0.72571346022327998,0.57700503023915839]
[-17,-0.30573068145866039,-0.53271616755911899,0.44658619481721434,0.48322574458019424,1.1024167762872814,0.92417715700389524,0.76537414402151127,0.64162784500456693]
[-16,-0.28674538575880792,-0.49589052958667679,0.44009284126087056,0.43958912626282054,1.1280773339470525,1.0011458768380654,0.80460636365863736,0.71407191618329435]
[-15,-0.2679491924311227,-0.45943169209010037,0.43366416452495871,0.39914208728990325,1.1510479769486395,1.0864906967577728,0.842625601075774,0.79536639197759973]
[-14,-0.24932800284318068,-0.42331230805611386,0.42729534259319629,0.36177461995363125,1.1700995169599513,1.1811092294090804,0.87836094126855624,0.88662562410086621]
[-13,-0.23086819112556312,-0.38750594748635386,0.42098171514377186,0.32738646382268871,1.1836346040752181,1.2858861366112375,0.91037102407875048,0.98901593025836232]
[-12,-0.2125565616700221,-0.35198701495687507,0.4147187690128612,0.29588651606979433,1.1896014040526526,1.4016142895644372,0.93674381984939004,1.1036919753870498]
[-11,-0.19438030913771848,-0.31673067204642452,0.4085021245166392,0.26719230434958752,1.1854034225178218,1.5288693494037371,0.95498433879589806,1.2316872526354561]
[-10,-0.17632698070846498,-0.28171276411157709,0.40232752253976056,0.24122951685636662,1.1678204549044264,1.6678204549044271,0.96190220008154281,1.3737387097273108]
[-9,-0.15838444032453627,-0.24690975093071738,0.3961908123060226,0.21793158486037489,1.1329690971086559,1.8179595791947982,0.95352442075810628,1.5300230687114007]
[-8,-0.14054083470239145,-0.21229864077722915,0.39008793975368999,0.19723931361713745,1.076350535214919,1.9777392883798628,0.92507933256344854,1.6997861579672433]
[-7,-0.1227845609029046,-0.17785692751571033,0.38401493644385964,0.17910055807731018,0.99305624407343818,2.1441303174393043,0.87112426919299346,1.8808642178939139]
[-6,-0.10510423526567646,-0.14356253034408697,0.37796790893537036,0.16346994030377329,0.87821975145587783,2.3121554227829244,0.78591513608389529,2.0691380952559384]
[-5,-8.7488663525924007E-2,-0.10939373582956438,0.3719430285641766,0.1503086059362404,0.72779422806947092,2.4745291611709286,0.6641204837337914,2.2580359120041584]
[-4,-6.9926811943510414E-2,-7.5329141907819391E-2,0.36593652156889539,0.13958401743851104,0.53966881946927103,2.6216219326836341,0.50193149941846704,2.4383002688098836]
[-3,-5.2407779283041196E-2,-4.1347603532999933E-2,0.35994465950743471,0.13126978222584526,0.31498188563962698,2.7420222187019552,0.29847438449886926,2.5983189234750284]
[-2,-3.492076949174773E-2,-7.428179681217062E-3,0.35396374991227908,0.1253455141053389,5.9261631612715769E-2,2.8239044088551277,5.7192169835463255E-2,2.7252914939267678]
[-1,-1.7455064928217585E-2,2.6449918577489122E-2,0.34799012713417676,0.12179672677561632,-0.21716444503650151,2.8571385811974408,-0.21337382554828904,2.807267041753724]
[0,0,6.0307379214091683E-2,0.34202014332566888,0.12061475842818334,-0.50000000000000011,2.8356409098088533,-0.50000000000000011,2.8356409098088533]
[1,1.7455064928217585E-2,9.4164839850694237E-2,0.33605015951716105,0.12179672677561627,-0.77313112054457978,2.7591066559305792,-0.78662617445171112,2.8072670417537249]
[2,3.492076949174773E-2,0.12804293810940043,0.33007653673905868,0.1253455141053389,-1.0215199085768212,2.633333463068062,-1.0571921698354636,2.7252914939267674]
[3,5.2407779283041196E-2,0.1619623619611833,0.32409562714390311,0.13126978222584523,-1.2338129858594,2.4689278952737768,-1.2984743844988695,2.5983189234750284]
[4,6.9926811943510414E-2,0.19594390033600276,0.31810376508244237,0.13958401743851107,-1.4037703164856901,2.2789411776500272,-1.5019314994184669,2.4383002688098827]
[5,8.7488663525924007E-2,0.23000849425774775,0.31209725808716116,0.15030860593624046,-1.530241683934686,2.0763765064759498,-1.6641204837337911,2.2580359120041575]
[6,0.10510423526567646,0.26417728877227031,0.3060723777159674,0.16346994030377332,-1.616060348962961,1.8723465436348632,-1.7859151360838952,2.0691380952559379]
[7,0.1227845609029046,0.29847168594389373,0.30002535020747811,0.17910055807731023,-1.6665033830606824,1.6751781983726131,-1.8711242691929932,1.8808642178939132]
[8,0.14054083470239145,0.33291339920541252,0.29395234689764782,0.19723931361713742,-1.6878653301929096,1.4903334508060635,-1.9250793325634488,1.6997861579672433]
[9,0.15838444032453627,0.36752450935890074,0.28784947434531516,0.21793158486037498,-1.6864214959679542,1.3208249484797505,-1.9535244207581057,1.5300230687114003]
[10,0.17632698070846498,0.40232752253976045,0.28171276411157725,0.24122951685636662,-1.6678204549044267,1.1678204549044271,-1.9619022000815429,1.3737387097273108]
[11,0.19438030913771848,0.43734543047460789,0.27553816213469856,0.26719230434958752,-1.6368189628036458,1.0312353973121604,-1.9549843387958983,1.2316872526354561]
[12,0.2125565616700221,0.47260177338505843,0.26932151763847656,0.29588651606979433,-1.5972399812689677,0.91021896237727995,-1.9367438198493898,1.1036919753870498]
[13,0.23086819112556312,0.50812070591453717,0.26305857150756584,0.32738646382268871,-1.5520516639005988,0.80351083681345292,-1.9103710240787504,0.98901593025836221]
[14,0.24932800284318068,0.54392706648429723,0.25674494405814147,0.3617746199536313,-1.5034970295981858,0.70968202272190484,-1.8783609412685558,0.88662562410086609]
[15,0.2679491924311227,0.58004645051828374,0.25037612212637905,0.39914208728990325,-1.453232993936284,0.62728569624512409,-1.8426256010757742,0.79536639197759973]
[16,0.28674538575880792,0.61650528801486015,0.24394744539046717,0.43958912626282065,-1.4024580026719433,0.55494422135595856,-1.8046063636586369,0.71407191618329413]
[17,0.30573068145866039,0.65333092598730236,0.23745409183412342,0.48322574458019429,-1.3520201134045293,0.49139371090506218,-1.7653741440215114,0.64162784500456682]
[18,0.32491969623290629,0.69055171634505896,0.23089106225075748,0.53017235557439002,-1.3025041933710662,0.43550188881615592,-1.7257134602232798,0.57700503023915828]
[19,0.34432761328966521,0.72819710984487918,0.2242531636773521,0.58056051220573623,-1.2543001022894651,0.38627009409465718,-1.6861902628597794,0.51927355367944483]
[20,0.36397023426620234,0.76629775680596279,0.21753499163566509,0.63453372467177938,-1.2076548921057586,0.34282652470235181,-1.6472053260982169,0.46760517521093481]
[21,0.38386403503541577,0.80488561535739112,0.21073091104528641,0.69224837067922262,-1.1627121845987889,0.30441517809355151,-1.6090355753637233,0.42126921668256695]
[22,0.40402622583515679,0.84399406807052624,0.20383503565819949,0.75387470870001561,-1.1195415608595132,0.2703831728347717,-1.5718657123591828,0.37962506568453941]
[23,0.4244748162096047,0.88365804792531666,0.19684120584752293,0.81959800598268817,-1.0781603194188123,0.24016799017405208,-1.5358122228486015,0.34211325366261303]
[24,0.4452286853085361,0.9239141746692705,0.18974296456374423,0.88961979475623765,-1.0385494793564365,0.21328545709320149,-1.5009414986781673,0.30824626075023775]
[25,0.46630765815499858,0.96480090275330033,0.18253353124963928,0.96415927198404638,-1.0006654821333965,0.1893188569083839,-1.4672834597035631,0.27759968971791366]
[26,0.48773258856586144,1.0063586821721027,0.17520577347977345,1.043454860243817,-0.96444869875535755,0.16790929838482357,-1.4348417591382847,0.2498041351303312]
[27,0.50952544949442879,1.0486301337010584,0.1677521760615085,1.1277659498792711,-0.9298295748451314,0.14874733190824443,-1.4036014069213105,0.22453788305988967]
[28,0.53170943166147877,1.0916602402101314,0.16016480730119997,1.2173748455534723,-0.89673303518425707,0.13156572758687321,-1.3735344476741513,0.2015204658282185]
[29,0.55430905145276899,1.1354965559518639,0.15243528210107726,1.3125889438077796,-0.86508160937103729,0.11613329734354402,-1.3446041756907319,0.1805070352361263]
[30,0.57735026918962573,1.1801894359699667,0.14455472150831958,1.4137431722854559,-0.83479762032171201,0.10224963369735152,-1.3167682511333114,0.16128348723705804]
[31,0.60086061902756038,1.2257922880627037,0.13651370828711254,1.5212027260242971,-0.80580468802231486,8.9740641369934079E-2,-1.289980991682713,0.14366225869540294]
[32,0.62486935190932746,1.2723618500678873,0.12830223802582288,1.6353661417906118,-0.77802873469958223,7.845474768441818E-2,-1.2641950459181441,0.12747871502419036]
[33,0.64940759319751062,1.3199584956216404,0.11990966522347862,1.7566687579777507,-0.75139862858445539,6.8259690211327453E-2,-1.2393626035053968,0.1125880513438733]
[34,0.67450851684242674,1.3686465719905945,0.11132464372083774,1.8855866153211769,-0.72584656725380359,5.9039793142504633E-2,-1.2154362587873333,9.8862636449739111E-2]
[35,0.70020753820970971,1.4184947740981326,0.10253506074947019,2.0226408628266097,-0.70130827482433433,5.0693656315327781E-2,-1.1923696154651799,8.6189736606732556E-2]
[36,0.7265425280053609,1.4695765594732295,9.3527963765081545E-2,2.1684027441592169,-0.6777230675582121,4.3132192124828897E-2,-1.1701176983495036,7.4469564029615007E-2]
[37,0.75355405010279419,1.5219706095618162,8.4289479105872936E-2,2.3234992526579057,-0.65503382788731179,3.6276955548598611E-2,-1.1486372218461323,6.3613602327644125E-2]
[38,0.78128562650671729,1.5757613436752664,7.4804721369556432E-2,2.4886195585604582,-0.63318691611777156,3.0058721154159543E-2,-1.127886752572701,5.3543167943077792E-2]
[39,{"$f":"+TAN(A145*PI()/180)","v":0.80978403319500702},{"$f":"+B145*$C$9+$C$10","v":1.6310394928326981},{"$f":"+$C$8*(1-B145)","v":6.505769222947437E-2},{"$f":"(C145^2+D145^2)","v":2.66452233049817},{"$f":"-C145/E145","v":-0.61213204114065434},{"$f":"D145/E145","v":2.4416268343793884E-2},{"$f":"+F145*(1+B145)","v":-1.1078267942634255},{"$f":"+G145*(1+B145)","v":4.4188172598802866E-2}]
[40,0.83909963117727993,1.687902741912839,5.5031167205899706E-2,2.8520440955209239,-0.59182210561318294,1.9295342344925526E-2,-1.0884198161557659,3.5486056989991882E-2]
[41,0.86928673781622645,1.7464564499032806,4.4706568666659965E-2,3.0521088086907171,-0.57221303674703172,1.4647763716470525E-2,-1.0696302407967755,2.7380870453864073E-2]
[42,0.90040404429783993,1.8068144596644,3.4063823043909758E-2,3.2657388356927246,-0.55326361064666729,1.0430663552030235E-2,-1.051424403235752,1.9822475198988332E-2]
[43,0.93251508613766154,1.8691000105668496,2.3081199911517417E-2,3.4940675912903529,-0.53493527578743671,6.6058252476431266E-3,-1.033770490566432,1.2765856947459395E-2]
[44,0.96568877480707394,1.9334467696831577,1.1735130158163874E-2,3.7383541244780663,-0.51719197949260565,3.1391167790457211E-3,-1.0166384685088654,6.1705266153787115E-3]
[45,0.99999999999999989,2,3.7971863800575365E-17,4,-0.5,9.4929659501438412E-18,-1,1.8985931900287682E-17]
[46,1.0355303137905694,2.0689178874737753,-1.2152083015056525E-2,4.2805688982305536,-0.48332778578309948,-2.8388943862297828E-3,-0.98382835945877345,-5.7786555808205945E-3]
[47,1.0723687100246826,2.1403730528106721,-2.4751556574935711E-2,4.5818094447509585,-0.46714580311993109,-5.4021357442727664E-3,-0.96809834540509598,-1.1195217083736782E-2]
[48,1.1106125148291928,2.2145542787807573,-3.7831708175493181E-2,4.9056818918096354,-0.45142639242020643,-7.7118143837772591E-3,-0.9527861933662819,-1.6276651950440063E-2]
[49,1.1503684072210094,2.2916684898859225,-5.142902418938218E-2,5.2543894120650965,-0.43614363347790852,-9.7878212207285539E-3,-0.93786949044147372,-2.1047421528582053E-2]
[50,1.19175359259421,2.3719430285641767,-6.5583591222283619E-2,5.6304149381918105,-0.42127321957658748,-1.1648092004271639E-2,-0.92332709247071509,-2.5529747497230255E-2]
[51,1.2348971565350511,2.4556282811746311,-8.0339559144910241E-2,6.0365647000682712,-0.40679234021079219,-1.3308821016032783E-2,-0.90913904443733851,-2.9743846245565593E-2]
[52,1.2799416321930788,2.5430007182156777,-9.5745677165498477E-2,6.4760198875413328,-0.39267957207913179,-1.4784648414946268E-2,-0.89528650449497549,-3.3708135438573407E-2]
[53,1.3270448216204098,2.6343664271633527,-0.11185591676453038,6.9523982186806412,-0.37891477793734279,-1.6088824783364798E-2,-0.88175167183454106,-3.7439416398087164E-2]
[54,1.3763819204711734,2.7300652337351634,-0.12873019838474123,7.4698276444256075,-0.36547901286216244,-1.7233355910267451E-2,-0.86851771847729431,-4.0953035414204607E-2]
[55,1.4281480067421144,2.8304755292818746,-0.14643524263053742,8.0330350021477734,-0.35235443746044892,-1.8229130408542397E-2,-0.85556872498632808,-4.4263026666144289E-2]
[56,1.4825609685127403,2.9360199497034634,-0.16504557161410102,8.6474531857661532,-0.33952423755657901,-1.9086032392261885E-2,-0.84288962002201062,-4.7382239060799206E-2]
[57,1.5398649638145827,3.0471720865319973,-0.18464469230037062,9.3193513873344642,-0.32697254990012287,-1.9813041125513669E-2,-0.83046612362043737,-5.0322448981309609E-2]
[58,1.6003345290410507,3.1644644559839095,-0.20532650166596808,10.055994265471925,-0.31468439345171023,-2.0418319287529164E-2,-0.81828469404282156,-5.309446066834695E-2]
[59,1.6642794823505174,3.2884980100547816,-0.22719696376182508,10.86583762247685,-0.30264560582538635,-2.0909291271926436E-2,-0.80633247802411911,-5.5708195726284354E-2]
[60,1.7320508075688767,3.4199535494817153,-0.25037612212637889,11.758770483143627,-0.29084278448875839,-2.1292712744525186E-2,-0.79459726423809318,-5.8172773049012153E-2]
[61,1.8040477552714236,3.5596054976594544,-0.27500052849861462,12.74641658964193,-0.27926323234657829,-2.1574732519105581E-2,-0.78306743979126492,-6.0496580290779395E-2]
[62,1.8807264653463318,3.7083386257631359,-0.30122619190846217,13.842512582018497,-0.2678949073580969,-2.1760947669266107E-2,-0.77173194955797353,-6.2687337861871445E-2]
[63,1.9626105055051504,3.8671684942193334,-0.32923218305966612,15.063385993044861,-0.25672637586296343,-2.1856452673501215E-2,-0.76058025817187935,-6.4752156303590824E-2]
[64,2.050303841579296,4.0372666110944522,-0.35922507043245144,16.428564340285281,-0.24574676931413139,-2.1865883286683683E-2,-0.74960231449459602,-6.6697587788895757E-2]
[65,2.1445069205095586,4.2199916281507956,-0.39144442098989918,17.961558076386918,-0.2349457441389001,-2.1793455741710394E-2,-0.73878851838903947,-6.8529672401627106E-2]
[66,2.2460367739042164,4.4169283355698887,-0.42616967599977418,19.690876514301937,-0.22431344447068022,-2.1643001807981344E-2,-0.72812968963294944,-7.0253979766382882E-2]
[67,2.3558523658237518,4.6299368288634479,-0.46372882048748681,21.651359458216834,-0.21384046751421681,-2.1418000166797777E-2,-0.71761703881644168,-7.1875646530961831E-2]
[68,2.4750868534162964,4.8612150845898956,-0.50450941702325158,23.885941850509489,-0.20351783132580159,-2.1121604506145541E-2,-0.70724214007608843,-7.3399410142364771E-2]
[69,2.6050890646938005,5.113379414490721,-0.54897279195703741,26.448020162846571,-0.19333694480745486,-2.0756668687368092E-2,-0.69699690552666438,-7.4829639304302933E-2]
[70,2.7474774194546216,5.389569055506132,-0.59767247746023966,29.404666994382719,-0.18328957973017415,-2.0325769292827402E-2,-0.6868735612601552,-7.6170361457914823E-2]
[71,2.9042108776758222,5.6935837878480511,-0.65127847730498245,32.841060004246856,-0.17336784461621466,-1.9831225825864392E-2,-0.676864624789837,-7.7425287586985442E-2]
[72,3.0776835371752527,6.0300674253872026,-0.71060962117006266,36.866679188415304,-0.16356416032399371,-1.9275118801406962E-2,-0.66696288382504276,-7.8597834613594347E-2]
[73,3.2708526184841404,6.404756066966045,-0.77667733804541617,41.624127964771674,-0.15387123719172377,-1.8659305936757457E-2,-0.65716137626966764,-7.9691145619097251E-2]
[74,3.4874144438409087,6.8248194415544958,-0.85074584459280655,47.301928901912149,-0.1442820536073024,-1.7985436626843682E-2,-0.64745337134443703,-8.0708108098083639E-2]
[75,3.7320508075688776,7.2993387910535343,-0.93441640877771692,54.153480811571917,-0.13478983588241955,-1.7254964866045025E-2,-0.63783235173947994,-8.1651370428940967E-2]
[76,4.010780933535842,7.8399895595823814,-1.0297477264101198,62.525816674407551,-0.12538803931834719,-1.6469160759184549E-2,-0.62829199670981661,-8.2523356723458605E-2]
[77,4.3314758742841573,8.4620391696752613,-1.1394318560086756,72.904411863605759,-0.11607033035952044,-1.5629120747046112E-2,-0.61882616603197516,-8.3326280199150338E-2]
[78,4.7046301094784511,9.1858436860966428,-1.2670581210124083,85.98516050742505,-0.1068305697388728,-1.4735776656519638E-2,-0.60942888474511125,-8.4062155201331631E-2]
[79,5.1445540159703071,10.039160841226206,-1.417520958563141,102.79411606397542,-9.7662796526001419E-2,-1.3789903671927351E-2,-0.600094328604733,-8.4732807987184897E-2]
[80,5.6712818196177066,11.060850875123837,-1.5976724774602393,124.89497942696168,-8.8561212995692903E-2,-1.2792127312007403E-2,-0.59081681018145749,-8.5339886370830106E-2]
[81,6.3137515146750411,12.307044601705121,-1.8174100546461476,154.76632613508806,-7.9520170240152205E-2,-1.1742929486223108E-2,-0.58159076554113032,-8.5884868316586455E-2]
[82,7.1153697223841954,13.861937523886192,-2.0915796289392983,196.52801726031791,-7.0534154453534684E-2,-1.064265369435252E-2,-0.57241074144618564,-8.6369069556968728E-2]
[83,8.1443464279745932,15.857836046680482,-2.4435103892641008,257.44170710584046,-6.1597773822098474E-2,-9.491509424537475E-3,-0.56327138302129309,-8.6793650302356445E-2]
[84,9.5143644542225871,18.515249902537391,-2.9120841509601898,351.29471305568438,-5.2705745957533114E-2,-8.2895757969992274E-3,-0.554167421829172,-8.7159621100552545E-2]
[85,11.430052302761348,22.231095486077258,-3.5672879834846589,506.94715006819871,-4.3852885814796565E-2,-7.0368044933377333E-3,-0.54509366430494255,-8.7467847896494089E-2]
[86,14.300666256711896,27.799204189680196,-4.54909577944749,793.49002599011999,-3.5034094039168594E-2,-5.7330220046195417E-3,-0.53604498049957827,-8.7719056335069018E-2]
[87,19.081136687728161,37.071847408607681,-6.1841129614277959,1412.5651234067914,-2.6244345690199875E-2,-4.3779312252259896E-3,-0.52701629308489317,-8.7913835343236324E-2]
[88,28.636253282915515,55.605836559041563,-9.4521553088072512,3181.3522994126561,-1.7478679292861579E-2,-2.9711124135960408E-3,-0.51800256657409638,-8.8052640021346704E-2]
[89,57.289961630759876,111.18522319950685,-19.252300744748894,12732.804941890416,-8.7321861684782395E-3,-1.5120235354748582E-3,-0.50899879671324866,-8.8135793867635384E-2]
[90,1.6324552277619072E+16,3.1664613590531508E+16,-5583325709718649,1.0338212798184779E+33,-3.06287113727155E-17,-5.4006681993419502E-18,-0.5,-8.8163490354232529E-2]

{"sheet":"Determine Link Lengths","index":1,"n_rows":50,"n_cols":12,"rows_kept":50,"cut":false,"hidden":false,"merged":[[1,1,4,7]]}
[]
[null,"Note: The mechanism satisfies the given swing angle and the corresponding crank angle specified in the first sheet (Geometric Loci sheet)."]
[]
[]
[]
[]
[null,"Determine the link lengths for a given value of the l parameter."]
[null,"l"]
[null,0.25]
[null,null,"s",{"$f":"+f","v":100},null,null,2]
[null,"a2",{"$f":"B9/2*SQRT(1/('Geometric Loci'!D7^2+B9^2*'Geometric Loci'!D8^2))","v":0.41489770888467281},{"$f":"+C11*D10","v":41.489770888467284},null,null,45,0,{"$f":"+D13","v":88.313077045175561}]
[null,"a3",{"$f":"+C11/B9","v":1.6595908355386912},{"$f":"+C12*D10","v":165.95908355386914},null,null,{"$f":"SliderCrnk(D11,D12,-D13,1,G11*PI()/180)","v":146.38774090855674},{"$f":"+D11*COS(G11*PI()/180)","v":29.337698345111427},{"$f":"+D11*SIN(G11*PI()/180)+D13","v":117.65077539028698},null,{"$f":"+SQRT((H13-H12)^2+(I13-I12)^2)","v":165.95908355386914}]
[null,"c",{"$f":"0.5*(1-B9^2)*'Geometric Loci'!C8/((1+B9^2)+(1-B9^2)*'Geometric Loci'!C7)","v":0.88313077045175559},{"$f":"+C13*D10","v":88.313077045175561},null,null,null,{"$f":"+G12","v":146.38774090855674},0]
[null,null,null,null,null,null,null,null,null,null,{"$f":"+H13-12","v":134.38774090855674},6]
[null,"b",{"$f":"+ATAN((C11+C12)/C13)-PI()/2","v":-0.40247197301634041},null,null,null,null,null,null,null,{"$f":"+H13+12","v":158.38774090855674},6]
[null,null,{"$f":"+C15*180/PI()","v":-23.059945426139457},null,null,null,null,null,null,null,{"$f":"+K15","v":158.38774090855674},-6]
[null,null,null,null,null,null,null,null,null,null,{"$f":"+K14","v":134.38774090855674},-6]
[null,null,null,null,null,null,null,null,null,null,{"$f":"+K17","v":134.38774090855674},6]
[0,{"$f":"+D13","v":88.313077045175561}]
[{"$f":"+D11*COS(C15)","v":38.174553532200306},{"$f":"+D11*SIN(C15)+D13","v":72.061783219923356}]
[{"$f":"SliderCrnk(D11,D12,-D13,1,C15)","v":187.67210138234026},0]
[]
[0,{"$f":"+B19","v":88.313077045175561}]
[{"$f":"+D11*COS(C15+'Geometric Loci'!C6)","v":-30.314076412664949},{"$f":"+D11*SIN(C15+'Geometric Loci'!C6)+'Determine Link Lengths'!B23","v":116.64076420146522}]
[{"$f":"SliderCrnk(D11,D12,-D13,1,+C15+y*PI()/180)","v":87.7424758855379},0]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[0]

{"sheet":"Optimum","index":2,"n_rows":35,"n_cols":7,"rows_kept":35,"cut":false,"hidden":false,"merged":[]}
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["lopt=",{"$f":"SQRT(0.5/'Geometric Loci'!C11^2*(SQRT(5+4*'Geometric Loci'!C11^2)-1))","v":0.40518527345362754},{"$f":"+B11^2","v":0.16417510582369094}]
[]
["s",1,{"$f":"+f","v":100}]
["a2",{"$f":"+B11/2*SQRT(1/('Geometric Loci'!D7^2+B11^2*'Geometric Loci'!D8^2))","v":0.46554164644585572},{"$f":"+$C$13*B14","v":46.554164644585569}]
["a3",{"$f":"+B14/B11","v":1.1489599374571935},{"$f":"+$C$13*B15","v":114.89599374571935}]
["c",{"$f":"0.5*(1-B11^2)*'Geometric Loci'!C8/((1+B11^2)+(1-B11^2)*'Geometric Loci'!C7)","v":0.37737815609162328},{"$f":"+$C$13*B16","v":37.737815609162325}]
[]
[]
[null,2]
[null,32,0,{"$f":"+C16","v":37.737815609162325}]
[null,{"$f":"SliderCrnk(C14,C15,-C16,1,B20*PI()/180)","v":135.9496494735825},{"$f":"+C14*COS(B20*PI()/180)","v":39.480170694993589},{"$f":"+C14*SIN(B20*PI()/180)+C16","v":62.40776428461259},null,{"$f":"+SQRT((C22-C21)^2+(D22-D21)^2)","v":114.89599374571935}]
[null,null,{"$f":"+B21","v":135.9496494735825},0]
[null,null,null,null,null,{"$f":"+C22-8","v":127.9496494735825},5]
[null,null,null,null,null,{"$f":"+C22+8","v":143.9496494735825},5]
[null,null,null,null,null,{"$f":"+F24","v":143.9496494735825},-5]
["b",{"$f":"+ATAN((C14+C15)/C16)-PI()/2","v":-0.22962024333860032},{"$f":"+B26*180/PI()","v":-13.156270834068755},null,2866.8437291659311,{"$f":"+F23","v":127.9496494735825},-5]
["maxmmin",{"$f":"+ACOS((C14+C16)/C15)","v":0.74713722773369562},{"$f":"+B27*180/PI()","v":42.807809866245393},null,null,{"$f":"+F26","v":127.9496494735825},5]
[]
[0,{"$f":"+C16","v":37.737815609162325},0,{"$f":"+B29","v":37.737815609162325}]
[{"$f":"+C14*COS(B26)","v":45.332252865952391},{"$f":"+C14*SIN(B26)+B29","v":27.141726903770497},{"$f":"+C14*COS(B26+'Geometric Loci'!C6)","v":-38.974307724026694},{"$f":"+C14*SIN(B26+'Geometric Loci'!C6)+C16","v":63.199425597300426},null,{"$f":"+ACOS((C16+C14)/C15)*180/PI()","v":42.807809866245393},{"$f":"180/PI()*ACOS((B16+B14)/B15)","v":42.8078098662454}]
[{"$f":"SliderCrnk(C14,C15,-C16,1,B26)","v":156.97640201626623},0,{"$f":"SliderCrnk(C14,C15,-C16,1,B26+'Geometric Loci'!C6)","v":56.978399288270076},0]
[]
[{"$f":"SliderCrnk($B$14,$B$15,-$B$16,1,+PI()/2)","v":0.78076574231443763},{"$f":"+ATAN(A33/(B16+B14))*180/PI()","v":42.807809866245385}]
[{"$f":"SliderCrnk(B14,B15,-B16,1,-PI()/2)","v":1.1455724057649945},{"$f":"+ATAN(A34/(B14-B16))*180/PI()","v":85.599179724998379}]
[{"$f":"SliderCoupler(B14,B15,B16,1,+PI()/2)*180/PI()-90","v":85.599179724998379}]