DIY Laser-Cut Clock: 4 Cov Kauj Ruam (nrog Duab)

2024 Tus sau: John Day | [email protected]. Kawg hloov kho: 2024-01-30 09:29

Txais tos rau kuv cov lus qhia yuav ua li cas kom ntxim hlub, laser-txiav moos! Kuv tau txais kev tshoov siab rau txoj haujlwm no los ntawm qhov tseeb tias kuv yuav tsum mus rau qee lub tshoob nyob rau lub caij ntuj sov dhau los no thiab kuv xav ua qee yam khoom plig tshwj xeeb rau cov tib neeg sib yuav. Kuv kuj xav tias nws yuav yog ib txoj hauv kev zoo los siv qee cov hauv paus ntsiab lus zauv uas kuv tau kawm, uas kuv yuav hais hauv thawj feem ntawm qhov kev qhia no. Kuv tsis paub meej tias kuv tuaj yeem npog qhov ntawd tau zoo li cas, tab sis ob txoj hauv kev kuv yuav muab qee qhov Python code kom koj tuaj yeem tsim ntau yam qauv raws li koj nyiam. Ib qho ntxiv, Kuv muaj cov pawg tsim qauv uas kuv tau tsim uas yuav suav nrog hauv cov phiaj xwm cov ntaub ntawv ua SVGs.

Rau qhov haujlwm no, koj yuav xav tau:

• plywood lossis acrylic rau lub moos hu
• vector duab kho software
• nkag mus rau lub tshuab txiav laser
• lub moos txav nrog 1/4 "ncej

Cov ntaub ntawv xaiv muaj xws li:

• xim dawb
• 120 & 220 grit xuab zeb ntawv
• tsaus nti
• ntoo kua nplaum
• 4 X 3/8 "screws
• ntoo foob

Cia peb pib!

Kauj Ruam 1: Math…

Kuv xav tias qhov no yog ib qho tseem ceeb tshaj plaws ntawm txoj haujlwm no, txawm li cas los xij kuv yuav tsis tuav nws tawm tsam koj kom hla ntu no. Vam tias kuv ua txoj haujlwm OK ntawm kev piav qhia txog dab tsi tshwm sim, tab sis thov xa mus rau phau ntawv Tsim Kom Zoo Nkauj: Kev Txawj Ntse ntawm Kev Ua Lej Ntawm Cov Duab Wallpaper los ntawm Frank Farris. Nws ua txoj haujlwm zoo tiag tiag ntawm kev piav qhia tias cov xwm txheej no tshwm sim li cas. Rau qhov luv dua tab sis ntau dua "tes-yoj" saib, txheeb xyuas qhov Quanta Magazine puzzle thiab nws yog kev daws teeb meem. Kuv yuav tsim qhov kev daws teeb meem rau Quanta Magazine thiab kom nws npaj mus rau hauv tus lej kuv tshaj tawm hauv qab no.

Txhawm rau nkag siab tias peb ua tau zoo li cas, thawj zaug peb yuav tsum paub tias e^(i * 2 pi * C) = 1 rau txhua tus lej C. Qhov no los ntawm Euler tus kheej, uas kuv yuav tsis tham txog ntawm no tab sis nws tseem ceeb heev thiab txhua tus xav tias nws yog qhov loj tshaj, yog li tshawb xyuas nws. Kuv siv qhov tseeb saum toj no kom tau txais qhov "A" nkhaus los ntawm Quanta teeb meem (saib daim duab), uas tau tham txog hauv Quanta teeb meem kev daws teeb meem me ntsis. Hauv qhov muab los, "k" yog tus naj npawb ntawm cov khoom sib npaug uas peb xav tau hauv peb txoj kab nkhaus. Zoo li ob qho tib si "m" thiab "n", "k" yuav tsum yog ib tus lej txhawm rau kom muaj qhov nkhaus sib npaug. Hauv cov cai hauv qab no, peb pom tias C1 = 1 thiab C2 = -3 nrog mod = 5 txhawm rau tsim cov nkhaus los ntawm qhov teeb meem. Tus qauv sib txawv sawv cev rau "modulus" thiab yuav tsum yog tus lej tib yam li "k". (Faj seeb: kom khiav cov cai, tus lej, matplotlib, thiab tsev qiv ntawv sympy yuav tsum tau teeb tsa.)

import numpy as np

ntshuam matplotlib.pyplot li plt los ntawm sympy ntshuam exp, kuv, re, im, cim, lambdify t = cim ('t') fig = plt.figure (figsize = (6, 6)) # Rau mod = 12, tseem tshuav tau tsuas yog [1, 5, 7, 11] seem = 1 mod = 5 l = seem m = 1*mod + seem n = -3*mod + coeffs seem = np.array ([1, 1/2, I/ 3]) exps = np.array ([exp (l*I*t), exp (I*m*t), exp (I*n*t)]) f = (coeffs*exps. T).sum () x = lambdify (t, re (f)) y = lambdify (t, im (f)) xarray = [x (t) for t in np.linspace (0, 2*np.pi, 5000)] yarray = [y (t) for t in np.linspace (0, 2*np.pi, 5000)] plt.plot (xarray, yarray) plt.axis ('off') plt.gca (). set_position ([0, 0, 1, 1]) #plt.savefig (r'path / to / folder / test.svg ') plt.show () print (' / t / t / t ' + str (f))

Tab sis vim li cas kuv thiaj hla dhau txhua qhov teeb meem no? Zoo, kuv xav tias nws zoo nkauj heev, tab sis kuv kuj xav kawm txhua yam ntawm no kom ua lub moos nrog 12-npaug sib npaug. Txoj kev ntawd, tsis tas yuav tso qee tus lej tsis zoo ntawm lub ntsej muag thiab tib neeg tseem tuaj yeem pom lub sijhawm twg nws yooj yim. Dab tsi yog qhov zoo yog txhua yam peb yuav tsum tau ua kom nkhaus nrog 12-npaug sib npaug yog hloov pauv mus rau 12 hauv cov cai saum toj no! Tom qab ntawd, sim hloov qee qhov coefficients ntawm mod rau n thiab m thiab cov lej hauv cov coeffs vector thiab saib seb nkhaus nws zoo li cas. Ib yam uas yuav tsum nco ntsoov, yog tias koj hloov qhov seem, koj yuav tau txais nkhaus nrog 2, 3, 4, lossis 6-fold symmetry. Nws yog qhov txawv heev, tab sis nws los ntawm qhov tseeb tias cov lej sib koom muaj teeb meem! Cia peb saib ib qho piv txwv:

Yog tias k = 12, thiab m = 1 * k + 2 = 14, ces (m - 2)/k = m/k - 2/k = 14/12 - 2/12 = 1 2/12 - 2/12 = 1 1/6 - 1/6 = 1 k = 6, seem = 1

Peb pom tias vim ob faib kaum ob, peb tau txais cov lus teb zoo ib yam li yog peb muaj tus lej ntawm 6 thiab seem ntawm 1! Qhov tseeb, nrog k = 12 thiab seem = 2, txhua qhov haujlwm tau ua raws kab nkhaus rau k = 6 nrog seem = 1 ob zaug, ib qho nyob rau lwm qhov! Yog li, rau 12 qhov sib xyaw ua ke qhov seem tsuas yog tus lej uas tsis faib 12, uas yog [1, 5, 7, 11] txog 12, tab sis kuj tseem muaj lwm tus lej tseem ceeb yav dhau los 12. Zoo nkauj heev!

Kuv vam tias qhov kuv tau tham txog ntawm no tau ua rau txhua tus nyiam hauv cov ncauj lus. Ib zaug ntxiv, Frank Farris phau ntawv saum toj no yog cov peev txheej zoo thiab kuv vam tias tib neeg muaj kev lom zem ua qee qhov nkhaus zoo nrog kuv cov ntawv nab nab. Tam sim no, rov qab mus rau txoj haujlwm ntawm tes!

Kauj Ruam 2: Npaj rau Laser Txiav

Cov duab uas peb tab tom txiav tawm los ua lub moos yog qhov tsis yooj yim rau kev npaj. Kuv tau suav nrog cov kab nkhaus uas kuv tus kheej nyiam, yog li xav tias siv tau cov ntawd. Cov khoom tuaj yeem yog txhua yam uas tuaj yeem muab tso rau hauv lub tshuab txiav laser kom nyab xeeb, tab sis kuv tau xaiv 1/4 "plywood nrog lub ntsej muag ntoo ntoo zoo nkauj. duab program. Tom qab ntawd koj tuaj yeem rov ntsuas qhov nkhaus hauv daim disk yooj yim kom ua tau zoo. Kuv kuj tau coj lwm qhov nkhaus uas tuaj yeem raug txiav tawm rau ciam teb rau kuv lub moos, uas kuv tau hais qhia zoo vim tias nws tau ntxiv ntau heev. Ib yam uas koj yuav tsum paub txog ua ntej txiav yog hom kev txav mus los uas koj yuav siv. Amazon muaj pawg rau pheej yig, thiab Michael's muaj lawv ib yam yog tias koj xav tawm mus thiab yuav ib qho tam sim no. Koj yuav xav paub lub taub taub, uas kuv xav tias yog 5/16 "rau feem ntau.

Kev hu xov tooj tiav yuav tsum yog 10 "disk nrog txoj kab nkhaus koj xav taug hauv, thiab lub qhov nyob hauv nruab nrab rau qhov txav txav uas yog 5/16" hauv txoj kab uas hla. Nco ntsoov tias ntau txoj kab ntawm tus qauv hla ib leeg, qhov tob ntawm lub laser yuav txiav rau hauv koj cov khoom! Yog tias koj sim txiav qhov tsim qauv nyuaj, koj yuav tsuas yog ua yuam kev txiav los ntawm koj lub xov tooj.

Tus tsim kuv siv uas suav nrog ciam teb thiab tsim yog thawj.svg cov ntaub ntawv.

Kauj Ruam 3: Txiav Koj Dial

Tam sim no koj nqa koj cov ntawv thiab thauj nws mus rau hauv koj lub tshuab txiav laser. Koj yuav xav kom muaj tus tsim thiab ob lub voj voos ntawm cov chaw sib cais. Txog kev tsim qauv, ib qho ntawm cov txheej txheem uas kuv tau siv los taug nws tawm yog txav lub rooj me ntsis tawm ntawm kev tsom mus los ntawm lub tshuab txiav laser. Txoj kev ntawd, kab tau txiav tuab dua rau saum npoo.

Qhov no lom zem heev. Koj tau pom lub laser taug qab koj tus tsim ntawm lub xov tooj, uas yog zoo nkauj zoo saib thaum nws tshwm sim.

Kauj ruam 4: Ua tiav Koj Lub Sijhawm

Yog tias koj siv ntoo, ntoo uas nyias ua kom yooj yim yog li nws yuav yog lub tswv yim zoo los muab nws khi yam tsawg. Ib yam uas kuv tau ua yog kuv pleev xim tshaj qhov tsim xim dawb thiab tom qab ntawd pleev xim rau ntawm lub ntsej muag. Qhov no tau muab cov qauv tsim kom zoo nkauj tawm tsam cov ntoo, txawm li cas los xij koj yuav tsum tau ceev faj thaum txhuam vim tias cov ntoo zoo nkauj laminate zoo nkauj nyias thiab nws yooj yim rau xuab zeb hla.

Kuv kuj tau mus thiab tau txais ib qho piv txwv ntawm qhov tsaus ntuj nti los ntawm Tsev Depot rau ciam teb ntawm lub ntsej muag lub ntsej muag. Tom qab ntawd kuv muab qee cov ntoo nplaum rau ntawm ciam teb thiab txuas nws nrog 4 3/8 screws. Cov ntsia hlau ntxiv tau ua kom cov ciam teb txuas rau hauv qab kev ntxhov siab ntawm kev ua rog. cov lus qhia ntawm lub moos txav pob los teeb tsa lub zog thiab saib koj lub moos tshiab pib zuam!

Kuv zoo siab heev nrog qhov tshwm sim, thiab cov neeg kuv muab rau nws los hlub nws ib yam. Kuv vam tias koj tau pom qhov kev qhia no lom zem thiab nthuav, thiab thov qhia rau kuv paub tias lub moos txias twg uas koj ua!