Tsarin Motsi Mai Sanin Singularity don Ƙirƙirar Ƙari ta Multi-Axis

1. Gabatarwa

Ƙirƙirar Ƙari ta Multi-Axis (MAAM) tana wakiltar babban ci gaba fiye da buga 3D na yau da kullun na tushen layer mai lebur. Ta ba da damar sanya kayan aiki tare da hanyoyi masu canzawa (misali, tare da ma'auni na saman), tsarin MAAM suna ba da mafita ga matsalolin da suka daɗe kamar buƙatar tsarin tallafi, raunin ƙarfi tsakanin layer, da kuma abubuwan da ba su dace ba akan saman da suka lanƙwasa. Duk da haka, wannan ƙarin 'yancin geometric yana gabatar da ƙalubalen tsara motsi masu rikitarwa, musamman lokacin aiwatar da hanyoyin kayan aiki da aka tsara akan dandamalin kayan aiki waɗanda galibi suna haɗa axis uku na motsi da axis biyu na juyawa.

1.1 Matsalar Tsarin Motsi a cikin MAAM

Babban ƙalubalen yana cikin maƙasudin da ba na layi ba tsakanin tsarin ma'auni na aikin (WCS), inda aka tsara hanyar kayan aiki, da tsarin ma'auni na injin (MCS), wanda ke sarrafa na'urorin motsa jiki. Hanyar kayan aiki mai santsi, wacce aka yi samfurin daidai a cikin WCS, za a iya sanya ta zuwa motsi mara ci gaba a cikin MCS lokacin da alkiblar kayan aiki ta kusanci tsaye—wani yanki da aka sani da kinematic singularity. A cikin ƙirƙirar ƙari ta tushen filament, wannan rashin ci gaba yana rushewar kwararar fitarwa mai tsayi, yana haifar da wuce gona da iri ko ƙarancin fitarwa, wanda ke bayyana a matsayin abubuwan da ba su dace ba akan saman kuma yana lalata amincin injiniya. Ba kamar a cikin niƙa na CNC inda za a iya dakatar da motsi ba, ƙirƙirar ƙari tana buƙatar motsi mai ci gaba kuma dole ne ta bi ƙuntatawa na gudu ($f_{min} \leq v_{tip} \leq f_{max}$) waɗanda iyakokin jiki na injin fitarwa suka ƙaddara. Bugu da ƙari, dole ne a haɗa kariya daga karon juna cikin tsarin tsara.

2. Bayanan Baya da Ayyukan Da Suka Danganta

2.1 Tsarin Ƙirƙirar Ƙari ta Multi-Axis

Akwai nau'ikan tsarin kayan aiki daban-daban, gami da tsarin da ke da teburin aiki mai karkatarwa (misali, axis 3+2) ko hannun robot (6-DOF). Waɗannan tsarin suna ba da damar buga abubuwan da ba su da tallafi ta hanyar daidaita alkiblar sanyawa da ma'auni na saman.

2.2 Samarwar Hanyar Kayan Aiki don Layer Mai Lanƙwasa

Bincike ya mayar da hankali kan samar da hanyoyin kayan aiki marasa lebur, masu lanƙwasa don inganta ƙarfi da ƙarewar saman. Duk da haka, aiwatar da waɗannan hanyoyi masu rikitarwa a zahiri galibi ana yin watsi da su.

2.3 Singularity a cikin Injiniyanci na CNC na Multi-Axis

Singularity wata sananniya matsala ce a cikin injiniyanci na CNC na axis 5, inda axis na kayan aiki ya yi daidai da axis na juyawa, yana haifar da rashin ci gaba na lissafi a cikin mafita na kinematics na baya. Mafita na CNC na gargajiya galibi sun haɗa da gyara hanyar kayan aiki ko sake daidaita ma'auni, amma ba za a iya amfani da su kai tsaye ga ƙirƙirar ƙari ba saboda buƙatar ci gaba da fitarwa da iyakacin gudu.

3. Hanyar Da Aka Gabatar

3.1 Tsarin Matsala

Shigarwa shine hanyar kayan aiki da aka ayyana a matsayin jerin maki hanya $\mathbf{W}_i = (\mathbf{p}_i, \mathbf{n}_i)$ a cikin WCS, inda $\mathbf{p}_i$ shine matsayi kuma $\mathbf{n}_i$ shine alkiblar bututu (yawanci ma'auni na saman). Manufar ita ce nemo jerin motsi daidai a cikin MCS, $\mathbf{M}_j = (x_j, y_j, z_j, A_j, C_j)$ don na'urar axis 5 na yau da kullun (XYZAC), wanda:

1. Ya guje wa kinematic singularities ko ya sarrafa tasirinsu.
2. Ya ci gaba da ci gaba don tabbatar da fitarwa mara katsewa.
3. Ya kiyaye gudun ƙarshen bututu a cikin $[v_{min}, v_{max}]$.
4. Ya guje wa karon juna tsakanin kan bugawa da ɓangaren.

3.2 Algorithm na Tsarin Motsi Mai Sanin Singularity

Takardar ta gabatar da algorithm wanda ke gano yankunan singular a cikin hanyar kayan aiki (misali, inda ɓangaren tsaye na vector na al'ada yana kusa da 1). Maimakon yin samfurin maki hanya daidai a cikin WCS, yana yin samfurin daidaitacce da inganta hanyar kayan aiki na gida a cikin waɗannan yankuna. Wannan na iya haɗawa da ɗan bambanci a cikin alkibla ko sake daidaita lokacin motsi don sassauta tsalle-tsalle marasa ci gaba a cikin axis na juyawa ($A$, $C$), ta haka yana hana canje-canje kwatsam a cikin gudun ƙarshen bututu.

3.3 Haɗin Kariya daga Karon Juna

Mai tsara motsi ya haɗa mai duba karon juna na tushen samfurin. Lokacin da aka gano yuwuwar karon juna yayin tsara motsin gujewa singularity, algorithm yana daidaita hanyar kayan aiki ko matsayin injin a jere har sai an sami mafita mara karon juna kuma an sarrafa singularity.

4. Cikakkun Bayanan Fasaha da Tsarin Lissafi

Ana iya bayyana kinematics na baya don na'urar axis 5 na yau da kullun tare da tebur mai karkatarwa (axis AC akan tebur). Vector alkiblar kayan aiki $\mathbf{n} = (n_x, n_y, n_z)$ a cikin WCS ana sanya shi zuwa kusurwoyin juyawa $A$ (karkata) da $C$ (juyawa). Tsarin gama gari shine:

$A = \arccos(n_z)$

$C = \operatorname{atan2}(n_y, n_x)$

Singularity yana faruwa lokacin da $n_z \approx \pm 1$ (watau $A \approx 0^\circ$ ko $180^\circ$), inda $C$ ya zama mara ma'ana—yanayin kulle gimbal. Matrix Jacobian da ke da alaƙa da gudun haɗin gwiwa zuwa gudun ƙarshen kayan aiki ya zama mara kyau a nan. Algorithm na takardar yana iya sa ido kan lambar yanayin wannan Jacobian ko ƙimar $n_z$ don gano yankunan singular. Tushen tsarin ya haɗa da warware matsalar ingantawa wacce ke rage aikin farashi $J$:

$J = \alpha J_{continuity} + \beta J_{speed} + \gamma J_{singularity} + \delta J_{collision}$

inda $J_{continuity}$ yana hukunta rashin ci gaba a cikin motsin MCS, $J_{speed}$ yana tabbatar da iyakokin gudun ƙarshen, $J_{singularity}$ yana hukunta kusanci da tsarin singular, kuma $J_{collision}$ hukunci ne na karon juna. Ma'auni $\alpha, \beta, \gamma, \delta$ suna daidaita waɗannan manufofin.

5. Sakamakon Gwaji da Bincike

5.1 Saitin Gwaji

An tabbatar da hanyar akan na'urar buga 3D ta axis 5 na al'ada (juyawa XYZ, teburin juyawa AC) tana ƙirƙira samfura kamar Stanford Bunny tare da layer masu lanƙwasa.

5.2 Kwatancen Ingancin Ƙirƙira

Hoto 1 (An ambata daga PDF): Yana nuna kwatancen gani bayyananne. Bunny da aka buga tare da tsarin gargajiya (Hoto 1a) yana nuna abubuwan da ba su dace ba akan saman (wuce gona da iri/ƙarancin fitarwa) a yankunan da aka kewaye, wanda ya dace da yankunan inda ma'auni na saman yake kusa da tsaye (yankin singular). Bunny da aka buga tare da tsarin tsara mai sanin singularity da aka gabatar (Hoto 1c) yana nuna saman da suka fi santsi sosai a waɗannan yankuna guda. Hoto 1b yana nuna maki hanya da ke cikin yankin singular a rawaya, yana nuna ikon gano algorithm.

5.3 Ci gaba da Motsi da Binciken Gudu

Zane-zane na kusurwoyin axis na juyawa ($A$, $C$) da ƙididdige gudun ƙarshen bututu akan lokaci zai nuna cewa hanyar da aka gabatar tana sassauta kusancin tsalle-tsalle marasa ci gaba a cikin kusurwoyin juyawa da aka gani a cikin hanyar gargajiya. Saboda haka, gudun ƙarshen bututu ya kasance a cikin taga fitarwa mai tsayi $[v_{min}, v_{max}]$, yayin da hanyar gargajiya ke haifar da haɓaka gudu ko faɗuwa zuwa kusan sifili, yana bayyana kuskuren fitarwa kai tsaye.

6. Tsarin Bincike: Nazarin Lamari Ba tare da Code ba

Yanayi: Buga abu mai siffar kumfa tare da axis na tsaye na daidaito.
Kalubale: Koli na kumfa yana da ma'auni na tsaye ($n_z=1$), yana sanya shi kai tsaye a cikin tsarin singular. Hanyar kayan aiki ta karkace daga tushe zuwa koli zai haifar da axis C ya yi juyawa ba tare da sarrafawa ba yayin da yake gabatowa saman.
Aikace-aikacen Hanyar Da Aka Gabatar:

1. Gano: Algorithm yana gano maki hanya a cikin kofa (misali, $n_z > 0.98$) a matsayin yankin singular.
2. Tsara: Maimakon tilasta kayan aiki su nuna daidai tsaye a koli, mai tsara na iya gabatar da ɗan karkata, mai sarrafawa (misali, $A=5^\circ$) na 'yan layer a kusa da koli. Wannan yana kiyaye axis C da kyau.
3. Ingantawa: Hanyar kayan aiki a wannan yanki ana sake daidaita lokacinta don tabbatar da bututu yana motsawa a madaidaicin gudu mai kyau, kuma ana rama ɗan bambancin geometric a cikin hanyar da ba ta singular da ke kusa don kiyaye amincin siffar gaba ɗaya.
4. Sakamako: An sami motsi mai santsi, mai ci gaba, wanda ya haifar da kumfa tare da ƙarewar saman daidai a koli, ba tare da kuraje ko gibi ba.

7. Duban Aikace-aikace da Hanyoyin Gaba

• Kayan Aiki Masu Ci Gaba & Hanyoyin Aiki: Wannan tsarin yana da mahimmanci don buga tare da haɗaɗɗen fiber mai ci gaba ko siminti, inda sarrafa kwarara ya fi muni ga rashin ci gaba na motsi.
• Haɗin kai tare da Ƙirar Samarwa: Software na gaba CAD/CAE na iya haɗa "ƙuntatawa na iya yin kera" bisa wannan samfurin singularity yayin lokacin ƙirar samarwa, yana guje wa ƙira waɗanda ke da wahalar bugawa da santsi akan tsarin multi-axis.
• Koyon Injini don Tsara Hanya: Za a iya horar da wakilan ƙarfafawa don kewaya sararin ciniki mai rikitarwa tsakanin gujewa singularity, kiyaye gudu, da gujewa karon juna da kyau fiye da ingantawa na gargajiya.
• Daidaituwa & Yankawa na Girgije: Yayin da buga multi-axis ya zama mai sauƙi, sabis na yankawa na tushen girgije na iya ba da tsarin hanyar kayan aiki mai ingantacce na singularity a matsayin fasali mai daraja, kamar yadda ake inganta tallafi a yau.

8. Nassoshi

1. Ding, D., et al. (2015). A review on 5-axis CNC machining. International Journal of Machine Tools and Manufacture.
2. Chen, X., et al. (2021). Support-Free 3D Printing via Multi-Axis Motion. ACM Transactions on Graphics.
3. ISO/ASTM 52900:2021. Additive manufacturing — General principles — Terminology.
4. Müller, M., et al. (2022). Real-time trajectory planning for robotic additive manufacturing. Robotics and Computer-Integrated Manufacturing.
5. The MathWorks, Inc. (2023). Robotics System Toolbox: Inverse Kinematics. [Online] Available: https://www.mathworks.com/help/robotics/ug/inverse-kinematics.html

9. Bincike na Asali & Sharhin Kwararru