MUTUMMIN-INJI MAI NAUYIN GRAM 281 YANA TSALLE MITA 7.6

Tsalle yana ba wa na’ura damar ketare cikas, sauya alkibla da sauri, da tashi sama da ramuka. Masu bincike ma suna tunanin ƙananan motocin bincike masu tsalle don duniyoyi masu ƙarancin nauyi (gravity). Amma sa mutummin-inji ya yi tsalle sama yawanci yana buƙatar spring.

Akwai manyan hanyoyi uku na ba wa mutummin-inji mai tsalle ƙarfi. Tsarin series-elastic yana sanya spring tsakanin mota da ƙafa: spring ɗin yana adana makamashi kuma yana sakin sa da sauri fiye da yadda motar za ta iya ita kaɗai. Tsarin parallel-elastic yana amfani da ƙaramar mota da babban rage giya (gear reduction) don cika spring a hankali, wanda makulli ke riƙe shi har sai wani mai saki ya sake shi. Haka masu riƙe da tarihi ke aiki: wani mutummin-inji na Hawkes da abokan aikinsa yana kaiwa mita 32, ta amfani da rage giya na 1,000 zuwa 1 — amma dole ne ya zauna a ƙasa na kusan daƙiƙa 120 don sake cika ƙarfi tsakanin tsalle-tsalle.

Zaɓi na uku shi ne tuƙi kai tsaye (direct drive): motar tana haɗe da ƙafar kai tsaye, ba tare da wani spring ba. Tsallen ba zai taɓa fi ƙarfin motar a wannan lokacin ba. A madadin haka, na’urar ta fi sauƙi da rashin nauyi, tana ɓata ƙarancin lokaci a ƙasa, kuma ana iya daidaita turawarta a kai a kai. Har zuwa yanzu, masu tsalle masu tuƙi kai tsaye sun kasance ƙanana: mita 1.14 ga mai ƙafa huɗu Stanford Doggo, mita 1.6 ga mai ƙafa ɗaya RAMIEL, mita 0.59 ga wani mutummin-inji mai ƙafa ɗaya na baya na Wagner da Yim, wanda rack and pinion ke tuƙa shi.

Abubuwa biyu masu tasiri: tsawon ƙafa da ƙarfi a kowane gram

Gihyeok Na da Justin Yim, a University of Illinois Urbana-Champaign, sun fara ne daga wata ƙa’idar girma mai sauƙi. Idan aka yi watsi da jan iska, mafi girman tsayin tsalle na wani mai tuƙi mai iyakar ƙarfi yana ƙaruwa tare da tsawon motsin ƙafar da kuma ƙarfin motar a kowane nauyi:

h_max ∝ l_leg (P_max / M)^(2/3)

Don haka maimakon ƙara springs, sun tura waɗannan abubuwa biyu iyakar abin da za su iya.

Mutummin-injinsu yana da nauyin gram 281. Ƙafarsa bututu ne na carbon fibre mai tsawon millimetre 1,981, faɗin millimetre 6 kuma nauyinsa gram 27 kacal; motsin da ake amfani da shi millimetre 1,867 ne. A ƙasa akwai jikin, mai motar brushless, batir da microcontroller (gram 192). A sama akwai sashen daidaitawa (gram 55).

Tsalle ɗaya a tsaye, an haɗa shi daga hotunan bidiyo masu tazarar millisecond 166.7, tare da mutum mai tsawon mita 1.83 don kwatanta girma. — Hoto na 1, Na & Yim (2026), arXiv:2609.30530.

Zaren da aka naɗe a jikin ƙafa

Muhimmin ɓangaren shi ne abin da marubutan ke kira fabric-wrap transmission (isar da ƙarfi ta naɗaɗɗen yadi). Wani zaren yadin Dyneema composite, mai faɗin millimetre 6 da kaurin millimetre 0.13, yana murɗewa a jikin ƙafar a ɗan karkataccen kusurwa na digiri 2.5. Ƙarshensa ɗaya an ɗaure shi kusa da saman ƙafar; ɗayan kuma yana naɗewa a kan wata kwarkwata (spool) da motar ke juyawa. Yayin da motar ke jan zaren ciki, jikin yana zamewa sama a jikin ƙafar, yana tura tafin ƙafar a ƙasa.

Ga ɓangaren basira. Yayin da zaren ke taruwa a kan kwarkwatar, radius ɗinta yana girma. A farkon turawa, radius ƙarami ne kuma motar tana da babbar fa’idar inji; yayin da ƙafar ke miƙewa, radius yana girma kuma fa’idar tana raguwa. Wannan yana riƙe motar kusa da ƙarfin ƙolinta a mafi yawan motsin, ba tare da wani akwatin giya ba. Rack and pinion, mai tsayayyen radius, a maimakon haka zai sa motar ta ratsa dukkan kewayon saurinta a cikin motsi ɗaya.

Naɗin yana yin ƙarin ayyuka biyu. Yana ƙarfafa dogon bututun siriri don kada ya lanƙwasa (buckle) a ƙarƙashin ƙarfin tsallen, kuma yana rage girgizar bututun.

Ka’idar naɗin yadi: zaren yana murɗewa a jikin ƙafar (a) kuma yana naɗewa a kan kwarkwata wadda radius ɗinta ke girma daga r₀ zuwa r(x) yayin da ƙafar ke miƙewa (b, c); rack and pinion yana riƙe tsayayyen radius (d). — Hoto na 4, Na & Yim (2026), arXiv:2609.30530.

Farfela a kan dogon lefa

Mutummin-inji mai ƙafa ɗaya dole ya tsaya a tsaye. Sashen daidaitawa da ke sama yana ɗauke da ƙananan farfela huɗu, kowanne mai faɗin millimetre 76.3. Tare suna turawa da ƙarfin da bai wuce newton 0.50 ba, kusan kashi 18% na nauyin mutummin-injin. Wannan yana kama da rauni, amma suna aiki ne a ƙarshen lefa mai tsawon kusan mita biyu, wanda ya isa ya riƙe ƙafar a tsaye a ƙasa ko ya karkatar da ita bisa umarni.

Mita 7.6 a fili mai ciyawa

Ƙungiyar ta gwada mutummin-injin a waje, ta ɗauki bidiyonsa da kyamarorin GoPro biyu a hotuna 120 a kowace daƙiƙa, sannan ta sake gina hanyarsa a 3D. Jikin ya hau kusan mita 7.6; dukkan tsallen ya ɗauki kusan daƙiƙa 2.5, kuma mutummin-injin ya karkata gefe ƙasa da mita 1.6. Tafin ƙafarsa ya kasance a ƙasa na millisecond 190 kacal. Bayanan motar sun nuna ƙarfin yana hawa, sannan ya tsaya kusa da ƙolinsa a sauran motsin — daidai abin da aka ƙera zaren ya yi.

Marubutan sun bayyana wannan a matsayin tsalle mafi tsawo da aka taɓa rahotonsa ga tsarin da ke amfani da lantarki ba tare da springs ba. Idan aka haɗa tsayi da sauri a wani ma’auni da ake kira ƙwarewar tsalle a tsaye (vertical jumping agility), mutummin-injin ya samu mita 5.30 a kowace daƙiƙa, mafi girma a cikin dukkan mutummin-inji masu tsalle na lantarki a teburin kwatantawarsu, ko da wane irin isar da ƙarfi suke amfani da shi.

Mutummin-injin kuma zai iya karkata kusan digiri 20 kafin ya tashi, don zaɓar alkiblar tsallensa. A sama, farfela suna rage girgiza amma ba sa kawar da ita gaba ɗaya: jikin yana tsayawa a saman ƙafar, kusa da farfela, wanda ke gajarta lefarsu. Har yanzu ba a aiwatar da mayar da jikin zuwa wajen tafin ƙafa yayin tashi ba.

Mataki na gaba: tsalle-tsalle a jere

Wannan bincike yana nuna tsalle guda-guda. Tsalle a jere — sake tashi nan da nan bayan sauka — shi ne buri na gaba, tare da sake sanya jikin a wani wuri a tsakiyar iska. Marubutan kuma sun nuna Wata (Moon), inda ƙarancin nauyi zai bar irin wannan mutummin-inji ya ketare bakin ramuka (craters) ko ya ɗauki hotuna daga sama a wurin da jirage marasa matuƙa (drones), saboda babu iskar da za su tura, ba za su iya tashi ba.