SI9300154A - Driving mechanism of muscular drive vehicle - Google Patents
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- SI9300154A SI9300154A SI9300154A SI9300154A SI9300154A SI 9300154 A SI9300154 A SI 9300154A SI 9300154 A SI9300154 A SI 9300154A SI 9300154 A SI9300154 A SI 9300154A SI 9300154 A SI9300154 A SI 9300154A
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Abstract
Predmet izuma je pogonski mehanizem vozila na mišični pogon, ki je vgrajen v samo pogonsko kolo vozila (dvokolesa, trokolesa, invalidskega vozička ipd.) in katerega konstrukcija omogoča enostaven prenos sile z ročičnega pogona ali direktnega vplivanja na pedale ali ročice v krožno gibanje. Pogonski mehanizem vozila na mišični pogon po izumu, ki omogoča enostaven prenos sile z ročičnega ali direktnega vplivanja na pedale ali ročice je izveden s pomočjo prečno na os vrtenja pogonskega kolesa nameščenim kolutom, katerega izmenično vrtenje je omogočeno z izmeničnim premikanjem jeklene žice ali drugega prenosnega sredstva, pri čemer je zaradi enosmernih rotacijskih zapor omogočen prenos izmeničnega vrtenja koluta v enosmerno vrtenje pogonskega kolesa. Glede na uporabljena prenosna sredstva se ustrezno spreminja tudi oblika koluta, popolni izkoristek izmeničnega vrtenja koluta pa omogočajo zobniški in vrvni prenosi, ki v kombinaciji z enosmernimi rotacijskimi zaporami omogočajo enosmerno vrtenje pogonskega kolesa.The subject of the invention is the driving mechanism of the vehicle to a muscular drive that is built into the drive wheel itself vehicles (two - wheeled, three - wheeled, wheelchair etc.) and whose construction makes it easy transfer of force from manual drive or direct impact on pedals or levers in a circular motion. Propulsion the muscle-driven vehicle mechanism of the invention which makes it easy to transfer force from the crank or direct impact on pedals or levers is made by assist transverse to the axis of rotation of the drive wheel mounted reel whose alternating rotation is enabled by alternately moving steel wire or other means of transport, whereby one-way rotary barriers allowed for alternating transfer rotate the disc into one-way rotary drive bikes. Depending on the means of transmission used the shape of the reel, perfect, also changes accordingly however, the alternating rotation of the disc is made possible gear and rope transmissions combined with one-way Rotary barriers allow one way rotating the drive wheel.
Description
POGONSKI MEHANIZEM VOZILA NA MIŠIČNI POGONDRIVING MECHANISM OF A VEHICLE VEHICLE
Predmet izuma je pogonski mehanizem vozila na mišični pogon, ki je vgrajen v samo pogonsko kolo vozila (dvokolesa, trokolesa, invalidskega vozička ipd.) in katerega konstrukcija omogoča enostaven prenos sile z ročičnega pogona ali direktnega vplivanja na pedale ali ročice v krožno gibanje. Izum spada v razred B 62 M 1/04 mednarodne patentne klasifikacije.The object of the invention is the drive mechanism of a muscular-powered vehicle, which is built into the vehicle's drive wheel itself (two-wheeled, three-wheeled, wheelchair, etc.) and whose construction makes it easy to transfer force from the manual drive or directly affect pedals or levers in a circular motion. The invention belongs to Class B 62 M 1/04 of the International Patent Classification.
-2Tehnični problem, ki ga predložen izum uspešno rešuje je takšna konstrukcija in izvedba pogonskega mehanizma, ki bo primeren za pogon najrazličnejših vozil (dvokoles, trokoles, invalidskih vozičkov) tako s spodnjimi kot zgornjimi okončinami in pri katerem bo dosežen zvezni (kontinuiran) pogon ob čimmanjši poti gibanja okončin. Konstrukcijska rešitev mehanizma naj bo enostavna za izdelavo in primerna za namestitev v samo pogonsko kolo.-2Technical problem that the present invention successfully solves is such construction and implementation of a drive mechanism that will be suitable for driving a wide variety of vehicles (two-wheeled, three-wheeled, wheelchairs) with both lower and upper extremities and which will achieve continuous (continuous) drive at minimize movement of the limbs. The design of the mechanism should be simple to manufacture and suitable for installation in the drive wheel itself.
Izvedbe pogonskih mehanizmov vozil na mišični pogon, predvsem dvokoles in njim podobnim ter iz njih izpeljanih vozil (npr. skirojev, triciklov, ipd.), ki so zasnovane na principu prenosa ponavljajočega gibanja človeškega telesa, predvsem nog in rok, lahko glede na osnovni princip razdelimo v dve skupini in sicer v izvedbe s krožnim gibanjem nog ali rok ter izvedbe s ritmičnimi nihaji nog ali rok gor - dol ali naprej - nazaj.Designs of the propulsion mechanisms of muscular-powered vehicles, in particular two-wheelers and the like, and derived vehicles (eg scooters, tricycles, etc.), based on the principle of transmission of repetitive movement of the human body, in particular the legs and arms, may be based on the basic principle We divide into two groups: circular movements of the legs or arms, and rhythmic oscillations of the legs or arms up and down or backwards.
Osnovni konstrukcijski princip, ki je realiziran v velikem številu praktičnih izvedb, je pri prvi skupini ta, da krožno gibanje npr. nog voznika preko prenosnega mehanizma prenašamo v krožno vrtenje pogonskega kolesa ali koles vozil.The basic construction principle, which is realized in a large number of practical embodiments, is that in the first group, circular motion, e.g. The leg of the driver is transmitted through the transmission mechanism into a circular rotation of the drive wheel or wheels of the vehicles.
V ta namen so izdelane različne konstrukcije pogonskih mehanizmov, pri katerih se stopalke, ki so nameščene na središčno povezana rotirajoča ročična elementa, ki sta na središčno gred nameščena v diametralno nasprotnih straneh. Središčna gred, ki povezuje oba ročična elementa je prednostno vležajena na spodnjem vozlišču paličja osnovnega okvirja dvokolesa. Voznik s potiskanjem ene stopalke istočasno premika na središčno gred togo pritrjeno ozobljeno ploščo, ki preko znanihFor this purpose, various designs of drive mechanisms are made, in which the feet, which are mounted on centrally connected rotating crank elements, which are mounted centrally on the diametrically opposite sides. The center shaft connecting the two crank elements is preferably mounted on the lower node of the rod of the base frame of the two-wheeler. By pushing one foot at a time, the driver moves a rigidly mounted toothed plate to the center shaft, which through known
-3konstrukcijskih elementov npr. verige, zobatega jermena ali podobno prenaša navor na pogonsko kolo, ter sočasno dviguje drugo stopalko v zgornji položaj. Sila potiska je odvisna od teže voznika, njegovih mišičnih sposobnosti ter konstrukcijskih značilnosti dvokolesa.-3 structural elements e.g. a chain, a timing belt or the like, transmits torque to the drive wheel and simultaneously raises the other foot to the up position. The thrust force depends on the weight of the rider, his muscular abilities and the construction characteristics of the two-wheeler.
Zaradi krožnega gibanja nog voznika nastaja v vrtišču ročičnega sistema navor, ki se po svoji velikosti ciklično spreminja, praktično od vrednosti nič, ko sta ročici stopalk v vertikalnem položaju pa do maksimalne vrednosti, ko sta ročici v približno horizontalnem položaju. Sili obeh nog povzročata nastanek navora, ki se ciklično spreminja in katerega vrednost je enaka seštevku pozitivnih polovic sinusoidne krivulje. Maksimalen navor je določen s trenutnim kotnim zamikom stopalčne ročice, oziroma z efektivno dolžino stopalčne ročice na katero deluje sila voznikove noge.The circular movement of the driver's legs generates torque in the rotation of the crank system, which varies cyclically in size, from practically zero when the pedal arms are in the vertical position to maximum when the cranks are in approximately horizontal position. The forces of both legs give rise to cyclically varying torques equal to the sum of the positive halves of the sinusoidal curve. Maximum torque is determined by the instantaneous angular offset of the foot lever, or by the effective length of the foot lever to which the force of the driver's foot is acting.
Prenos navora na pogonsko kolo, ki je lahko izveden na razne načine, ne vpliva na spremembo njegove izhodiščno sinusoidne oblike, za spremembo hitrosti pogonskega kolesa pa je možno v katerem koli delu sistema gonila vgraditi menjalnik.The transfer of torque to the drive wheel, which can be done in various ways, does not affect the change of its initial sinusoidal shape, and to change the speed of the drive wheel, it is possible to install a gearbox in any part of the gearbox system.
Glavna pomanjkljivost opisanih pogonov leži v dejstvu, da ob konstantni pogonski sili na stopalko energetski potencial npr. dvokolesnega pogona lahko definiramo predvsem z razdaljo med zgornjo in spodnjo mrtvo točko pogonskega pedala. Ker je obseg krožnice za 3,14 krat večji od njenega premera lahko ugotovimo, da v enem obratu pedala voznikova noga opravi, za 1,54 krat daljšo pot kot bi jo opravila ob le aksialnem potiskanju pedala v navpični smeri.The main disadvantage of the actuators described is the fact that with a constant driving force on the pedal, the energy potential e.g. Two-wheel drive can be defined primarily by the distance between the upper and lower dead points of the drive pedal. Since the circumference of the circle is 3.14 times larger than its diameter, we can conclude that in one turn of the pedal the driver's foot performs a 1.54 times longer distance than it would have done if only the axial pushing of the pedal in a vertical direction.
Druga pomanjkljivost opisanega načina pogona je v izgubah, kiAnother disadvantage of the described drive mode is in the losses that
-4posledično nastanejo zaradi cikličnega spreminjanja, trenutnih vrednosti navora pogojenih z načinom vpetja stopalk in stopalčnih vzvodov, ki ležita v diametralni smeri.-4 are consequently due to cyclical changes, the instantaneous torque values conditioned by the method of clamping of the feet and the foot levers lying in the diametrical direction.
Drugo skupino pogonskih mehanizmov pa predstavljajo mehanizmi, pri katerih je gibanje pogonskih ročic linearno gor - dol.The second group of drive mechanisms are mechanisms in which the movement of the drive arms is linear up and down.
V kolikor ne vsebujejo elementov ekscentričnega pogona oz. ekscentričnega načina pretvorbe linearnega gibanja v rotacijo, ti mehanizmi odpravljajo pomanjkljivosti izvedb s krožnim gibanjem, saj je velikost navora v katerikoli legi pogonske ročice enaka, oziroma manj spremenljiva glede dovedeno vertikalno silo na to ročico.If they do not contain elements of eccentric drive or. eccentric way of converting linear motion into rotation, these mechanisms eliminate the disadvantages of circular motion, since the torque size in any position of the drive lever is equal to, or less variable in terms of the applied vertical force on that lever.
V praksi pa je večina tovrstnih mehanizmov konstruirana tako, da se sila preko gibanja na enem koncu vpetih ročic prenaša preko ekscentra v krožno gibanje samega pogonskega kolesa ali pomožnega kolesa in ustreznega prenosa. Takšne izvedbe znova povzročajo pojav sinusoidne oblike nastalega navora. Tehnični problemi, ki nastopajo pri tovrstnih izvedbah se odražajo predvsem v tem, da ni možno uskladiti vseh zahtev, med katerimi izstopajo:In practice, however, most of these mechanisms are designed so that the force is transmitted through movement at one end of the clamped arms by an eccentric movement into the circular motion of the drive wheel itself or the auxiliary wheel and the corresponding transmission. Such embodiments again cause the appearance of a sinusoidal torque shape. The technical problems that arise with this kind of implementation are reflected in the fact that it is not possible to harmonize all the requirements, which include:
- položaj stopalk naj bi bil za ugodno vožnjo s konvencionalno obliko okvirja dvokolesa približno tam, kjer je pri mehanizmu s krožnim gibanjem nog- the position of the pedals is intended to be advantageous when traveling in the conventional frame of the two-wheeler approximately where it is in the circular movement of the legs
- vertikalni pomik stopalk z ročicami je omejen glede na majhno višino od tal- the vertical movement of the pedal arms is limited by its low height from the ground
- celotni mehanizem naj bi se čimbolj vklapijal v samo konstrukcijo kolesa, tako, da bi bil čimmanj moteč za voznika.- the whole mechanism should fit as closely as possible into the wheel structure itself, so as to be as disturbing to the driver as possible.
-5Praktične izvedbe tovrstnih pogonov so pokazale, da s konstrukcijo ekscentrične pretvorbe linearnega gibanja v krožno ni možno zadovoljivo ugoditi vsem zahtevam.-5Practical implementations of such drives have shown that the construction of an eccentric conversion of linear motion into a circular motion cannot satisfy all requirements satisfactorily.
Ena izmed izvedb takega mehanizma je opisana v DE patentnem dokumentu 3 709 648.One embodiment of such a mechanism is described in DE Patent Document 3 709 648.
Za doseganje ustreznega pomika stopalk z ročicami morajo biti ročice primerno dolge, kar pogojuje njuno vpetje blizu vrtišča pogonskega kolesa, kar pa spet onemogoča enostavno namestitev ekscentričnega dela pogona. Zato so dosedanje izvedbe, ki so konstrukcijsko tako izvedene, da je vrtišče ekscentra oddaljeno od vrtišča pogonskega kolesa, kar pogojuje izvedbo prenosnega mehanizma, ki je ob morebitni zahtevi po vgraditvi menjalnika, oblikovno ter funkcionalno nesprejemljiv.In order to achieve proper movement of the pedals with the levers, the levers must be sufficiently long, which causes them to be clamped close to the pivot of the drive wheel, which again prevents the eccentric part of the drive from being easily fitted. Therefore, the designs to date are designed in such a way that the pivot of the eccentric is away from the pivot of the drive wheel, which makes the transmission mechanism, which is formally and functionally unacceptable, when required to install the gearbox.
Tovrstni pogonski mehanizmi sicer odpravljajo pomanjkljivosti izvedb mehanizmov s krožnim gibanjem predvsem v pogledu zmanjšanja oziroma odpravljanja sinusoidnega gibanja, ne odpravijo pa sinusoidne oblike nastalega navora v celoti, poleg tega pa so za izdelavo mehanizma potrebni dražji konstrukcijski sklopi.Such drive mechanisms, while eliminating the disadvantages of circular motion mechanisms, in particular in terms of reducing or eliminating sinusoidal movement, do not completely eliminate the sinusoidal torque generated altogether, and more expensive structural assemblies are required to make the mechanism.
Pogonski mehanizem vozila na mišični pogon po izumu, ki omogoča enostaven prenos sile z ročičnega ali direktnega vplivanja na pedale ali ročice je izveden s pomočjo prečno na os vrtenja pogonskega kolesa nameščenim kolutom, katerega izmenično vrtenje je omogočeno z izmeničnim premikanjem jeklene žice ali drugega prenosnega sredstva, pri čemer je zaradi ensomernih rotacijskih zapor omogočen prenos izmeničnega vrtenja koluta v enosmerno vrtenje pogonskega kolesa. GledeThe propulsion mechanism of a muscular-powered vehicle according to the invention, which enables easy transfer of force from the manual or direct action on the pedals or levers, is made by means of transversely rotating axles of the drive wheel mounted reels whose alternating rotation is made possible by alternating movement of steel wire or other transmission means , which, due to the ensomeric rotary barriers, allows the transfer of alternating rotation of the disc to a one-way rotation of the drive wheel. Regarding
-6na uporabljena prenosna sredstva se ustrezno spreminja tudi oblika koluta, popolni izkoristek izmeničnega vrtenja koluta pa omogočajo zobniški in vrvni prenosi, ki v kombinaciji z enosmernimi rotacijskimi zaporami omogočajo enosmerno vrtenje pogonskega kolesa.-6The form of the reel is modified accordingly by the gears used, and the full utilization of the alternating rotation of the reel is facilitated by gears and ropes, which, in combination with the one-way rotary barriers, allow the drive wheel to rotate in one direction.
Glede na različne konstrukcijske variante je osnovni kolut, ki ima lahko obliko vrvenice, zobnika ali jermenice lahko nameščen tudi na glavni osi pogonskega kolesa tako, da leži na eni ali na obeh straneh, aii pa je nameščen prečno znotraj osi vrtenja pogonskega kolesa. Delovanje pogonskega mehanizma po izumu je podobno kot pri prečno na os postavljenemu kolutu, le da je tu možno voditi oba dela prenosnega sredstva skupaj v okvirju, pri namestitvi dveh osnovnih kolutov, vsakega na eno stran glavne osi pogonskega kolesa pa se izognemo dodatnim zobniškim ali vrvnim prenosom za popoln izkoristek vrtenja koluta v obe smeri.Depending on the various design variants, a base reel, which may be in the form of a rope, pinion or pulley, may also be mounted on the main axis of the drive wheel so that it lies on one or both sides, and aii is positioned transversely within the axis of rotation of the drive wheel. The operation of the drive mechanism according to the invention is similar to that of a transverse axle mounted on the axle, except that it is possible to guide the two parts of the transmission together in a frame, while installing two basic rings, avoiding additional gear or ropes on each side of the main axis of the drive wheel. transmission for full utilization of rotation of the reel in both directions.
Izum bom podrobneje obrazložil na osnovi izvedbenega primera in slik, od katerih kaže:I will explain the invention in more detail on the basis of an embodiment and illustrations, of which:
slika 1 prerez pesta pogonskega kolesa vozila z vgrajenim pogonskim mehanizmom po izumu slika 2 prerez pesta pogonskega kolesa vozila z vgrajenim pogonskim mehanizmom po izumu v pogledu A-A z jekleno žico slika 3 prerez pesta pogonskega kolesa vozila z vgrajenim pogonskim mehanizmom po izumu v pogledu A-A z verigofigure 1 cross section of a drive wheel hub of a vehicle with a built-in drive mechanism according to the invention figure 2 cross section of a hub wheel of a vehicle with a built-in drive mechanism according to the invention in view A-A with steel wire Figure 3 cross section of a hub wheel of a vehicle with a built-in drive mechanism according to the invention in view A-A with a chain
-7slika 4 prerez pesta pogonskega kolesa vozila z vgrajenim pogonskim mehanizmom po izumu v pogledu A-A z zobatim jermenom slika 5 primer konstrukcijske izvedbe in namestitve pogonskega mehanizma po izumu na dvokolo z ročičnim pogonom slika 6 primer konstrukcijske izvedbe in namestitve pogonskega mehanizma po izumu na dvokolo z aksialnim delovanjem stopalk na sredstvo 6-7figure 4 is a cross section of the drive wheel hub of a vehicle with a drive gear according to the invention in view AA with a toothed belt Fig. 5 Example of a construction and installation of a drive mechanism according to the invention on a two-wheel with a manual drive Figure 6 Example of a design and installation of a drive mechanism of the invention on a two-wheel with by the axial action of the feet on the means 6
Pogonski mehanizem vozila na mišični pogon po izumu sestavlja v pesto 1 pogonskega kolesa, prečno na os vrtenja kolesa, vrtljivo viežajena preko ležajev 3,4 večja vrvenica 2, ki leži na isti osi z zobnikoma 5,7, pritrjenima preko enosmernih rotacijskih zapor. Na vrvenico 2 je z večimi ovoji navita gibka pletena jeklena vrv 6, ki poteka skozi vrtišče pogonskega kolesa in je preko pomožnih kolutov 8,9 speljana v okvir 11 vozila. Zobnika 5,7 ležita v oprijemu z, na pesto 1 togo pritrjenim zobnikom ali ozobljenim delom 10 jeklena žica pa se aksialno pomika skozi vrtišče pogonskega kolesa.The propulsion mechanism of the muscular-powered vehicle according to the invention consists of a drive wheel hub 1 transversely to the axis of rotation of the wheel, pivotally connected via bearings 3.4 larger rope 2, which lies on the same axis with gears 5.7 secured via one-way rotary locks. A flexible braided steel rope 6 is wound onto lane 2 by a number of wraps which passes through the drive wheel pivot and is routed to the frame 11 of the vehicle via the auxiliary rings 8.9. The sprockets 5.7 are in contact with the steel wire which is rigidly fixed to the hub 1 or the toothed portion 10 and moves axially through the drive wheel pivot.
Pri premiku jeklene vrvi 6 v eno smer, se le-ta odvija z večje vrvenice 2, medtem ko se istočasno druga polovica vrvi 6 navija na vrvenico 2. Vrv 6 je v določeni točki tudi pritrjena na vrvenico 2, kar preprečuje njeno popolno odvitje. Pri premiku vrvi 6 v drugo smer je navijanje in odvijanje obrnjeno. Tako dobimo vrtenje večje vrvenice 2 enkrat v eni, drugič v drugi smeri.When the steel rope 6 is moved in one direction, it is unwound from the larger rope 2, while at the same time the other half of the rope 6 is bent on the rope 2. The rope 6 is also fixed at some point to the rope 2, which prevents it from completely unwinding. When the rope 6 is moved in the other direction, the winding and unwinding are reversed. Thus, we get the rotation of the larger lane 2 once in one direction, the other in the other direction.
-8Glede na to, da sta na isti osi z večjo vrvenico 2 nameščena preko nasprotno delujočih rotacijskih zapor 24,24’ tudi zobnika 5,7, prenašata le-ta izmenično vrtenje vrvenice 2 v vrtenje pesta 1 glede na okvir 11 le v eno smer. Pesto 1 namreč leži preko ozobijenega dela 10 v oprijemu z zobnikoma 5,6.-8As the fact that, in the same axis with a larger rope 2, they are mounted via rotary locks 24.24 'in the opposite direction of rotation, the gears 5.7 also transfer the alternate rotation of the rope 2 into the rotation of hub 1 relative to the frame 11 in one direction only. . Namely, the hub 1 lies over the toothed portion 10 in the gearing grip 5.6.
Namesto jeklene vrvi 6 lahko kot prenosno sredstvo uporabimo tudi pogon z verigo 12, ki ga prikazuje slika 3, oziroma pogon z zobatim jermenom 13, ki je prikazan na sliki 4.Instead of the steel rope 6, the drive with the chain 12 shown in Fig. 3 or the drive with the toothed belt 13 shown in Fig. 4 can also be used as the transmission means.
Glede na spremenjeno prenosno sredstvo se ustrezno spremeni tudi vrvenica 2 v verižnik 2a oziroma 2b, samo delovanje mehanizma pa je identično osnovni izvedbi.Depending on the modified gear, lane 2 is changed accordingly to sprocket 2a and 2b, respectively, and the mechanism itself is identical to the basic version.
Jeklena vrv 6 je v obeh variantnih primerih nadomeščena le v dolžini, ki se premika skozi pesto, v okvirju 11 pa ostaja žica 6.In both variants, the steel rope 6 is only replaced by a length that moves through the hub, and wire 6 remains in the frame 11.
Na sliki 5 je prikazan primer konstrukcijske izvedbe in namestitve pogonskega mehanizma po izumu na dvokolo z ročičnim pogonom. Jeklena vrv je vodena v okvirju dvokolesa in je preko manjših vodilnih vrvenic pripeljana na enostransko vpeti ročici. Izmenično premikanje teh ročic povzroči izmenično sukanje večje vrvenice v mehanizmu po izumu, ki se prenaša v enosmerno rotacijo pogonskega kolesa.Figure 5 shows an example of the construction and installation of the drive mechanism according to the invention on a two-wheeler with manual drive. The steel rope is guided in the frame of a two-wheeler and is routed via small guide ropes to a single-lever arm. The alternating movement of these levers results in the alternating twisting of a larger cord in the mechanism of the invention, which is transmitted in a one-way rotation of the drive wheel.
Na sliki 6 je shematsko prikazana rešitev primera konstrukcijske izvedbe in namestitve pogonskega mehanizma po izumu na dvokolo z aksialnim delovanjem stopalk na jekleno vrvenico 6. V tem izvedbenem primeru je jeklena vrv ravno tako vodena preko manjših vodilnih vrvenic in je neposredno povezana s stopalko 28, ki je lahko še dodatno vodena vFigure 6 schematically shows a solution of an example of a construction and installation of the drive mechanism according to the invention on a two-wheeler with axial action of the feet on the steel rope 6. In this embodiment, the steel rope is also guided through smaller guide ropes and is directly connected to the pedal 28, which can be further guided into
-9vodilu, ki tvori z navpičnim nosilcem 29 voznikovega sedeža 30 približno enak kot. Taka rešitev odpravlja pomanjkljivosti dosedanjih krožnih in ročičnih pogonov predvsem v pogledu gibanja človekovih okončin po večji ali manjši sinusoidi, medtem ko je lahko v konkretnem primeru gibanje premočrtno in tako odpravljeno sinusoidno gibanje v celoti.-9 a guide which forms approximately the same angle with the vertical support 29 of the driver's seat 30. Such a solution eliminates the disadvantages of the current circular and manual actuators, especially in terms of the movement of the human limbs along the larger or smaller sinusoids, whereas in the specific case the movement can be straight and thus eliminate the sinusoidal motion altogether.
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1993
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