The Method of Virtual Reality for Creation a Disk Ridging Tool

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1 The ethod of Vtual Realt fo Ceato a Dsk Rdgg Tool at Heloo ad Jü Olt Estoa Uest of Lfe Sceces Keutwald Tatu Estoa at.heloo@eau.ee olt@eau.ee ABSTRACT The peset pape cocetates the a atteto to the descpto of the ethod of tual ealt fo ceato a dsk dgg tool ad to stud ts cople wokg pocess. The fluece of the agula eloct of otato of the dsk dgg tool ad ts adustet agle to the qualt of tual tllage ad to the foce sste appled to the blades of the tual dsk dgg tool s studed. The ethod of tual ealt s llustated b the tual poectos of a sgle blade b the tual poectos of assebl of the blades of the dsk dgg tool ad b the pocessed tual egos. The foce sstes appled to a sgle blade ad to the assebl of the blades of the dsk dgg tool ae chaacteed b gaphs of the depedeces of the foces ad oets o the agle of otato of the dsk dgg tool. Substatal depedece of the qualt of the tual pocessg a lateal suface of a tual dge o the alue of the adustet agle ad o the agula eloct of the dsk dgg tool s detected. The esults of ths pape ca be used b desges of potato feld tllage aches wth the foced de dsk dgg tools b the agcultual egees usg the featues of copute gaphcs ad b the uses of ode copute package athcad.. INTRODUCTION Low epoducto coeffcet ad hgh cost of seed potatoes hae popted the eed fo ew techologes. Sä (98) has ade a poposal fo a ew techolog of gowg seed potatoes cludg the ceasg the gowg space of potatoes step b step. Ths techolog as well as the dea of ceatg a ew cobed wde ow potato feld tllage ache had bee descbed b Olt () ad Olt Heloo (c) detals. Thoough stud of the wokg pocess of the otatg fee acte tools de ol b sol the stuctue of ths ache had bee ade b Olt () the thess fo PhD Agcultual Egeeg. The esults of ths thess wee publshed b Olt (999) Heloo Olt () Heloo Olt. (a c a) ad eewed b Heloo Olt (b c). Fgue. The pcpal schee (a) of the cobed wde ow potato feld pocessg ache ad ts wokg pocess (b) whee suppotg wheel S-te fee-acte ccula lks duckfoot shea fee-acte dsk dgg tool dge botto foe agle of attack Δc shft of the S-te speed of the ache. Heloo ad J. Olt. The ethod of Vtual Realt fo Ceato a Dsk-Rdgg Tool. Agcultual Egeeg Iteatoal: the CIGR Eoual. auscpt P 8. Vol. VIII. Jaua.

The pcpal schee of a ew cobed wde ow potato feld tllage ache descbed b Olt () ad Olt Heloo (c) detals s see Fg.. Fg. shows the fst cobed wde ow potato feld tllage ache ceated accodg to the schee Fg.

The cobed wde ow potato feld tllage ache fo the epeets Heloo Olt (a b c) dffeetl fo the peous papes hae peseted the esults of stud a foced de dsk dgg tool de b tassso fo tacto the stuctue cobed wde

2 The pcpal schee of a ew cobed wde ow potato feld tllage ache descbed b Olt () ad Olt Heloo (c) detals s see Fg.. Fg. shows the fst cobed wde ow potato feld tllage ache ceated accodg to the schee Fg. fo the epeets. The esults of the epeetal stud o the ablt of dsk dgg tools ouldg dges of a potato feld ae dscussed b Olt (999) detal. Fgue. The cobed wde ow potato feld tllage ache fo the epeets Heloo Olt (a b c) dffeetl fo the peous papes hae peseted the esults of stud a foced de dsk dgg tool de b tassso fo tacto the stuctue cobed wde ow potato feld tllage ache. Ths pape cocetates the a atteto to the descpto of the ethod of tual ealt o ceato a dsk dgg tool fo the cobed wde ow potato feld pocessg ache suppotg the ew techolog of gowg seed potatoes of Sä (98).. DESCRIPTION OF A DISK RIDGING TOOL I the peset pape a dsk dgg tool s cosdeed as a dsk of adus wth tapeodal blades claped to t (Fgs. ) ude adustet agle ξ to the adal decto of the dsk. Fgue. The schee of the dsk dgg Fgue. The schee of the dgg tool o a tool lateal suface of a potato dge The tapeodal blades of the dsk dgg tool hae the wdth d ad the agle of clato ζ to the plae of the dsk of the dsk dgg tool. The dsk dgg tool has a agle of attack (Fg. ) to the decto of ts fowad oto togethe wth whole ache ad the agle of. Heloo ad J. Olt. The ethod of Vtual Realt fo Ceato a Dsk-Rdgg Tool. Agcultual Egeeg Iteatoal: the CIGR Eoual. auscpt P 8. Vol. VIII. Jaua.

3 clato (Fgs. ) to the lateal suface of the dge. The dsk dgg tool has the cople oto the stuctue of potato feld tllage ache: t taesg togethe wth the whole ache ad otates elatel to the fae of the ache. Fg. shows the dsk dgg tool a wokg posto o the lateal suface of a dge of a potato feld. Accodg to the agcultual egeeg equeets the toleace betwee the uppe edges of the lateal suface of the potato dge s δ ad the dstace betwee the cete of dsk ad the lateal suface s H.. DETERINATION OF POSITIONS OF A DISK RIDGING TOOL The postos of the dsk dgg tool ca be deteed b the co-odate sstes show Fg.. The aes of the otoless obseato sste O ae dected as follows. As O s pepedcula to the lateal suface of the dge. As O s pepedcula to the as O ad shows the decto of taesg of the ache cag the dsk dgg tool. As O s pepedcula to the aes O ad O ad fos togethe wth these aes the ectagula ght had co-odate sste. The aula co-odate sste O was supposed to be fowad oto togethe wth the whole ache. Its posto at the tal posto s O. The posto of gdl coected to the tool co odate sste O detees the posto of the dsk dgg tool elate to the sste O b the agle of attack b the agle of clato b the agle of otato ad b the co-odates of the og O. Fgue. Used co odate sstes The co odates of a pot P (Fg. ) the co odate sste O ae deteed b the tasfoato ( ) ( ) t A B C ( ) t () ( H ) H whee ( ) cos( ) ( ) s( ) the eloct of fowad oto of the ache (og O ); H the dstace betwee the lateal suface of the dge ad og O ; ad pola adus ad pola agle of a pot P (Fg. ) of the dsk dgg tool the co odate sste O ad cos( ) s( ) A ( ) cos( ) s( ) B ( ) s cos s cos s cos cos C s. Dug coputatos the alues of the tal alues of paaetes of the dsk dgg tool. Heloo ad J. Olt. The ethod of Vtual Realt fo Ceato a Dsk-Rdgg Tool. Agcultual Egeeg Iteatoal: the CIGR Eoual. auscpt P 8. Vol. VIII. Jaua.

4 wee specfed ad hae the peset pape the followg fal alues (Fgs. ): δ. ; h. ; d. ; ξ o (- o ); 8 o ; o ; H. ; ζ 7.8 ο ; T. s; N ; 8; ω (8 ) /s; π.;... DELVING PROCESS OF A BLADE INTO A SOIL Fo stud heeafte the foces appled to the udegoud pat of the blades of the dsk dgg tool the detal kow-how of the delg pocess of the blades to the sol of the dge s eeded. (a) (b) (c) Fgue. The delg pocess of a blade to the dge Let us suppose that the pocess of delg a blade to a sol of a dge s the followg. Fstl deles to a sol of a dge the coe pot of a blade. The dug soe te the udegoud pat of a blade has the tagula fo (hatched ego Fg. a). Afte delg the coe pot of the blade to a sol of a dge the udegoud pat of the blade chages to the tetagoal fo (hatched egos ad Fg. b). Fall afte delg the pot of the blade to a sol the udegoud pat of a blade chages to the petago fo (hatched egos ad Fg. c). The blade leaes the sol of the dge o the opposte ode. VIRTUAL PROJECTIONS OF A BLADE π π Let s the pola agle of the ed of a -th blade (Fg. ) ω t the agle of otato (Fg. ) at the -th ( N) posto of the dsk dgg tool the ube of the blades ω the agula eloct of the dsk dgg tool ad t the oet of the te at the -th posto. The co-odates of the coe pots (Fg. ) of the -th blade at the -th posto of the dsk dgg tool ae ( h) h t ( h H ) ( ) ( t ) ( H ) ( ) ( h. t ) ( h H ) ( ) ( t ) h. Heloo ad J. Olt. The ethod of Vtual Realt fo Ceato a Dsk-Rdgg Tool. Agcultual Egeeg Iteatoal: the CIGR Eoual. auscpt P 8. Vol. VIII. Jaua.

5 . Heloo ad J. Olt. The ethod of Vtual Realt fo Ceato a Dsk-Rdgg Tool. Agcultual Egeeg Iteatoal: the CIGR Eoual. auscpt P 8. Vol. VIII. Jaua. H. Let us copose the followg ectos of coe s co-odates of the -th blade at the -th posto h h h s t h t h t t t h s h h h s () whee N T ω ξ s acs d ξ cos d d π π ζ d ta h h N T ω N T t. Hee N; ; ω agula eloct T ge teal of te N ube of postos the coputatos ube of blades of the dsk dgg tool. I the eoet of copute package athcad the ectos () ca be used fo dawg tual poectos of -th blade at -th posto. Fg. 7 shows the tual poectos of the th blade o the co-odate plaes O (Fg. 7a) O (Fg. 7b) O (Fg. 7c) of the otoless obseato sste O (Fg. ) at the -th posto ceated the eoet of copute package athcad. I Fg. 7 the hatchg deotes the ego to be pocessed b the blades of the tual dsk-dgg tool.

6 .. () () a. () () b. () () c Fgue 7. Vtual poectos of the th blade o the co-odate plaes O (a) O (b) O (c) of the otoless obseato sste O (Fg. ) at the -th posto B aato the oto of the blade Fg. 7 oe ca cof the assupto ade Fg... VIRTUAL PROJECTION OF ASSEBLY OF BLADES Let us copose ew ectos S () S () S () b puttg the ectos s ( ) s ( ) s ( ). Heloo ad J. Olt. The ethod of Vtual Realt fo Ceato a Dsk-Rdgg Tool. Agcultual Egeeg Iteatoal: the CIGR Eoual. auscpt P 8. Vol. VIII. Jaua.

7 aboe the ectos s ( ) s ( ) ( ) s ( N; ) accodgl. The athcad pogas 7 S () S s ( ) S () S s ( ) fo S.. stack S s ( ) fo.. S stack S s ( ) S () S s ( ) fo.. S stack S s ( ). do ths pocedue. I the eoet of copute package athcad ectos S () S () S () age the tual poectos of assebl of blades at the -th posto o the co-odate plaes of the otoless obseato sste O (Fg. ). Ths assebl of blades s aed below as tual dsk-dgg tool. Fg. 8 shows the tual poectos at the -th posto of the tual dsk-dgg tool wth 8 blades o the co odate plaes O (Fg. 8a) O (Fg. 8b) O (Fg. 8c) of the sste O. These poectos wee obtaed the eoet of copute package athcad b usg the ectos S () S () S (). I Fg.. the blades of the tual dsk-dgg tool ae coected togethe wth a aula le.. Heloo ad J. Olt. The ethod of Vtual Realt fo Ceato a Dsk-Rdgg Tool. Agcultual Egeeg Iteatoal: the CIGR Eoual. auscpt P 8. Vol. VIII. Jaua.

8 8.... () () a () () b () () c Fgue 8. Vtual poectos of the th dsk dgg tool o the co-odate plaes O (a) O (b) O (c) of the sste O at the -th posto. Heloo ad J. Olt. The ethod of Vtual Realt fo Ceato a Dsk-Rdgg Tool. Agcultual Egeeg Iteatoal: the CIGR Eoual. auscpt P 8. Vol. VIII. Jaua.

9 . Heloo ad J. Olt. The ethod of Vtual Realt fo Ceato a Dsk-Rdgg Tool. Agcultual Egeeg Iteatoal: the CIGR Eoual. auscpt P 8. Vol. VIII. Jaua. 9 Fg. 8 was used fo akg a deo clp wth the oto of the tual dsk-dgg tool. 7. DETERINATION OF THE UNDERGROUND PART OF A BLADE OF THE DISK RIDGING TOOL The co-odates ad of the pot (Fg. ) wee foud out fo codtos ad ae. The pot a be located o thee sdes of a blade thus ts co-odates ad ae f (Fg. a) ad f ad (Fg. b) f (Fg.c). Let us copose ow the followg ectos s s s s s s

10 f ad s f < s f ad s f < s f ad f. < s ( ) s s s ' ( ) s' ( ) s s ' ' ( ) s ( ) s' ( ) s ( ) s ( ) s ( ) ' '' ( ) s' ( ) s' ' ( ) s' ( ) s ' ( ) s' ( ) ' '' ( ) s ( ) s' ' ( ) s ( ) s ' ( ) s ( ) ' ''' ( ) s'' ( ) s' '' ( ) s'' ( ) s '' ( ) s'' ( ) ' ''' ( ) s ( ) s' '' ( ) s ( ) s '' ( ) s ( ) ' I the eoet of the copute package athcad ectos s' '' ( ) s' '' ( ) s' '' ( ) ca be used fo agato of tual poectos of the udegoud pat of -th blade at -th posto o the co-odate plaes of the obseato sste O. Fg. 9 shows the tual poectos (hatchg deote the ego to be pocessed) of the udegoud pat of the -th blade -th posto blade o the co-odate plaes O (Fg. 7a) O (Fg. 7b) O (Fg. 7c) of the sste O (Fg. ).. Heloo ad J. Olt. The ethod of Vtual Realt fo Ceato a Dsk-Rdgg Tool. Agcultual Egeeg Iteatoal: the CIGR Eoual. auscpt P 8. Vol. VIII. Jaua.

11 .. () () a. () () b. () () c Fgue 9. Vtual poectos of the ugegoud pat of the th blade o the co-odate plaes O (a) O (b) O (c) of the otoless obseato sste O (Fg. ) at the -th posto. Heloo ad J. Olt. The ethod of Vtual Realt fo Ceato a Dsk-Rdgg Tool. Agcultual Egeeg Iteatoal: the CIGR Eoual. auscpt P 8. Vol. VIII. Jaua.

12 8. IAGINATION OF PROCESSED AREA Let us copose ow ectos S () S () S () b puttg the ectos s' '' ( ) s '' ( ) s' '' ( ) aboe the ectos s' '' ( ) s' '' ( ) s '' ( ) ) accodgl. The athcad pogas ' ' ( N; S' () S' s''' ( ) S' S' s''' ( ) fo.. N S' stack S' s''' ( ) fo.. N S' stack S' s''' ( ) S' () S' s''' ( ) fo.. N S' stack S' s''' ( ). do ths pocedue. I the eoet of copute package athcad ectos S () S () S () ca be used fo pesetato the tual poectos at all postos of the udegoud pat of -th blade o the co-odate plaes of the sste O (Fg. ). The set of these poectos detee the lateal space ego o of the tual dge pocessed b -th blade. All N tual poectos of all blades fo the space lae pocessed b assebl of blades. Fgs. show the tual poectos of ths lae o the co-odate plae O whe ξ o (Fg. ) ad the cobed wde ow potato feld tllage ache togethe wth dsk dgg tool oes the decto of -as of the sste O (Fg. ) wth the taesg eloct. /s ad the dsk dgg tool otates wth the agula eloctes ω 8 /s (Fg. ) ω /s (Fg. ) ω /s (Fg. ).. Heloo ad J. Olt. The ethod of Vtual Realt fo Ceato a Dsk-Rdgg Tool. Agcultual Egeeg Iteatoal: the CIGR Eoual. auscpt P 8. Vol. VIII. Jaua.

13 () () Fgue. Vtual poecto of the pocessed pat of the lateal lae o the co-odate plae O (ω 8 /s ξ o ). Fo Fgs. oe ca tu out that the qualt of pocessg depeds substatall fo the agula eloct of otato of the dsk dgg tool. Fg. shows that the dsk dgg tool wth 8 blades wokg wth foced agula eloct ω /s ad taesg wth eloct. /s ges suffcet qualt of pocessg of the space lateal lae of a dge decto of co-odate plae O whe ξ o () () Fgue. Vtual poecto of the pocessed pat of the lateal lae o the co-odate plae O (ω /s ξ o ).. Heloo ad J. Olt. The ethod of Vtual Realt fo Ceato a Dsk-Rdgg Tool. Agcultual Egeeg Iteatoal: the CIGR Eoual. auscpt P 8. Vol. VIII. Jaua.

14 () () Fgue. Vtual poecto of the pocessed pat of the lateal lae o the co-odate plae O (ω /s ξ o ). Fgs. ad show the tual poectos of the pocessed space lae to the co-odate plaes O (Fg. ) ad O (Fg. ). It follows fo Fgs. ad that the dsk dgg tool wth ge ths pape paaetes s able pocess a sol up to depth. c but o ufol.. Heloo ad J. Olt. The ethod of Vtual Realt fo Ceato a Dsk-Rdgg Tool. Agcultual Egeeg Iteatoal: the CIGR Eoual. auscpt P 8. Vol. VIII. Jaua.

15 () () Fgue. Vtual poecto of the pocessed pat of the lateal lae o the co-odate plae O (ω /s ξ o )... () () Fgue. Vtual poecto of the pocessed pat of the lateal lae o the co-odate plae O (ω /s ξ o ). It tued out that the alue of the adustet agle ξ (Fg..) of the dsk dgg tool cosdeable affect the qualt of pocessg. Fg. shows that the case whe ω /s but ξ - o the lae has seeal egos ot pocessed.. Heloo ad J. Olt. The ethod of Vtual Realt fo Ceato a Dsk-Rdgg Tool. Agcultual Egeeg Iteatoal: the CIGR Eoual. auscpt P 8. Vol. VIII. Jaua.

16 . Heloo ad J. Olt. The ethod of Vtual Realt fo Ceato a Dsk-Rdgg Tool. Agcultual Egeeg Iteatoal: the CIGR Eoual. auscpt P 8. Vol. VIII. Jaua () () -.. Fgue. Vtual poecto of the pocessed pat of the lateal lae o the co-odate plae O (ω /s ξ - o ). Fg. was used fo akg deo clps wth sulato the wokg pocess of the tual dsk-dgg tool. 9. AREA OF THE UNDERGROUND PART OF A BLADE The aea of the udegoud pat of a blade s S whee. f (Fg. a) () S whee () () () () () () ()

17 . Heloo ad J. Olt. The ethod of Vtual Realt fo Ceato a Dsk-Rdgg Tool. Agcultual Egeeg Iteatoal: the CIGR Eoual. auscpt P 8. Vol. VIII. Jaua. 7. f ad (Fg. b) ad S whee f (Fg. c). Fg. shows the depedece of the aea of the udegoud pat of the -th blade ( ) o agle of otato of the dsk dgg tool... S Fgue. The depedece of the udegoud aea of the -th blade o agle of otato of the dsk dgg tool whe ξ o.. CENTRE OF ASS OF THE UNDERGROUND PART OF A BLADE The co-odates of the cete of ass of the udegoud pat of a blade ae f (Fg. a) () () () () () whee

18 . Heloo ad J. Olt. The ethod of Vtual Realt fo Ceato a Dsk-Rdgg Tool. Agcultual Egeeg Iteatoal: the CIGR Eoual. auscpt P 8. Vol. VIII. Jaua. 8 f ad (Fg. b) ad () () () whee () () () f (Fg. c).. ODELLING THE FORCE SYSTE The poectos of the ecto N oal to the -th blade o the -th posto o aes O O O of co-odate sste O ae N N N. The tasfoato t A B C tasfos the co-odates of the cetes of ass of the udegoud pats of the blades the sste O to the coespodet co-odates the sste O (Fg. ) gdl coected to the dsk dgg tool. The eloct of the cete of ass of -th blade at the -th posto the sste O s deteed b the followg foulas [ ] ω s cos cos.

19 . Heloo ad J. Olt. The ethod of Vtual Realt fo Ceato a Dsk-Rdgg Tool. Agcultual Egeeg Iteatoal: the CIGR Eoual. auscpt P 8. Vol. VIII. Jaua. 9 [ ] [ ] ω s cos cos s cos s s [ ] [ ] ω s cos s cos s s cos whch ae deed fo tasfoato () afte ts epadg substtuto ad dffeetato b te t. The poecto of the aea S of the udegoud pat of a -th blade at -th posto o the plae pepedcula to the decto of the eloct of the blade the sste O s N N N N N N S S. Foce appled to the cete of ass of udegoud pat of -th blade at the -th posto ca be deteed b the foula Goachk (98) a S c k F ' whee k a s the tal esstt of sol dest of a sol c shape coeffcet of a blade - eloct of the cete of ass of the udegoud pat of the -th blade at the -th posto the sste O (Fg. ) odulus of the eloct. The poectos o aes O O O of the foces F ' ae a cs S k F ' a cs S k F ' a cs S k F '. The coputatos show that fo ξ o ad ξ - o the dsk dgg tool has the sae wokg depth. Let us copae below the paaetes of the foce sstes appled to the dsk dgg tool fo ξ o ad ξ - o whe k a Pa; kg/ ; c. ω /s. Fg. 7 shows the depedece of ' F (N) ' F (N) ' F (N) o agle of otato (deg) whe ξ o (Fg. 7a) ad ξ - o (Fg. 7b).

20 F' F' F' a F' F' F' b Fgue 7. The depedece the poectos of the foce otato whe ξ o (a) ad ξ - o (b). ' F o the agle of The poectos of the esultat foce F of the foce sste appled to the dsk dgg tool at the -th posto ae 7 F F' 7 F F' F Fg. 8 shows the depedece of F (N) F (N) F (N) o the agle of otato (deg) whe ξ o (Fg. 8a) ad ξ - o (Fg. 8b). 7 F'. Heloo ad J. Olt. The ethod of Vtual Realt fo Ceato a Dsk-Rdgg Tool. Agcultual Egeeg Iteatoal: the CIGR Eoual. auscpt P 8. Vol. VIII. Jaua.

21 F F F a F F F b Fgue 8. The depedece the poectos of the esultat foce F o the agle of otato whe ξ o (a) ad ξ - o (b). The oets ' ' ' of the foce F appled to the cete of ass of the udegoud pat of the -th blade the -th posto elate to the aes O O O (Fg. ) accodgl ae deteed b foulas ' F ' ( t ) F ' ( H ) ( ' F' F H ) ' ' F' F ( t ) ' Fg. 9 shows the depedece the oets '. (N) ' (N) ' (N) o the agle of otato whe ξ o (Fg. 9a) ad ξ - o (Fg. 9b).. Heloo ad J. Olt. The ethod of Vtual Realt fo Ceato a Dsk-Rdgg Tool. Agcultual Egeeg Iteatoal: the CIGR Eoual. auscpt P 8. Vol. VIII. Jaua.

22 ' ' ' a ' ' ' b Fgue 9. The depedece of the oets '. ' ' o the agle of otato whe ξ o (a) ad ξ - o (b) The esultat oets elate to the aes O O O (Fg. ) appled to the dsk dgg tool the -th posto ae deteed b foulas accodgl. 7 ' 7 ' ' 7 Fg. shows the depedece the oets (N) (N) otato (deg) whe ξ o (Fg. a) ad ξ - o (Fg. b). (N) o the agle of. Heloo ad J. Olt. The ethod of Vtual Realt fo Ceato a Dsk-Rdgg Tool. Agcultual Egeeg Iteatoal: the CIGR Eoual. auscpt P 8. Vol. VIII. Jaua.

23 a b Fgue. The depedece of the oets o the agle of otato whe ξ o (a) ad ξ - o (b). The followg tasfoato C ( ) B( ) A( ) tasfos the oets elate to the aes O O O (Fg. ). to the coespodg oets Fg. shows the depedece the oets (N) (N) otato (deg) whe ξ o (Fg. a) ad whe ξ - o (Fg. b). (N) o agle of. Heloo ad J. Olt. The ethod of Vtual Realt fo Ceato a Dsk-Rdgg Tool. Agcultual Egeeg Iteatoal: the CIGR Eoual. auscpt P 8. Vol. VIII. Jaua.

24 a b Fgue. The depedece the oets o the agle of otato whe ξ o (a) ad ξ - o (b). It follows fo Fgs. 7 that the foce sste appled to a blade ad to the tual dsk dgg tool substatall depeds fo alue of the adustet agle ξ (Fg. ). I the case of the alue ξ ο the alues of foces ad oets ae appoatel twce geate tha the case ξ ο. It eas that the dsk dgg tool whch blades hae the adustet agle ξ ο has bette ablt fo og sol fo the lateal suface of the dge to ts top.. Heloo ad J. Olt. The ethod of Vtual Realt fo Ceato a Dsk-Rdgg Tool. Agcultual Egeeg Iteatoal: the CIGR Eoual. auscpt P 8. Vol. VIII. Jaua.. CONCLUSIONS The ethod of tual ealt cosdeed ths pape ca be used to pedct useful foato fo epeetal stud of the wokg pocess of ache eleets. B applcato of ths ethod to the aalss of a tual wokg pocess of a tual dsk dgg tool the sutable alues of t paaetes ae foud out. Oe ca coclude ow that fo the fed wokg depth eloct of fowad oto ad ube of blades of the dsk dgg tool the qualt of pocessg a sol the dge ad the foce sste appled to the dsk dgg tool ae substatall deped o the alue of the adustet agle ξ ad o the agula eloct ω of the dsk dgg tool. The ablt to oe sol fo the botto of the dge to ts top depeds to a lage etet o the alue of the adustet agle ξ.. REFERENCES Sä K. 98. The ethod of the epoducto of the seed potato. VASHNIL Sbea dep. Noosbsk ol. pp. 7- ( Russa) Olt J.. Cobed Techolog of the Wde Row Potato Gowg Thess fo PhD

25 Agcultual Egeeg Agcultual ache p. Olt J.999. The Stud of the ew Cobed Wde Row Potato Feld Pocessg ache. Poc. It. Cof. Teds Agcultual Egeeg Pague. pp. 8. Heloo. Olt J.. Chaactestcs of the Ceatc Coeffcet Resultg Fo Sol Resstt o the Ccula Lk of a New Wde-Fuow Potato Feld Cobe Pocessg ache. CD Papes fo the Cof. AgEg. 8 p. Olt J. () New Techolog fo Wde Fuow Potato Gowg ad Possbltes Fo ts Realsato Poceedgs XXIX CIOSTA-CIGR V Cogess Kakow Jue 7 pp.. Heloo. Olt J. a. A tual poecto based stud o the oto of a fee-acte dgg tool fo ew cobe wde ow potato feld tllage ache Poceedgs XXIX CIOSTA-CIGR V Cogess Kakow Jue 7 pp. 7. Heloo. Olt J. b. oto of the Fee-Acte Ccula Lk o the Top of a Potato Rdge odelled as a Polgoal Clde. Poc. It. Cof. Pespecte Sustaable Techologcal Pocess Agcultual Egeeg Raudodas (Lthuaa) pp. 99. Olt J. Heloo. c. Cobed Sustaable Techolog fo Cultato a Potato Feld of Elaged Rdges. Poc. It. Cof. Pespecte Sustaable Techologcal Pocess Agcultual Egeeg Raudodas (Lthuaa). Heloo. Olt J. a. Aalss of Foces Appled to the Dsk Rdgg Tool of the Cobe Wde Row Potato Feld Tllage ache Poc. of the Uo of Scetsts - Rousse Eeg Effcec ad Agcultual Egeeg ol. pp. 8. Heloo. Olt J. b. Ceato of Cobe Tllage ache fo Suppotg Wde Row Seed Potato Gowg ethod. Balka Ag. Eg. Reew (The Electoc Joual) Vol. p. Olt J.; Heloo. c. O Kow-How fo Ceatg a New Sustaable Cobe Wde Row Potato Feld Tllage ache. Poc. d It Cof. Idustal Egeeg New Challeges to SE Tall pp.. Heloo. Olt J. b. The Iagato of the Foced De Dsk dgg Tool ad t s Wokg Poccess the athcad Eoet. Poc. th It. DAAA Cof. I dustal Egeeg Ioato as Copete Edge Fo SE Tall pp. 8. Heloo. Olt J. c. Aato of oto of the Dsk dgg Tool. Poc. of the Uo of Scetsts Secod Cof. Eeg Effcec ad Agcultual Egeeg Rousse (Bulgaa) pp. 7. Heloo. Olt J. a. Aato of the Wokg Pocess of the Dsk dgg Tool CD Papes It. Cof. AgEg Leue (Belgu). Goachk V. P. (98) Selected woks. Publshg House Kolos oscow p.. Heloo ad J. Olt. The ethod of Vtual Realt fo Ceato a Dsk-Rdgg Tool. Agcultual Egeeg Iteatoal: the CIGR Eoual. auscpt P 8. Vol. VIII. Jaua.

Consider two masses m 1 at x = x 1 and m 2 at x 2.

Consider two masses m 1 at x = x 1 and m 2 at x 2. Chapte 09 Syste of Patcles Cete of ass: The cete of ass of a body o a syste of bodes s the pot that oes as f all of the ass ae cocetated thee ad all exteal foces ae appled thee. Note that HRW uses co but