DOI: https://doi.org/10.32515/2664-262X.2022.5(36).2.22-30
Kinematic Dependencies of Two-axis Parallel Manipulator With Rotary Fastening of Hinges of Variable Length Links
Oleksandr Kropivny, Рostgraduate, Central Ukrainian National Technical University, Kropyvnytskyi, Ukraine, e-mail: a.krp78@gmail.com, ORCID ID: 0000-0002-6445-092Х
Andrii Hrechka, Associate Professor, PhD in Technics (Candidate of Technics Sciences), Central Ukrainian National Technical University, Kropyvnytskyi, Ukraine, e-mail: angre17@gmail.com, ORCID ID: 0000-0003-1188-7412
Andrii Kyrychenko, Professor, Doctor in Technics (Doctor of Technics Sciences), Central Ukrainian National Technical University, Kropyvnytskyi, Ukraine, e-mail: amkyrychenko@gmail.com, ORCID ID: 0000-0002-4335-9588
Kyryl Shcherbyna, Associate Professor, PhD in Technics (Candidate of Technics Sciences), Central Ukrainian National Technical University, Kropyvnytskyi, Ukraine, e-mail: kir2912s@ukr.net, ORCID ID: 0000-0002-1665-7686
Abstract
In the article the kinematic problem for a new two-axis parallel manipulator with rotary hinged parallelogram, the source of which is a spindle unit, is performed. The analysis of the received kinematic dependencies is carried out. The presence of special provisions of the source body of the mechanism is established. The directions of further scientific researches are outlined.
The parallel manipulator structure for consideration differs from previously developed fastenings of hinges of rods of variable length on rotary levers which rotation is coordinated with rotation of an initial link with a spindle unit. On the basis of the developed scheme mathematical dependences for lengths of actuators are established. The performed mathematical transformations allowed to solve direct and inverse kinematic problems for the mechanism. Analysis of the obtained kinematic dependences showed the presence of special positions of the initial body of the mechanism in the form of kinematic parallel singularities. Their graph is given. Graphs of changes of coordinates of an output link at change of lengths of rods of the drive of giving are shown. The analysis of graphic dependences shows existence of such combinations of constructive parameters of the mechanism at which the drive of giving starts to work in a multiplicative mode.
The obtained dependences will allow to ensure the functioning of the kinematic circuits of the feed drive of this mechanism. The established points of the kinematic parallel singularity of the feed drive and its operation in the multiplicative mode require further consideration taking into account the dynamic loads. By selecting the design parameters of the mechanism, it is possible to achieve close to rectilinear relationships between changes in the length of the rods and the movement of the spindle unit.
Keywords
parallel manipulator, two-axis manipulator, rotating hinged parallelogram, kinematics
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References
1. Kuznetsov, Yu.N., Dmytriev, D.A. & Dynevych, H.E. (2010). Komponovky stankov s mekhanyzmamy parallel'noj struktury [Layouts of machine tools with mechanisms of a parallel structure]. Yu.N. Kuznetsova (Eds.). Kherson: PP Vyshemyrs'kyj V.S. [in Russian].
2. Xin-Jun Liu & Jinsong Wang. (2014). Parallel Kinematics: Type, Kinematics, and Optimal Design. Springer Science & Business Media, 309 p. [in English].
3. Kuleshkov, Yu.V., Hrechka, A.I. & Shaposhnyk, L.Yu. (2015). Optymizatsiia pryvodu poperechnykh peremischen' holovky pozdovzhn'o-frezernoho verstata [Optimization of the drive of transverse movements of the head of a longitudinal milling machine]. Zbirnyk prats' molodykh naukovtsiv KNTU – Collection of works of young scientists of KNTU, Vol.5, 508-517 [in Ukrainian].
4. Reimund Neugebauer. (2006). Parallelkinematische Maschinen: Entwurf, Konstruktion, Anwendung. Springer ist ein Unternehmen von Springer Science+Business Media, 262 p. [in German].
5. Valiavs'kyj, I.A. & Shaposhnyk, V.Yu. (2013). Kinematychnyj analiz verstata z paralel'noiu kinematykoiu typu «del'ta» [Kinematic analysis of a machine tool with parallel kinematics of the "Delta" type]. Tekhnika v sil's'kohospodars'komu vyrobnytstvi, haluzeve mashynobuduvannia, avtomatyzatsiia: zb. naukovykh prats' Kir-koho nats. tekhn. univ. – Collected Works of Kirovohrad National Technical University. Machinery in Agricultural Production, Industry Machine Building, Automation, Issue 26, 78-81. [in Ukrainian].
6. Verstat : pat. na kor. mod. 35361 Ukraina : MPK V23B 41/00. № u 2008 05562 ; zaiavl. 29.04.2008 ; opubl. 10.09.2008, Biul. № 17. [in Ukrainian].
7. Verstat : pat. na kor. mod. 35360 Ukraina : MPK V23D 5/00. № u 2008 05560 ; zaiavl. 29.04.2008 ; opubl. 10.09.2008, Biul. № 17. [in Ukrainian].
8. Verstat : pat. na kor. mod. 44556 Ukraina : MPK V23V 41/00. № u 2009 03558 ; zaiavl. 13.04.2009 ; opubl. 12.10.2009, Biul. № 19. [in Ukrainian].
9. Verstat : pat. na kor. mod. 52723 Ukraina : MPK V23V 41/00. № u 2010 01443 ; zaiavl. 12.02.2010 ; opubl. 10.09.2010, Biul. № 17. [in Ukrainian].
10. Verstat z paralel'noiu kinematykoiu : pat. na kor. mod. 148653 Ukraina : MPK V23B 41/00. № u 2021 01754 ; zaiavl. 05.04.2021 ; opubl. 01.09.2021, Biul. № 35. [in Ukrainian].
11. Kyrychenko, A.M., Zaika, S.M. & Fedot'iev, A.M. (2010). Osoblyvi polozhennia ploskykh mekhanizmiv paralel'noi struktury. Novi tekhnolohii v mashynobuduvanni. Visnyk KDU imeni Mykhajla Ostrohrads'koho. Issue 5/2010 (64), part. 1, 94-99 [in Ukrainian].
GOST Style Citations
Кузнецов Ю.Н., Дмитриев Д.А., Диневич Г.Е. Компоновки станков с механизмами параллельной структуры ; под ред. Ю.Н. Кузнецова. Херсон: ПП Вишемирський В.С., 2010. 471 с.
Xin-Jun Liu, Jinsong Wang. Parallel Kinematics: Type, Kinematics, and Optimal Design. Springer Science & Business Media, 2014. 309 p.
Ю.В. Кулешков, А.І. Гречка, Л.Ю. Шапошник. Оптимізація приводу поперечних переміщень головки поздовжньо-фрезерного верстата. Збірник праць молодих науковців КНТУ, 2015. Вип.5. С. 508-517.
Reimund Neugebauer. Parallelkinematische Maschinen: Entwurf, Konstruktion, Anwendung. Springer ist ein Unternehmen von Springer Science+Business Media, 2006. 262 p.
І.А. Валявський, В.Ю.Шапошник. Кінематичний аналіз верстата з паралельною кінематикою типу «дельта». Техніка в сільськогосподарському виробництві, галузеве машинобудування, автоматизація: зб. наук. пр. Кіровоградського нац. техн. ун-ту. 2013. Вип. 26. С. 78-81.
Верстат : пат. на кор. мод. 35361 Україна : МПК В23B 41/00. № u 2008 05562 ; заявл. 29.04.2008 ; опубл. 10.09.2008, Бюл. № 17.
Верстат : пат. на кор. мод. 35360 Україна : МПК В23D 5/00. № u 2008 05560 ; заявл. 29.04.2008 ; опубл. 10.09.2008, Бюл. № 17.
Верстат : пат. на кор. мод. 44556 Україна : МПК В23В 41/00. № u 2009 03558 ; заявл. 13.04.2009 ; опубл. 12.10.2009, Бюл. № 19.
Верстат : пат. на кор. мод. 52723 Україна : МПК В23В 41/00. № u 2010 01443 ; заявл. 12.02.2010 ; опубл. 10.09.2010, Бюл. № 17.
Верстат з паралельною кінематикою : пат. на кор. мод. 148653 Україна : МПК В23B 41/00. № u 2021 01754 ; заявл. 05.04.2021 ; опубл. 01.09.2021, Бюл. № 35.
Кириченко А.М., Заїка С.М., Федотьєв А.М. Особливі положення плоских механізмів паралельної структури. Нові технології в машинобудуванні. Вісник КДУ імені Михайла Остроградського. Вип. 5/2010 (64). Частина 1. С. 94-99.
Copyright (c) 2022 Oleksandr Kropivny, Andrii Hrechka, Andrii Kyrychenko, Kyryl Shcherbyna
Kinematic Dependencies of Two-axis Parallel Manipulator With Rotary Fastening of Hinges of Variable Length Links
Oleksandr Kropivny, Рostgraduate, Central Ukrainian National Technical University, Kropyvnytskyi, Ukraine, e-mail: a.krp78@gmail.com, ORCID ID: 0000-0002-6445-092Х
Andrii Hrechka, Associate Professor, PhD in Technics (Candidate of Technics Sciences), Central Ukrainian National Technical University, Kropyvnytskyi, Ukraine, e-mail: angre17@gmail.com, ORCID ID: 0000-0003-1188-7412
Andrii Kyrychenko, Professor, Doctor in Technics (Doctor of Technics Sciences), Central Ukrainian National Technical University, Kropyvnytskyi, Ukraine, e-mail: amkyrychenko@gmail.com, ORCID ID: 0000-0002-4335-9588
Kyryl Shcherbyna, Associate Professor, PhD in Technics (Candidate of Technics Sciences), Central Ukrainian National Technical University, Kropyvnytskyi, Ukraine, e-mail: kir2912s@ukr.net, ORCID ID: 0000-0002-1665-7686
Abstract
Keywords
Full Text:
PDFReferences
1. Kuznetsov, Yu.N., Dmytriev, D.A. & Dynevych, H.E. (2010). Komponovky stankov s mekhanyzmamy parallel'noj struktury [Layouts of machine tools with mechanisms of a parallel structure]. Yu.N. Kuznetsova (Eds.). Kherson: PP Vyshemyrs'kyj V.S. [in Russian].
2. Xin-Jun Liu & Jinsong Wang. (2014). Parallel Kinematics: Type, Kinematics, and Optimal Design. Springer Science & Business Media, 309 p. [in English].
3. Kuleshkov, Yu.V., Hrechka, A.I. & Shaposhnyk, L.Yu. (2015). Optymizatsiia pryvodu poperechnykh peremischen' holovky pozdovzhn'o-frezernoho verstata [Optimization of the drive of transverse movements of the head of a longitudinal milling machine]. Zbirnyk prats' molodykh naukovtsiv KNTU – Collection of works of young scientists of KNTU, Vol.5, 508-517 [in Ukrainian].
4. Reimund Neugebauer. (2006). Parallelkinematische Maschinen: Entwurf, Konstruktion, Anwendung. Springer ist ein Unternehmen von Springer Science+Business Media, 262 p. [in German].
5. Valiavs'kyj, I.A. & Shaposhnyk, V.Yu. (2013). Kinematychnyj analiz verstata z paralel'noiu kinematykoiu typu «del'ta» [Kinematic analysis of a machine tool with parallel kinematics of the "Delta" type]. Tekhnika v sil's'kohospodars'komu vyrobnytstvi, haluzeve mashynobuduvannia, avtomatyzatsiia: zb. naukovykh prats' Kir-koho nats. tekhn. univ. – Collected Works of Kirovohrad National Technical University. Machinery in Agricultural Production, Industry Machine Building, Automation, Issue 26, 78-81. [in Ukrainian].
6. Verstat : pat. na kor. mod. 35361 Ukraina : MPK V23B 41/00. № u 2008 05562 ; zaiavl. 29.04.2008 ; opubl. 10.09.2008, Biul. № 17. [in Ukrainian].
7. Verstat : pat. na kor. mod. 35360 Ukraina : MPK V23D 5/00. № u 2008 05560 ; zaiavl. 29.04.2008 ; opubl. 10.09.2008, Biul. № 17. [in Ukrainian].
8. Verstat : pat. na kor. mod. 44556 Ukraina : MPK V23V 41/00. № u 2009 03558 ; zaiavl. 13.04.2009 ; opubl. 12.10.2009, Biul. № 19. [in Ukrainian].
9. Verstat : pat. na kor. mod. 52723 Ukraina : MPK V23V 41/00. № u 2010 01443 ; zaiavl. 12.02.2010 ; opubl. 10.09.2010, Biul. № 17. [in Ukrainian].
10. Verstat z paralel'noiu kinematykoiu : pat. na kor. mod. 148653 Ukraina : MPK V23B 41/00. № u 2021 01754 ; zaiavl. 05.04.2021 ; opubl. 01.09.2021, Biul. № 35. [in Ukrainian].
11. Kyrychenko, A.M., Zaika, S.M. & Fedot'iev, A.M. (2010). Osoblyvi polozhennia ploskykh mekhanizmiv paralel'noi struktury. Novi tekhnolohii v mashynobuduvanni. Visnyk KDU imeni Mykhajla Ostrohrads'koho. Issue 5/2010 (64), part. 1, 94-99 [in Ukrainian].