An algorithm to solve the inverse kinematics to a stewart platform
Main Article Content
Abstract
Mechanical systems in motion type parallel structures are solid, fast and accurate. Between mobile systems parallel the best known and used system is that of a Stewart platform, as being and the oldest system, quickly, solid and accurate. The paper presents a few main elements of the Stewart platforms. In the case where a motto element consists of a structure composed of two elements in a relative movement from the point of view of the train of propulsion and especially in the dynamic calculations, it is more convenient to represent the motto element as a single moving item. The paper presents an exact, original analytical geometry method for determining the kinematic and dynamic parameters of a parallel mobile structure. Compared with other methods already known, the presented method has the great advantage of being an exact analytical method of calculation and not one iterative-approximately.
Downloads
Article Details
1. Proposal of Policy for Free Access Periodics
Authors whom publish in this magazine should agree to the following terms:
a. Authors should keep the copyrights and grant to the magazine the right of the first publication, with the work simultaneously permitted under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 that allows the sharing of the work with recognition of the authorship of the work and initial publication in this magazine.
b. Authors should have authorization for assuming additional contracts separately, for non-exclusive distribution of the version of the work published in this magazine (e.g.: to publish in an institutional repository or as book chapter), with recognition of authorship and initial publication in this magazine.
c. Authors should have permission and should be stimulated to publish and to distribute its work online (e.g.: in institutional repositories or its personal page) to any point before or during the publishing process, since this can generate productive alterations, as well as increasing the impact and the citation of the published work (See The Effect of Free Access).
Proposal of Policy for Periodic that offer Postponed Free Access
Authors whom publish in this magazine should agree to the following terms:
a. Authors should keep the copyrights and grant to the magazine the right of the first publication, with the work simultaneously permitted under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 [SPECIFY TIME HERE] after the publication, allowing the sharing of the work with recognition of the authorship of the work and initial publication in this magazine.
b. Authors should have authorization for assuming additional contracts separately, for non-exclusive distribution of the version of the work published in this magazine (e.g.: to publish in institutional repository or as book chapter), with recognition of authorship and initial publication in this magazine.
c. Authors should have permission and should be stimulated to publish and to distribute its work online (e.g.: in institutional repositories or its personal page) to any point before or during the publishing process, since this can generate productive alterations, as well as increasing the impact and the citation of the published work (See The Effect of Free Access).
d. They allow some kind of open dissemination. Authors can disseminate their articles in open access, but with specific conditions imposed by the editor that are related to:
Version of the article that can be deposited in the repository:
Pre-print: before being reviewed by pairs.
Post-print: once reviewed by pairs, which can be:
The version of the author that has been accepted for publication.
The editor's version, that is, the article published in the magazine.
At which point the article can be made accessible in an open manner: before it is published in the magazine, immediately afterwards or if a period of seizure is required, which can range from six months to several years.
Where to leave open: on the author's personal web page, only departmental websites, the repository of the institution, the file of the research funding agency, among others.
References
AVERSA, R.; PARCESEPE, D.; PETRESCU, R. V.; BERTO, F.; CHEN, G.; PETRESCU, F. I. T.; TAMBURRINO, F.; APICELLA, A. (2017a) Processability of Bulk Metallic Glasses. Am. J. Applied Sci., v. 14, n. 2, p. 294-301. DOI: 10.3844/ajassp.2017.294.301
AVERSA, R.; PETRESCU, R. V.; PETRESCU, F. I. T.; APICELLA, A. (2017b) Nano-Diamond Hybrid Materials for Structural Biomedical Application. Am. J. of Biochemistry and Biotechnology, v. 13, n. 1, p. 34-41. DOI: 10.3844/ajbbsp.2017.34.41
AVERSA, R.; PARCESEPE, D.; PETRESCU, R. V.; CHEN, G.; PETRESCU, F. I. T.; TAMBURRINO, F.; APICELLA, A. (2016a) Glassy Amorphous Metal Injection Molded Induced Morphological Defects. Am. J. Applied Sci.,v. 13, n. 12, p. 1476-1482. DOI: 10.3844/ajassp.2016.1476.1482
AVERSA, R.; PETRESCU, F. I. T.; PETRESCU, R. V.; APICELLA, A. (2016b) Biomimetic Finite Element Analysis Bone Modeling for Customized Hybrid Biological Prostheses Development. Am. J. Applied Sci., v. 13, n. 11, p. 1060-1067. DOI: 10.3844/ajassp.2016.1060.1067
AVERSA, R.; TAMBURRINO, F.; PETRESCU, R. V.; PETRESCU, F. I. T.; ARTUR, M.; CHEN, G.; APICELLA, A. (2016c) Biomechanically Inspired Shape Memory Effect Machines Driven by Muscle like Acting NiTi Alloys. Am. J. Applied Sci., v. 13, n. 11, p. 1264-1271. DOI: 10.3844/ajassp.2016.1264.1271
AVERSA, R.; PETRESCU, R. V.; PETRESCU, F. I. T.; APICELLA, A. (2016d) Smart-Factory: Optimization and Process Control of Composite Centrifuged Pipes. Am. J. Applied Sci., v. 13, n. 11, p. 1330-1341. DOI: 10.3844/ajassp.2016.1330.1341
CAO, W.; DING, H.; BIN, Z.; ZIMING, C. (2013) New structural representation and digital-analysis platform for symmetrical parallel mechanisms. Int. J. Advanced Robotic Sys., DOI: 10.5772/56380
DONG, H.; GIAKOUMIDIS, N.; FIGUEROA, N.; MAVRIDIS, N. (2013) Approaching behavior monitor and vibration indication in developing a General Moving Object Alarm System , n. GMOAS). Int. J. Advanced Robotic Sys., DOI: 10.5772/56586
GARCIA, E.; JIMENEZ, M. A.; DE SANTOS, P. G.; ARMADA, M. (2007) The evolution of robotics research. Robotics Automation Magazine, IEEE, n. 14, p. 90-103.
GARCIA-MURILLO, M.; GALLARDO-ALVARADO, J.; CASTILLO-CASTANEDA, E. (2013) Finding the generalized forces of a series-parallel manipulator. IJARS, DOI: 10.5772/53824
GOUGH-STEWART PLATFORM, From Wikipedia, the free encyclopedia. Retrieved from: https://en.wikipedia.org/wiki/Stewart_platform
HE, B.; WANG, Z.; LI, Q.; XIE, H.; AND SHEN, R. (2013) An analytic method for the kinematics and dynamics of a multiple-backbone continuum robot. IJARS, DOI: 10.5772/54051
LEE, B. J. (2013) Geometrical derivation of differential kinematics to calibrate model parameters of flexible manipulator. Int. J. Advanced Robotic Sys., DOI: 10.5772/55592
LIN, W.; LI, B.; YANG, X.; ZHANG, D. (2013) Modelling and control of inverse dynamics for a 5-DOF parallel kinematic polishing machine. Int. J. Advanced Robotic Sys., DOI: 10.5772/54966
LIU, H.; ZHOU, W.; LAI, X.; ZHU, S. (2013) An efficient inverse kinematic algorithm for a PUMA560-structured robot manipulator. IJARS, DOI: 10.5772/56403
MELO, L. F.; REIS ALVES, S. F.; ROSARIO, J. M. (2012) Mobile robot navigation modelling, control and applications. Int. Rev. Modelling Simulations, n. 5, p. 1059-1068.
MIRSAYAR, M. M.; JONEIDI, V. A.; PETRESCU, R. V.; PETRESCU, F. I. T.; BERTO, F. (2017) Extended MTSN criterion for fracture analysis of soda lime glass, Engineering Fracture Mechanics, v. 178, p. 50–59, ISSN: 0013-7944, http://doi.org/10.1016/j.engfracmech.2017.04.018
PADULA, F.; PERDEREAU, V. (2013) An on-line path planner for industrial manipulators. Int. J. Advanced Robotic Sys.; DOI: 10.5772/55063
PERUMAL, S.; JAWAHAR, N. (2013) Automated trajectory planner of industrial robot for pick-and-place task. IJARS, DOI: 10.5772/53940
PETRESCU, F. I. T. ; PETRESCU, R.V. (2011) Mechanical Systems, Serial and Parallel – Course , n. in Romanian), LULU Publisher, London, UK, 124 pages, ISBN 978-1-4466-0039-9, Romanian edition.
PETRESCU, F. I. T.; PETRESCU, R. V. (2012) Mecatronica-sisteme seriale si paralele. Create Space publisher, USA, ISBN 978-1-4750-6613-5, 128 pages, Romanian edition.
PETRESCU, F. I. T.; APICELLA, A.; RAFFAELLA, A.; PETRESCU, R. V.; CALAUTIT, J. K.; MIRSAYAR, M. M.; ANIELLO, R. (2016b) Something about the Mechanical Moment of Inertia. Am. J. Applied Sci., v. 13, n. 11, p. 1085-1090. DOI: 10.3844/ajassp.2016.1085.1090
PETRESCU, F. I. T.; PETRESCU, R. V. (2016a) Parallel moving mechanical systems kinematics. ENGEVISTA, n. 18, p. 455-491.
PETRESCU, F. I. T.; PETRESCU, R. V. (2016b) Dynamic cinematic to a structure 2R. Revista Geintec-Gestao Inovacao E Tecnologias, n. 6, p. 3143-3154.
PETRESCU, F. I. T.; PETRESCU, R. V. (2014) Parallel Moving Mechanical Systems, IJM&P, v. 5, n. 3, p. 564-580.
PETRESCU, F. I. T. (2012) Teoria Mecanismelor Color: Curs si Aplicatii. 1st Edn.; CreateSpace Publisher, p. 284.
PETRESCU, R. V.; AVERSA, R.; APICELLA, A.; PETRESCU, F. I. T. (2016A) Future medicine services robotics. Am. J. Eng. Applied Sci., n. 9, p. 1062-1087.
PETRESCU, R. V.; AVERSA, R.; AKASH, B.; BUCINELL, R.; CORCHADO, J. (2017a) Modern propulsions for aerospace-a review. J. Aircraft Spacecraft Technol., n. 1, p. 1-8. DOI: 10.3844/jastsp.2017.1.8
PETRESCU, R.V.; AVERSA, R.; AKASH, B.; BUCINELL, R.; CORCHADO, J. (2017b) Modern propulsions for aerospace-part II. J. Aircraft Spacecraft Technol., n. 1, p. 9-17. DOI: 10.3844/jastsp.2017.9.17
PETRESCU, R.V.; AVERSA, R.; AKASH, B.; BUCINELL, R.; CORCHADO, J. (2017C) History of aviation-a short review. J. Aircraft Spacecraft Technol., n. 1, p. 30-49. DOI: 10.3844/jastsp.2017.30.49
PETRESCU, R.V.; AVERSA, R.; AKASH, B.; BUCINELL, R.; CORCHADO, J. (2017d) Lockheed martin-a short review. J. Aircraft Spacecraft Technol., n. 1, p. 50-68. DOI: 10.3844/jastsp.2017.50.68
PETRESCU, R. V.; AVERSA, R.; AKASH, B.; CORCHADO, J.; BERTO, F. (2017e) Our universe. J. Aircraft Spacecraft Technol., n. 1, p. 69-79. DOI: 10.3844/jastsp.2017.69.79
PETRESCU, R. V.; AVERSA, R.; AKASH, B.; CORCHADO, J.; BERTO, F. (2017f) What is a UFO? J. Aircraft Spacecraft Technol., n. 1, p. 80-90. DOI: 10.3844/jastsp.2017.80.90
PETRESCU, R. V.; AVERSA, R.; AKASH, B.; CORCHADO, J.; BERTO, F. (2017g) About bell helicopter FCX-001 concept aircraft-a short review. J. Aircraft Spacecraft Technol., n. 1, p. 91-96. DOI: 10.3844/jastsp.2017.91.96
PETRESCU, R. V.; AVERSA, R.; AKASH, B.; CORCHADO, J.; BERTO, F. (2017h) Home at airbus. J. Aircraft Spacecraft Technol., n. 1, p. 97-118. DOI: 10.3844/jastsp.2017.97.118
PETRESCU, R. V.; AVERSA, R.; AKASH, B.; CORCHADO, J.; BERTO, F. (2017i) Airlander. J. Aircraft Spacecraft Technol., n. 1, p. 119-148. DOI: 10.3844/jastsp.2017.119.148
PETRESCU, R. V.; AVERSA, R.; AKASH, B.; CORCHADO, J.; BERTO, F. (2017j) When boeing is dreaming-a review. J. Aircraft Spacecraft Technol., n. 1, p. 149-161. DOI: 10.3844/jastsp.2017.149.161
PETRESCU, R. V.; AVERSA, R.; AKASH, B.; CORCHADO, J.; BERTO, F. (2017k) About Northrop Grumman. J. Aircraft Spacecraft Technol., n. 1, p. 162-185. DOI: 10.3844/jastsp.2017.162.185
PETRESCU, R. V.; AVERSA, R.; AKASH, B.; CORCHADO, J.; BERTO, F. (2017l) Some special aircraft. J. Aircraft Spacecraft Technol., n. 1, p. 186-203. DOI: 10.3844/jastsp.2017.186.203
PETRESCU, R. V.; AVERSA, R.; AKASH, B.; CORCHADO, J.; BERTO, F. (2017m) About helicopters. J. Aircraft Spacecraft Technol., n. 1, p. 204-223. DOI: 10.3844/jastsp.2017.204.223
PETRESCU, R. V.; AVERSA, R.; AKASH, B.; BERTO, F.; APICELLA, A. (2017n) The modern flight. J. Aircraft Spacecraft Technol., n. 1, p. 224-233. DOI: 10.3844/jastsp.2017.224.233
PETRESCU, R. V.; AVERSA, R.; AKASH, B.; BERTO, F.; APICELLA, A. (2017o) Sustainable energy for aerospace vessels. J. Aircraft Spacecraft Technol., n. 1, p. 234-240. DOI: 10.3844/jastsp.2017.234.240
PETRESCU, R. V.; AVERSA, R.; AKASH, B.; BERTO, F.; APICELLA, A. (2017p) Unmanned helicopters. J. Aircraft Spacecraft Technol., n. 1, p. 241-248. DOI: 10.3844/jastsp.2017.241.248
PETRESCU, R. V.; AVERSA, R.; AKASH, B.; BERTO, F.; APICELLA, A. (2017q) Project HARP. J. Aircraft Spacecraft Technol., n. 1, p. 249-257. DOI: 10.3844/jastsp.2017.249.257
PETRESCU, R. V.; AVERSA, R.; AKASH, B.; BERTO, F.; APICELLA, A. (2017r) Presentation of romanian engineers who contributed to the development of global aeronautics-part I. J. Aircraft Spacecraft Technol., n. 1, p. 258-271. DOI: 10.3844/jastsp.2017.258.271
PETRESCU, R. V.; AVERSA, R.; AKASH, B.; BERTO, F.; APICELLA, A. (2017s) A first-class ticket to the planet mars, please. J. Aircraft Spacecraft Technol., n. 1, p. 272-281. DOI: 10.3844/jastsp.2017.272.281
PETRESCU, R. V.; AVERSA, R.; AKASH, B.; BERTO, F.; APICELLA, A.; PETRESCU, F. I. T. (2017t) Forces of a 3R Robot. J. of Mechatronics and Robotics, v. 1, n. 1, p. 1-14. DOI: 10.3844/jmrsp.2017.1.14
PETRESCU, R. V.; AVERSA, R.; AKASH, B.; BERTO, F.; APICELLA, A.; PETRESCU, F. I. T. (2017u) Direct Geometry and Cinematic to the MP-3R Systems. J. of Mechatronics and Robotics, v. 1, n. 1, p. 15-23. DOI: 10.3844/jmrsp.2017.15.23
PETRESCU, R. V.; AVERSA, R.; AKASH, B.; BERTO, F.; APICELLA, A.; PETRESCU, F. I. T. (2017v. Dynamic Elements at MP3R. J. of Mechatronics and Robotics 1, n. 2, p. 24-37. DOI: 10.3844/jmrsp.2017.24.37
PETRESCU, R. V.; AVERSA, R.; AKASH, B.; BERTO, F.; APICELLA, A.; PETRESCU, F. I. T. (2017w) Geometry and Direct Kinematics to MP3R with 4×4 Operators. J. of Mechatronics and Robotics, v. 1, n. 2, p. 38-46. DOI: 10.3844/jmrsp.2017.38.46
PETRESCU, R. V.; AVERSA, R.; APICELLA, A.; MIRSAYAR, M. M.; KOZAITIS, S.; ABU-LEBDEH, T.; PETRESCU, F. I. T. (2017x) Current Stage in the Field of Mechanisms with Gears and Rods. J. of Mechatronics and Robotics, v. 1, n. 2, p. 47-57. DOI: 10.3844/jmrsp.2017.47.57
PETRESCU, R. V.; AVERSA, R.; APICELLA, A.; MIRSAYAR, M. M.; KOZAITIS, S.; ABU-LEBDEH, T.; PETRESCU, F. I. T. (2017y) Geometry and Inverse Kinematic at the MP3R Mobile Systems. J. of Mechatronics and Robotics, v. 1, n. 2, p. 58-65. DOI: 10.3844/jmrsp.2017.58.65
PETRESCU, R. V.; AVERSA, R.; APICELLA, A.; MIRSAYAR, M. M.; KOZAITIS, S.; ABU-LEBDEH, T.; PETRESCU, F. I. T. (2017z) Synthesis of Optimal Trajectories with Functions Control at the Level of the Kinematic Drive Couplings. J. of Mechatronics and Robotics, v. 1, n. 2, p. 66-74. DOI: 10.3844/jmrsp.2017.66.74
PETRESCU, R. V.; AVERSA, R.; APICELLA, A.; MIRSAYAR, M. M.; KOZAITIS, S.; ABU-LEBDEH, T.; PETRESCU, F. I. T. (2017aa) The Inverse Kinematics of the Plane System 2-3 in a Mechatronic MP2R System, by a Trigonometric Method. J. of Mechatronics and Robotics, v. 1, n. 2, p. 75-87. DOI: 10.3844/jmrsp.2017.75.87
PETRESCU, R. V.; AVERSA, R.; APICELLA, A.; MIRSAYAR, M. M.; KOZAITIS, S.; ABU-LEBDEH, T.; PETRESCU, F. I. T. (2017ab) Serial, Anthropomorphic, Spatial, Mechatronic Systems can be Studied More Simply in a Plan. J. of Mechatronics and Robotics, v. 1, n. 2, p. 88-97. DOI: 10.3844/jmrsp.2017.88.97
PETRESCU, R. V.; AVERSA, R.; APICELLA, A.; MIRSAYAR, M. M.; KOZAITIS, S.; ABU-LEBDEH, T.; PETRESCU, F. I. T. (2017ac) Analysis and Synthesis of Mechanisms with Bars and Gears Used in Robots and Manipulators. J. of Mechatronics and Robotics, v. 1, n. 2, p. 98-108. DOI: 10.3844/jmrsp.2017.98.108
PETRESCU, R. V.; AVERSA, R.; APICELLA, A.; MIRSAYAR, M. M.; KOZAITIS, S.; ABU-LEBDEH, T.; PETRESCU, F. I. T. (2017ad) Speeds and Accelerations in Direct Kinematics to the MP3R Systems. J. of Mechatronics and Robotics, v. 1, n. 2, p. 109-117. DOI: 10.3844/jmrsp.2017.109.117
PETRESCU, R. V.; AVERSA, R.; APICELLA, A.; MIRSAYAR, M. M.; KOZAITIS, S.; ABU-LEBDEH, T.; PETRESCU, F. I. T. (2017ae) Geometry and Determining the Positions of a Plan Transporter Manipulator. J. of Mechatronics and Robotics, v. 1, n. 2, p. 118-126. DOI: 10.3844/jmrsp.2017.118.126
REDDY, P.; SHIHABUDHEEN, K. V.; JACOB, J. (2012) Precise nonlinear modeling of flexible link flexible joint manipulator. IReMoS, n. 5, p. 1368-1374.
TABAKOVIĆ, S.; ZELJKOVIĆ, M.; GATALO, R.; ŽIVKOVIĆ, A. (2013) Program suite for conceptual designing of parallel mechanism-based robots and machine tools. Int. J. Advanced Robotic Sys.; DOI: 10.5772/56633
TANG, X.; SUN, D.; SHAO, Z. (2013) The structure and dimensional design of a reconfigurable PKM. IJARS, DOI: 10.5772/54696
TONG, G.; GU, J.; XIE, W. (2013) Virtual entity-based rapid prototype for design and simulation of humanoid robots. Int. J. Advanced Robotic Sys.; DOI: 10.5772/55936
WANG, K.; LUO, M.; MEI, T.; ZHAO, J.; CAO, Y. (2013) Dynamics analysis of a three-DOF planar serial-parallel mechanism for active dynamic balancing with respect to a given trajectory. Int. J. Advanced Robotic Sys.; DOI: 10.5772/54201
WEN, S.; ZHU, J.; LI, X.; RAD, A.; CHEN, X. (2012) End-point contact force control with quantitative feedback theory for mobile robots. IJARS, DOI: 10.5772/53742