MATRIX EXPONENTIALS IN ROBOT ELASTOKINEMATICS

Iuliu NEGREAN, Adina CRIŞAN

Abstract


The main objective of this paper consists in the establishment of the generalized elastokinematics equations for robot structures with flexible links. For kinematics and differential matrices in the case of the robot structures with rigid and elastic links will be applied the matrix exponentials, in accordance with the algorithm developed by the main author. Consequently, the matrix exponentials will stay at the basis of establishment the linear and angular transfer matrices. By means of the same matrix exponentials will be also determined all kinematic parameters. In the second part of this paper elastokinematics structure of the serial robot will be analyzed. Applying the properties of the matrix exponentials, the locating matrices and their time derivatives corresponding to small deformations will be also established. On the basis of these differential transformations, in the final part of the paper, will be determined the linear and angular velocities and accelerations, as well as Jacobian matrix.

Key words: elastokinematics, elastodynamics, advanced mechanics, robotics.


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References


Appell, P., Sur une forme générale des equations de la dynamique, Paris, 1899

Book, W. J., Recursive Lagrangian Dynamics of Flexible Manipulator Arms, International Journal of Robotics Research, Vol. 3, 1984, pp.87-101.

J.J. Craig, 2005, Introduction to Robotics: Mechanics and Control, 3rd edition, Pearson Prentice Hall, Upper Saddle River, NJ.

Fu K., Gonzales R., Lee C., Control, Sensing, Vision and Intelligence, McGraw-Hill Book Co., International Edition, 1987

Negrean I., Vușcan I., Haiduc N., Robotics. Kinematic and Dynamic Modeling, Editura Didactică și Pedagogică, R.A. București, 1998

Negrean, I., Kinematics and Dynamics of Robots - Modelling•Experiment•Accuracy, Editura Didactica si Pedagogica R.A., ISBN 973-30-9313-0, Bucharest, Romania, 1999.

Negrean I., Mecanică avansată în Robotică, ISBN 978-973-662-420-9, UT Press, Cluj-Napoca, Romania, 2008.

Negrean, I., Negrean, D. C., Matrix Exponentials to Robot Kinematics, 17th International Conference on CAD/CAM, Robotics and Factories of the Future, CARS&FOF 2001,Vol.2, pp. 1250-1257, Durban, South Africa, 2001.

Negrean,I., Negrean, D.C., The Acceleration Energy to Robot Dynamics, Proceedings of A&QT-R (THETA 13) International Conference on Automation, Quality and Testing, Robotics, Tome II , pp. 59-64, Cluj-Napoca, Romania, 2002.

Negrean, I., Negrean, D. C., Albeţel, D. G., An Approach of the Generalized Forces in the Robot Control, Proceedings, CSCS-14, 14th International Conference on Control Systems and Computer Science, Polytechnic University of Bucharest, Romania,

ISBN 973-8449-17-0, 2003, pp. 131-136.

Negrean, I., Pîslă, D., Negrean, D. C., New Modeling with Matrix Exponentials in the Robot Accuracy, Proceedings, CSCS-14, 14th International Conference on control Systems and Computer Science, 2–5 July, 2003, Polytechnics University of Bucharest,

ISBN 973-8449-17-0, pp. 143-148.

Negrean, I., Albeţel, D. G., The Generalized Elastodynamics Equations in Robotics, Proceedings of AQTR 2004 IEEE-TTTC (THETA 14), International Conference on Automation, Quality and Testing, Robotics, Tome II, pp. 159-164, Cluj-Napoca, Romania, 2004.

Negrean, I., Negrean, D. C., The Acceleration Energy to Robot Dynamics, International Conference on Automation, Quality and Testing, Robotics, AQTR 2002, May 23-25, Cluj-Napoca, Tome II, pp. 59-64

Negrean, I., Energies of Acceleration in Advanced Robotics Dynamics, Applied Mechanics and Materials, ISSN: 1662-7482, vol 762, pp 67-73 Submitted: 2014-08-05 ©(2015)TransTech Publications Switzerland

Negrean I., New Formulations on Acceleration Energy in Analytical Dynamics, Applied Mechanics and Materials, vol. 823 pp 43-48 © (2016) TransTech Publications Switzerland Revised: 2015-09,

Negrean I., New Formulations on Motion Equations in Analytical Dynamics, Applied Mechanics and Materials, vol. 823 (2016),

pp 49-54 © (2016) TransTech Publications.

Negrean I., Advanced Notions in Analytical Dynamics of Systems, Acta Technica Napocensis, Series: Applied Mathematics, Mechanics and Engineering, Vol. 60, Issue IV, November. 2017, pg. 491-502.

Negrean I., Advanced Equations in Analytical Dynamics of Systems, Acta Technica Napocensis, Series: Applied Mathematics, Mechanics and Engineering, Vol. 60, Issue IV, November 2017, pg. 503-514.

Negrean I., New Approaches on Notions from Advanced Mechanics, Acta Technica Napocensis, Series: Applied Mathematics, Mechanics and Engineering, Vol. 61, Issue II, June 2018, pg. 149-158.

Negrean I., Generalized Forces in Analytical Dynamic of Systems, Acta Technica Napocensis, Series: Applied Mathematics, Mechanics and Engineering, Vol. 61, Issue II, June 2018, pg. 357-368.

Park, F.C., Computational Aspects of the Product-of-Exponentials Formula for Robot Kinematics, IEEE Transaction on Automatic Control, Vol. 39, No. 3, 1994

Bratu, P., et all., The Dynamic Isolation Performances Analysis of The Vibrating Equipment with Elastic Links to a Fixed Base, Acta Technica Napocensis, Series: Applied Mathematics, Mechanics and Engineering, Vol. 61, Issue I, March, pg. 23-28, 2018.

Mihălcică, M., Vlase, S., Identifiers for Human Motion Analysis, Acta Technica Napocensis, Series: Applied Mathematics, Mechanics and Engineering, Vol. 60, Issue II, June, pg. 239-244, 2017.

Vlase, S. Danasel, C. Scutaru, M. L. et al., Finite Element Analysis of a Two-Dimensional Linear Elastic Systems with a Plane "Rigid Motion". Romanian Journal of Physics, Vol. 59 (5-6), pp. 476-487, 2014.

Vlase, S., Dynamical Response of a Multibody System with Flexible Elements with a General Three-Dimensional Motion. Romanian Journal of Physics, Vol. 57 (3-4),pp. 676-693, 2012.

Vlase, S., Munteanu, M.V., Scutaru, M.L., On the Topological Description of the Multibody Systems. 19th International Symposium of the Danube-Adria-Association-for-Automation-and-Manufacturing, Trnava, Slovakia, pp. 1493-1494, 2008.

Vlase, S.; Teodorescu, P. P., Elasto-Dynamics of a Solid with A General "Rigid" Motion Using Fem Model Part I. Theoretical Approach. Romanian Journal of Physics, Vol.:58(7-8),pp. 872-881, 2013.

Vlase, S., Itu, C., Structures with Symmetries Used in Civil Engineering, Acta Technica Napocensis, Series: Applied Mathematics, Mechanics and Engineering, Vol. 55, Issue III, pg. 689-692, 2012.

Vlase, S., Năstac, C., Marin, M., Mihălcică, M., A Method for the Study of the Vibration of Mechanical Bars Systems with Symmetries, Acta Technica Napocensis, Series: Applied Mathematics, Mechanics and Engineering, Vol. 60, Issue IV, pg. 539-544, 2017.

Yuan, B.–S., Book, W. J., Huggins, J. D., Dynamics of Flexible Manipulator Arms: Alternative derivation, Verification, and Characteristics for Control, ASME Journal of Dynamics Systems, Measurements and Control, Vol. 115, 1993, pp.394-404.


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