The study of the relative motion of a mechanism using Lagrange equations
Keywords:Lagrange equations, relative motion, inertial or noninertial reference frame
The relative motion of a robotic arm formed by homogeneous bars of different lengths and masses, hinged to each other is studied. There are two cases studied: the first one when the first bar of the mechanism is hinged on a platform, which is considered initially to be fixed on the Earth’s surface, for the second case, the platform is in rotation with respect to Earth. For all the analyzed cases the motion equations are determined using the Lagrangian formalism, applied in its traditional form, valid with respect to an inertial reference system, conventionally considered as fixed. However, in the second case, a generalized form of the formalism valid with respect to a non-inertial reference frame will also be applied. The numerical calculations were performed using a program developed using the MATLAB software.
STROE, I., PARVU, P., Trajectories in non-inertial reference farmes, U.P.B. Sci. Bull. Series D, 72, 4, ISSN - 1454-2358, 2010.
NGUYEN, T.-V., PETRE, R.-A., STROE, I., Application of Lagrange Equations For Calculus of Internal Forces in a Mechanism, U.P.B. Sci. Bull., Series D, 78, 4, pp. 15-26, 2016.
NGUYEN, T.-V., PETRE R.-A., STROE I., Calculus of axial force in a mechanism using Lagrange equations, INCAS Bulletin, 8, 2, pp. 97-108, 2016.
STROE, I., CRAIFALEANU, A., Generalization of the Lagrange equations formalism, for motions with respect to non-inertial reference frames, International Conference on Smart Systems in All Fields of the Life, Aerospace, Robotics, Mechanical Engineering, Manufacturing Systems, Biomechatronics, Neurorehabilitation and Human Motility, ICMERA 2014, Applied Mechanics and Materials, 656, pp. 171-180, Trans Tech Publications, Switzerland, 2014.
STROE, I., CRAIFALEANU, A., Calculus of a compass robotic arm using Lagrange equations in non-inertial reference frames, Proceedings of the International Conference of Aerospace Sciences "AEROSPATIAL 2012", Bucharest, 11-12 October, pp. 137-141, 2012.
STROE, I., STAICU, S., CRAIFALEANU, A., Methods in dynamics of compass robotic arm, Conference Caius Iacob INCAS, 2011.
PETRE, Roxana-Alexandra, STROE, Ion, CRAIFALEANU, Andrei, Rotation-Rotation Mechanism moving with Respect to a Plane, INCAS BULLETIN, 11, 4, pp. 123-131, 2019.
PETRE, R. A., NICHIFOR, S. E., CRAIFALEANU, A., STROE, I., Using Lagrange Equations to Study the Relative Motion of a Mechanism, World Academy of Science, Engineering and Technology International Journal of Aerospace and Mechanical Engineering, 14, 10, pp. 421-425, 2020.
STROE, Ion, STAICU, Stefan, Calculus of Joint Forces Using Lagrange Equations and Principle of Virtual Work, Proceedings of the Romanian Academy, Series A, 11, 3, pp. 253-260, 2010.
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