**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**32726

##### Using Lagrange Equations to Study the Relative Motion of a Mechanism

**Authors:**
R. A. Petre,
S. E. Nichifor,
A. Craifaleanu,
I. Stroe

**Abstract:**

The relative motion of a robotic arm formed by homogeneous bars of different lengths and masses, hinged to each other is investigated. The first bar of the mechanism is articulated on a platform, considered initially fixed on the surface of the Earth, while for the second case the platform is considered to be in rotation with respect to the Earth. For both 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 MATLAB program.

**Keywords:**
Lagrange equations,
relative motion,
inertial or non-inertial reference frame.

**References:**

[1] I. Stroe, P. Pârvu, “Trajectories in non-inertial reference farmes”, U.P.B. Sci. Bull. Series D, Vol. 72, Issue 4, ISSN - 1454-2358, 2010.

[2] T.-V. Nguyen, R.-A. Petre, I. Stroe, Application of Lagrange Equations For Calculus of Internal Forces in a Mechanism, U.P.B. Sci. Bull., Series D, Vol. 78, Iss. 4, pg. 15-26, ISSN 1454-2358, 2016.

[3] T.-V. Nguyen, R.-A. Petre, I. Stroe, “Calculus of axial force in a mechanism using Lagrange equations”, INCAS Bulletin, volume 8, issue 2, (online) ISSN 2247–4528, (print) ISSN 2066–8201, ISSN–L 2066–8201, pp. 97-108, DOI: 10.13111/2066-8201.2016.8.2.8, April-June 2016.

[4] I. Stroe, A. Craifaleanu, “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 Vol. 656, pp. 171-180, Trans Tech Publications, Switzerland, 2014.

[5] I. Stroe, A. Craifaleanu, “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.

[6] I. Stroe, Ș. Staicu, A. Craifaleanu, “Methods in dynamics of compass robotic arm”, Conference Caius Iacob INCAS, 2011.

[7] Roxana-Alexandra, PETRE; Ion, STROE; Andrei, CRAIFALEANU,” Rotation-Rotation Mechanism moving with Respect to a Plane”, INCAS BULLETIN, vol.11, issue 4, pages 123-131, 2019-12-01, DOI 10.13111/2066-8201.2019.11.4.11