The robot equations of motion are obtained from the implemented program and verified against those obtained using only Lagrange equation. The output of program for the 3 DOF robot was used to find the optimal torque using analytical optimization analysis for a given set of parameters. This procedure analysis can be used as a benchmark analysis for any optimization technique. | Journal of Automation and Control Engineering, Vol. 1, No. 2, June 2013 Dynamics of a General Multi-axis Robot with Analytical Optimal Torque Analysis Atef A. Ata, Mohamed A. Ghazy, and Mohamed A. Gadou Department of Engineering Mathematics and Physics, Faculty of Engineering, Alexandria University, Alexandria 21544, Egypt Email: atefa@, {mohghazy, }@ Abstract—Robot dynamics is considered one of the most important issues in robot design and control. Many techniques were developed to find equations of motion. One of these techniques is Lagrange-Euler method which is suitable for numerical simulation. In this paper an implementation of Lagrange-Euler to find equations of motion for any general multi-axis robot giving only robot configurations is introduced. The program is verified for a 3 Degree-of-Freedom robot. The robot equations of motion are obtained from the implemented program and verified against those obtained using only Lagrange equation. The output of program for the 3 DOF robot was used to find the optimal torque using analytical optimization analysis for a given set of parameters. This procedure analysis can be used as a benchmark analysis for any optimization technique. generalized coordinates. In the comparison between Newton-Euler and Lagrange-Euler Silver [4] showed that the computational complexities of the two techniques are the same. In this paper, an implementation based of LagrangeEuler technique to determine the equations of motion for an n-axis robot is presented. An example for a 3 DOF robot is illustrated to verify the proposed algorithm. An analytical optimization approach is investigated as a benchmark for minimum energy using any optimization technique. The paper is organized as follows: section II contains the equations of motion in compact form and details of the algorithm to get each term. Section III presents the case study for a 3 DOF robot while section IV is devoted to analytical .
