Numerical Analysis of Robotic Manipulator Subject to Mechanical Flexibility by Lagrangian Method
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RESEARCH PAPER
Numerical Analysis of Robotic Manipulator Subject to Mechanical Flexibility by Lagrangian Method Ramalingam Sengalani1 • S. Rasool Mohideen1
Received: 7 November 2017 / Revised: 26 March 2019 / Accepted: 18 May 2019 The National Academy of Sciences, India 2019
Abstract In this work, a systematic approach is presented for the development of dynamic equations of motion of a robot manipulator with mechanical flexibility. A simple structural lightweight rotating manipulator with joint elastic flexibility is considered for the mechanical flexibility study. The complexity of mathematical equations involved in mechanical flexibility is analyzed. The analytical approach helps the design for controls of flexible manipulator. A set of decoupled dynamic equations are derived incorporating both the structural and joint flexibility. The dynamic equations are compared with a detailed model, and the results are showing that equations are accurate for small joints. Also the results from the simulation show that in a flexible joint system, there is no rigid mode. Keywords Manipulator Flexibility Mode shape Deflection Abbreviations ANN Artificial neural network RMSE Root mean square error AMM Assumed mode method FEM Finite element method MADL Maximum allowable dynamic load DOF Degrees of freedom MATLAB Math’s laboratory
& Ramalingam Sengalani [email protected] S. Rasool Mohideen [email protected] 1
Department of Mechanical Engineering, B.S. Abdur Rahman University School of Mechanical Sciences, Chennai, India
1 Introduction Nowadays, high speed vehicle, automotive crane, lightweight robots are used extensively in aerospace. Robotic manipulator is engaged to perform a tough task in adverse situations, with suitable structures. These structures are subjected to dynamic loading. The important aspects emphasized on the above are high standards of safety, fast performance and reliability on structural members. The necessity for accurate modeling is of prime importance in dynamic equation formulation and numerical analysis, and testing of flexible structure is inevitable for control of the system which is a complicated task. The characteristic parameters for a flexible link help to design control systems. The flexibility in the robot gives two meanings. One is performance flexibility, and the other is system component flexibility. The second is further subdivided into two groups, namely structural flexibility and joint flexibility, and the combination of both in the system is called as mechanical flexibility [1]. In industry, robot manipulator with mechanical flexibility is engaged for manufacturing unit of precision products; the necessity of analyzing the dynamic behavior of flexible robots and its control is a critical task for researchers. Mohammad et al. studied a dynamic model for planar robots with flexible joint drive and developed for servomotor control [2]. The virtual work method is used to form the mathematical model. Subuthi Band Ken Dutton present the modeling and control of a flexible m
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