Lagrangian Dynamics Analysis of a XY-Theta Parallel Robotic Machine Tool

  • Javad Enferadi Department of Mechanical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran
  • Mohammad Tavakolian Department of Mechanical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran

Abstract

Dynamics of a highly stiff parallel machine tool is the subject of this paper. High stiffness, good accuracy, relatively large workspace and free of singularities on the whole workspace makes the manipulator suitable for machining applications as an XY-Theta precision table. First, obtaining kinematics constraints, inverse kinematics analysis and velocity analysis are performed. Next, using six redundant generalized coordinates, we obtain Lagrangian of the manipulator. Also, a Lagrangian approach is proposed to obtain dynamics equations of the machine tool using three Lagrangian multipliers. This method allows elimination of constraint forces and moments at the joints from the motion equations. Dynamic equations of the manipulator are formed as inverse dynamics and direct dynamics problems. Finally, two examples are presented that confirms the obtained dynamics equations.

Keywords: parallel kinematics machine tool, Lagrangian dynamics, Lagrangian multipliers, inverse dynamics, forward dynamics
Published online
2017-03-30
How to Cite
Enferadi, J. and Tavakolian, M. (2017) “Lagrangian Dynamics Analysis of a XY-Theta Parallel Robotic Machine Tool”, Periodica Polytechnica Mechanical Engineering, 61(2), pp. 107-114. https://doi.org/10.3311/PPme.9368.
Section
Articles