Dynamic modelling and singularity-free simulation of closed loop multibody system driven by electric motors

Nguyen Quang Hoang, Vu Duc Vuong, Dinh Van Phong, Nguyen Tung Lam
Author affiliations


  • Nguyen Quang Hoang Hanoi University of Science and Technology, Vietnam https://orcid.org/0000-0003-2525-2856
  • Vu Duc Vuong \(^1\)Hanoi University of Science and Technology, Vietnam
    \(^2\)Thai Nguyen University of Technology, Vietnam
  • Dinh Van Phong Hanoi University of Science and Technology, Vietnam
  • Nguyen Tung Lam Hanoi University of Science and Technology, Vietnam




closed loop multibody system, electromechanical system, singularity-free, constrained stabilization, post-adjusting technique


This paper presents the dynamic model and singularity-free simulation of electromechanical systems including closed loop multibody systems, massless gear transmission and electric motors. The dynamic model of these systems is established in matrix form and written in a Differential-Algebraic Equations form by applying the Lagrangian equation with multipliers and substructure method. Moreover, this paper deals with two difficult issues in the simulation of closed-loop multibody systems which are to overcome smoothly the singular configurations and to stabilize the constrained equations due to accumulated errors. The singularity-free simulation is solved by using null-space of Jacobian matrix to eliminate the constraint forces – Lagrangian multipliers in equations of motion. The drift in the constraint equation during simulation is restricted by a combination of Baumgarte’s stabilization and post-adjusting technique. Some numerical experiments are carried out to the planar 3RRR parallel manipulator driven by electric motors. Simulation results confirm the effectiveness of the proposed approach in overcoming the singular configurations and in stabilization of the constraint.


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