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Review of Computer Engineering Research

June 2020, Volume 7, 1, pp 20-26

Dynamic Modelling of 3-RUS Spatial Parallel Robot Manipulator

Nguyen Hong Quang


Nguyen Van Quyen


Do Trung Hai


Nguyen Nhu Hien

Nguyen Hong Quang 1 ,

Nguyen Van Quyen 2
Do Trung Hai 1 Nguyen Nhu Hien 1 
  1. Department of Automation, Faculty of Electrical Engineering, Thai Nguyen University of Technology (TNUT) Vietnam. 1

  2. Department of Applied Mechanics, Hanoi University of Science and Technology, Vietnam. 2

Pages: 20-26

DOI: 10.18488/journal.76.2020.71.20.26

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Article History:

Received: 09 January, 2020
Revised: 12 February, 2020
Accepted: 16 March, 2020
Published: 07 April, 2020


Parallel manipulators are characterized as having closed-loop kinematic chains. Parallel robots have received increasing attention due to their inherent advantages over conventional serial mechanism, such as high rigidity, high load capacity, high velocity, and high precision. A definite advantage of parallel robots is the fact that, in most cases, actuators can be placed on the truss, thus achieving a limited weight for the moving parts, which makes it possible for parallel robots to move at a high speed. These advantages avoid the drawbacks on serial ones and make the mobile platforms of the parallel manipulators carry out higher performances. Therefore, parallel manipulators have been applied to the industrial manufacturing, flight simulation, medical resuscitation, and so on. The basis for model-based control of parallel manipulators is an efficient formulation of the motion equations. In this paper a formulation of the motion equations in redundant coordinates is presented for parallel manipulators. The fully coupled non-linear equations of motion of 3-RUS spatial parallel manipulator having 3 DOF with Revolute-Universal-Spherical joints are obtained by using the Lagrange equations with multipliers for constrained multibody systems.
Contribution/ Originality
This paper presented the modelling of motion for 3-RUS spatial parallel manipulator by using the redundant generalized coordinates and the Lagrangian multipliers. A novel formulation of Coriolis/centrifugal matrix is constructed directly in matrix based manner by using Kronecker product. The skew symmetry property of dynamic model of robot manipulators is guaranteed by the proposed Coriolis/centrifugal matrix. Then, the equations of motion in DAEs form were transformed to ordinary differential equations.


Dynamics, Modelling, 3-RUS robot, Lagrange equations, Redundant coordinates.


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This research was supported by Research Foundation funded by Thai Nguyen University of Technology.

Competing Interests:

The authors declare that they have no competing interests.


All authors contributed equally to the conception and design of the study.

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