Inverse dynamics of a 3-prismatic—revolute—revolute planar parallel manipulator using natural orthogonal complement

Abstract

The performance of robotic systems with parallel kinematics can be evaluated by their kinematic, static, and dynamic properties. These properties are directly used in model-based controllers which potentially offer higher accuracy for robotic systems. Inverse dynamic solution is an essential part of these controllers. In the present work, the inverse dynamics model of a 3-PRR (prismatic—revolute—revolute) planar parallel manipulator based on the natural orthogonal complement (NOC) method is developed. To drive the NOC for the 3-PRR closed-loop systems, the explicit expressions of the loop constraints equations and the associated Jacobian matrices are first obtained. Next the NOC matrix, which is a velocity transformation matrix relating the Cartesian angular/translational velocities of various bodies to the motor joint rates, is calculated. Finally results of the NOC method are compared with simulation of a 3-PRR planar parallel manipulator using two commercial softwares: SimMechanics toolbox of Matlab and COSMOSMotion of SolidWorks. In order to verify the theoretical results, two different configurations for the robot are considered: a horizontal and a vertical. Results of the NOC method as well as the two simulations are compared for the two robot configurations.

Keywords

inverse dynamics natural orthogonal complement planar parallel manipulator

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References

Notash

Kamalzadeh

, ‘Inverse dynamics of wire-actuated parallel manipulators with a constraining linkage.’ Mechanism and Machine Theory 42 (2002): 1103–1118.

Liu

M-J.

C-X.

C-N.

, ‘Dynamics analysis of the Gough-Stewart platform manipulator.’ IEEE Trans. Robotics Automn 16 (1) (2000): 94–98.

Dasgupta

Choudhury

, ‘A general strategy based on the Newton-Euler approach for the dynamic formulation of parallel manipulators.’ Mechanism and Machine Theory 34 (6) (1999): 801–824.

Harib

Srinivasan

, ‘Kinematicand dynamic analysis of Stewart platform-based machine tool structures.’ Robotica 21 (5) (2003): 541–554.

Enferadi

Akbarzadeh

, ‘Inverse dynamics analysis of a general spherical star-triangle parallel manipulator using principle of virtual work.’ Nonlinear dynamics 61 (3) (2010): 419–434 DOI:10.1007/s11071-010-9659-9.

Staicu

, ‘Power requirement comparison in the 3-RPR planar parallel robot dynamics.’ Mechanism and Machine Theory 44 (2002): 1045–1057.

Staicu

, ‘Inverse dynamics of the 3-PRR planar parallel robot.’ Robotics Autonomous Systems 57 (2002): 556–563.

Pierrot

Dauchez

Fournier

, ‘Fast parallel robots.’ J. Robotic Systems 8 (6) (1991): 829–840.

Codourey

Burdet

, ‘A body oriented method for finding a linear form of the dynamic equatiojns of fully parallel robot.’ IEEE International Conference on Robotics and automation, 1997, Albuquerque pp. 1612–1618.

10.

W. Q. D.

Yang

D. C. H.

, ‘Inverse dynamic analysis and simulation of a platform type of robot.’ J. Robotic Systems 5 (3) (1988): 209–227.

11.

Angeles

Lee

, ‘The formulation of dynamical equations of holonomic mechanical systems using a natural orthogonal complement.’ ASME J. Appl. Mech. 55 (1981): 243–244.

12.

Angeles

, ‘Dynamic simulation of n-axis serial robotic manipulators using a natural orthogonal complement.’ Int. J. Robotics Res. 7 (5) (1988): 32–47.

13.

Saha

S. K.

Angeles

, ‘Dynamics of nonholonomic mechanical systems using a natural orthogonal complement.’ ASME Trans. J. Appl. Mech. 58 (1991): 238–243.

14.

Sinatra

, ‘Inverse dynamics of hexapods using the natural orthogonal complement method.’ J. Mfg Systems. 21 (2) (2002): 73–82.

15.

Saha

S. K.

, ‘A decomposition of the manipulator inertia matrix.’ IEEE Trans. Robotics and Autom. 13 (2) (1997): 301–304.

16.

Saha

S. K.

, ‘Analytical expression for the inverted inertia matrix of serial robots.’ Int. J. Robotic Res. 18 (1) (1999): 20–36.

17.

Saha

S. K.

Schiehlen

W. O.

, ‘Recursive kinematics and dynamics for parallel structured closed-loop multibody systems.’ Mech. Structs Mach. 29 (2) (2001): 143–175.

18.

, Mechanical analysis of parallel manipulators with simulation, design, and control applications PhD Thesis, Department of Mechanics, McGill University

Montreal, Quebec

1991.

19.

Craig

, Introduction to robotics, mechanics and control third edition 2004 (Prentice Hall).