Nonlinear Effects in Stiffness Modeling of Robotic Manipulators
The paper focuses on the enhanced stiffness modeling
of robotic manipulators by taking into account influence of the external force/torque acting upon the end point. It implements the
virtual joint technique that describes the compliance of manipulator elements by a set of localized six-dimensional springs separated by
rigid links and perfect joints. In contrast to the conventional
formulation, which is valid for the unloaded mode and small
displacements, the proposed approach implicitly assumes that the loading leads to the non-negligible changes of the manipulator posture and corresponding amendment of the Jacobian. The
developed numerical technique allows computing the static
equilibrium and relevant force/torque reaction of the manipulator for
any given displacement of the end-effector. This enables designer
detecting essentially nonlinear effects in elastic behavior of
manipulator, similar to the buckling of beam elements. It is also proposed the linearization procedure that is based on the inversion of
the dedicated matrix composed of the stiffness parameters of the
virtual springs and the Jacobians/Hessians of the active and passive
joints. The developed technique is illustrated by an application example that deals with the stiffness analysis of a parallel
manipulator of the Orthoglide family
[1] S. Timoshenko and J. N. Goodier, Theory of elasticity, 3d ed., New York: McGraw-Hill, 1970.
[2] G. Piras, W.L. Cleghorn and J.K. Mills. "Dynamic finite-element analysis of a planar high-speed, high-precision parallel manipulator with
flexible links," Mechanism and Machine Theory, vol. 40, No. 7, pp. 849-862, 2005.
[3] F. Majou, C. Gosselin, P. Wenger, D. Chablat, "Parametric stiffness
analysis of the Orthoglide," Mechanism and Machine Theory, vol. 42,
pp. 296-311. 2007.
[4] C.M. Gosselin, "Stiffness mapping for parallel manipulators," IEEE
Transactions on Robotics and Automation, vol. 6, pp. 377-382, 1990.
[5] A. Pashkevich, D. Chablat, and P. Wenger, "Stiffness analysis of 3-
d.o.f. overconstrained translational parallel manipulators," IEEE
International Conference on Robotics and Automation, pp. 1562-1567,2008.
[6] A. Pashkevich, D. Chablat, P. Wenger, "Stiffness analysis of
overconstrained parallel manipulators," Mechanism and Machine
Theory, vol. 44, pp. 966-982, 2008
[7] Alici, G., Shirinzadeh, B., "Enhanced stiffness modeling, identification
and characterization for robot manipulators," IEEE Transactions on
Robotics vol. 21/4, pp. 554-564, 2005.
[8] C. Quennouelle and C. M. Gosselin, "Stiffness Matrix of Compliant
Parallel Mechanisms," Springer Advances in Robot Kinematics:
Analysis and Design, pp. 331-341, 2008
[9] A. Pashkevich, A. Klimchik, D. Chablat, "Stiffness analysis of multichain
parallel robotic systems with loading," Journal of Automation,
Mobile Robotics and Intelligent Systems, Vol. 3, No. 3, pp. 75-82,2009
[10] Y. Li and Q. Xu, "Stiffness analysis for a 3-PUU parallel kinematic
machine,"Mechanism and Machine Theory, vol. 43, no. 2, pp. 186-200,2008.
[11] R. Clavel, "DELTA, a fast robot with parallel geometry," Proceedings,
of the 18th International Symposium of Robotic Manipulators, IFR
Publication, pp. 91-100, 1988.
[12] D. Chablat and P. Wenger, "Architecture Optimization of a 3-DOF
Parallel Mechanism for Machining Applications, the Orthoglide," IEEE
Transactions on Robotics and Automation, vol. 19, no. 3, pp. 403-410,2003.
[13] R. Vertechy, V. Parenti-Castelli. "Static and Stiffness Analyses of a
Class of Over-Constrained Parallel Manipulators with Legs of Type US
and UPS," In: Proceedings of IEEE International Conference on
Robotics and Automation (ICRA), pp. 561 - 567, 2007.
[14] O. Company, S. Krut, F. Pierrot, "Modelling and Preliminary Design
Issues of a 4-Axis Parallel Machine for Heavy Parts Handling," Journal
of Multibody Dynamics, 216 (2002), pp. 1-11.
[15] S. M. LaValle, Planning Algorithms, Cambridge University Press 2006
[16] A. Pashkevich, A. Klimchik, D. Chablat, Ph. Wenger, "Accuracy
Improvement for Stiffness Modeling of Parallel Manipulators," In:
Proceedings of 42nd CIRP Conference on Manufacturing Systems, 2009
[1] S. Timoshenko and J. N. Goodier, Theory of elasticity, 3d ed., New York: McGraw-Hill, 1970.
[2] G. Piras, W.L. Cleghorn and J.K. Mills. "Dynamic finite-element analysis of a planar high-speed, high-precision parallel manipulator with
flexible links," Mechanism and Machine Theory, vol. 40, No. 7, pp. 849-862, 2005.
[3] F. Majou, C. Gosselin, P. Wenger, D. Chablat, "Parametric stiffness
analysis of the Orthoglide," Mechanism and Machine Theory, vol. 42,
pp. 296-311. 2007.
[4] C.M. Gosselin, "Stiffness mapping for parallel manipulators," IEEE
Transactions on Robotics and Automation, vol. 6, pp. 377-382, 1990.
[5] A. Pashkevich, D. Chablat, and P. Wenger, "Stiffness analysis of 3-
d.o.f. overconstrained translational parallel manipulators," IEEE
International Conference on Robotics and Automation, pp. 1562-1567,2008.
[6] A. Pashkevich, D. Chablat, P. Wenger, "Stiffness analysis of
overconstrained parallel manipulators," Mechanism and Machine
Theory, vol. 44, pp. 966-982, 2008
[7] Alici, G., Shirinzadeh, B., "Enhanced stiffness modeling, identification
and characterization for robot manipulators," IEEE Transactions on
Robotics vol. 21/4, pp. 554-564, 2005.
[8] C. Quennouelle and C. M. Gosselin, "Stiffness Matrix of Compliant
Parallel Mechanisms," Springer Advances in Robot Kinematics:
Analysis and Design, pp. 331-341, 2008
[9] A. Pashkevich, A. Klimchik, D. Chablat, "Stiffness analysis of multichain
parallel robotic systems with loading," Journal of Automation,
Mobile Robotics and Intelligent Systems, Vol. 3, No. 3, pp. 75-82,2009
[10] Y. Li and Q. Xu, "Stiffness analysis for a 3-PUU parallel kinematic
machine,"Mechanism and Machine Theory, vol. 43, no. 2, pp. 186-200,2008.
[11] R. Clavel, "DELTA, a fast robot with parallel geometry," Proceedings,
of the 18th International Symposium of Robotic Manipulators, IFR
Publication, pp. 91-100, 1988.
[12] D. Chablat and P. Wenger, "Architecture Optimization of a 3-DOF
Parallel Mechanism for Machining Applications, the Orthoglide," IEEE
Transactions on Robotics and Automation, vol. 19, no. 3, pp. 403-410,2003.
[13] R. Vertechy, V. Parenti-Castelli. "Static and Stiffness Analyses of a
Class of Over-Constrained Parallel Manipulators with Legs of Type US
and UPS," In: Proceedings of IEEE International Conference on
Robotics and Automation (ICRA), pp. 561 - 567, 2007.
[14] O. Company, S. Krut, F. Pierrot, "Modelling and Preliminary Design
Issues of a 4-Axis Parallel Machine for Heavy Parts Handling," Journal
of Multibody Dynamics, 216 (2002), pp. 1-11.
[15] S. M. LaValle, Planning Algorithms, Cambridge University Press 2006
[16] A. Pashkevich, A. Klimchik, D. Chablat, Ph. Wenger, "Accuracy
Improvement for Stiffness Modeling of Parallel Manipulators," In:
Proceedings of 42nd CIRP Conference on Manufacturing Systems, 2009
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:52149", author = "A. Pashkevich and A. Klimchik and D. Chablat", title = "Nonlinear Effects in Stiffness Modeling of Robotic Manipulators", abstract = "The paper focuses on the enhanced stiffness modeling
of robotic manipulators by taking into account influence of the external force/torque acting upon the end point. It implements the
virtual joint technique that describes the compliance of manipulator elements by a set of localized six-dimensional springs separated by
rigid links and perfect joints. In contrast to the conventional
formulation, which is valid for the unloaded mode and small
displacements, the proposed approach implicitly assumes that the loading leads to the non-negligible changes of the manipulator posture and corresponding amendment of the Jacobian. The
developed numerical technique allows computing the static
equilibrium and relevant force/torque reaction of the manipulator for
any given displacement of the end-effector. This enables designer
detecting essentially nonlinear effects in elastic behavior of
manipulator, similar to the buckling of beam elements. It is also proposed the linearization procedure that is based on the inversion of
the dedicated matrix composed of the stiffness parameters of the
virtual springs and the Jacobians/Hessians of the active and passive
joints. The developed technique is illustrated by an application example that deals with the stiffness analysis of a parallel
manipulator of the Orthoglide family", keywords = "Robotic manipulators, Stiffness model, Loaded mode, Nonlinear effects, Buckling, Orthoglide manipulator", volume = "3", number = "10", pages = "1202-6", }