Resolution of a 3 RRR Planar Parallel Mechanism

Abstract:

This paper proposes a methodology to analyze the resolution and variations in the positions of the 3RRR planar parallel mechanism driven by electrical actuators of discrete steps. This methodology consists of graphing and plotting all the possible combinations of angular movements of a three legs mechanism. This generates a “cloud of points” that will be the boundary of the control limits, so as to find the closest trajectory to a straight line. It was found that resolution, accuracy, and the approximation error improves when micro-steps are employed. For this purpose, it is necessary to determine direct and inverse kinematics, in order to calculate the workspace. A prototype was built to validate the methodology proposed.

• Periodical: Applied Mechanics and Materials (Volume 15)
• Pages: 61-66
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.15.61
• Online since: August 2009
• Authors: R. Yáñez-Valdez, M. Ruiz-Torres, E. Morales-Sánchez, E. Castillo-Castañeda, J.A. Briones-León
• Keywords: Microstep, Planar Parallel Mechanism, Resolution

References

[1] H. Slocum. Precision machine design. Prentice Hall, EUA, (1992).

[2] R L. Williams II and A R. Joshi. Planar parallel 3RPR manipulator. Proceedings of the Sixth Conference on Applied Mechanisms and Robotics, (1999).

[3] G. Yang W. Chen and I. Chen. A geometrical method for the singularity analysis of 3RRR planar parallel robot with different actuation schemes. Proceedings of the 2002 IEEE/RSJ International Conference on Intelligent Robots and Systems, EPFL, Lausanne, Switzerland, (2002).

DOI: 10.1109/irds.2002.1041568

[4] I. E Uphoff, Introducing parallel manipulators through laboratory experiments. IEEE Robotics & Automation Magazine, (2003).

DOI: 10.1109/mra.2003.1233552

[5] G. Liu, Y. Lou and Z. Li. Singularities of parallel manipulators: A geometrical treatment. Transactions on Robotics and Automation, Vol. XIX, (2003).

[6] J. Yoon, J. Park and J. Ryu. Walking control of a dual-planar parallel robot for omni-directional locomotion interface. (2004).

DOI: 10.1109/iros.2005.1545561

[7] J. Yoon and J. Ryu. The development of the 3-DOF planar parallel robot (RRR Type) for omnidirectional locomotion interfaces. 3 rd IFAC Symposium on Mechatronic Systems, Sept. 6-8, Sydney Australia, (2004).

DOI: 10.1016/s1474-6670(17)31082-0

[8] E. Castillo, J. Fonseca and C. Lopez. Non-linear control to compensate low velocity friction of a planar parallel robot. Proceedings of 12th World Congress in Mechanism and Machine Science, IFTOMM 2007, June 17-21, Besancon France, (2007).

[9] S. Briot and I. Bonev. Are parallel robots more accurate than serial robots? Transactions of the Canadian Society for Mechanical Engineering. Vol. 31, No. 4, pp.445-4, (2007).

DOI: 10.1139/tcsme-2007-0032

[10] P. Geradin and M. Duysinx. An introduction to robotics: Mechanical aspects. University of Liège. (2004).

[11] S. Briot and I. Bonev. Accuracy analysis of 3dof planar parallel robots. Mechanism and Machine Theory, Vol. 43, No. 4, pp.445-458, (2008).

DOI: 10.1016/j.mechmachtheory.2007.04.002

[12] L. W. Tsai. Robot Analysis, The mechanics of serial and parallel manipulators. Wiley Interscience. EUA (1999).

[13] R. Yañez, M. Ruiz and E. Morales. Diseño conceptual de una mesa de trabajo XY-THETA basado en un mecanismo paralelo planar. 10° Congreso Nacional de Ingeniería Electromecánica y de Sistemas - IPN, Noviembre 26-30, México D. F. (2007).

DOI: 10.5944/bicim2022.050