Abstract
This paper presents a graphical and intuitive tool for simulating the forward kinematics of planar parallel 3RPR robots with arbitrary geometric design. The proposed tool allows the user to visualize the singularity locus of the robot and the evolution of all the solutions to its forward kinematic problem in the complex plane. The user can modify all the geometric design parameters of the robot and instantaneously visualize the effect of these modifications on the singularity locus. As the presented examples illustrate, the proposed tool is especially useful for visualizing the coalescence of different solutions of the forward kinematic problem when approaching higher-order singularities, as well as for visualizing how these special singularities transform when perturbing the different geometric parameters of the robot.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Reduced configuration spaces are typically used for analyzing non-singular transitions in robots with 2 degrees of freedom, which can be accomplished in the 3RPR robot by keeping constant one input (e.g., \(\rho _3=\text {constant}\)). In that case, the (complete) configuration space is the real solution set \(\mathcal {S}\) of Eqs. (1) and (2) in the 4D space \((\rho _1,\rho _2,\theta _3,\phi )\). The projection of \(\mathcal {S}\) on a 3D subspace whose axes are the two inputs (\(\rho _1\) and \(\rho _2\)) and one output (\(\theta _3\) or \(\phi \)) is a reduced configuration space, which is a surface. For example, the self-intersection of this surface in the 3D subspace \((\rho _1,\rho _2,\phi )\) means that the \(\phi \) components of different solutions coincide, but this is not a kinematic singularity unless the \(\theta _3\) components of these very solutions also meet.
References
Bates, D.J., Hauenstein, J.D., Sommese, A.J., Wampler, C.W.: Numerically Solving Polynomial Systems with Bertini Software, Environments, and Tools, vol. 25. SIAM, Delhi (2013). ISBN 978-1-611972-69-6
Ben-Horin, P., Shoham, M., Caro, S., Chablat, D., Wenger, P.: SinguLab - a graphical user interface for the singularity analysis of parallel robots based on Grassmann-Cayley Algebra. In: Lenarčič, J., Wenger, P. (eds.) Advances in Robot Kinematics: Analysis and Design, pp. 49–58. Springer Science+Business Media B.V. (2008)
Coste, M., Wenger, P., Chablat, D.: Hidden cusps. In: 15th International Symposium on Advances in Robot Kinematics (2016)
Gosselin, C.M., Sefrioui, J.: Polynomial solutions for the direct kinematic problem of planar three-degree-of-freedom parallel manipulators. In: Fifth International Conference on Advanced Robotics: ‘Robots in Unstructured Environments’, pp. 1124–1129. IEEE (1991)
Hajimirzaalian, H., Moosavi, H., Massah, M.: Dynamics analysis and simulation of parallel robot Stewart platform. In: Proceedings of the 2nd International Conference on Computer and Automation Engineering, pp. 472–477. IEEE (2010)
Husty, M.L.: On Singularities of Planar 3-RPR Parallel Manipulators. In: Proceedings of the 14th IFToMM World Congress, pp. 417–422 (2015)
Li, Y., Xu, Q.: Dynamic modeling and robust control of a 3-PRC translational parallel kinematic machine. Robot. Comput.-Integr. Manuf. 25(3), 630–640 (2009)
Peidró, A., Gil, A., Marín, J.M., Payá, L., Reinoso, Ó.: On the stability of the quadruple solutions of the forward kinematic problem in analytic parallel robots. J. Intell. Robot. Syst. 86(3–4), 381–396 (2017)
Peidró, A., Gil, A., Marín, J.M., Reinoso, Ó.: A web-based tool to analyze the kinematics and singularities of parallel robots. J. Intell. Robot. Syst. 81(1), 145–163 (2016)
Peidró, A., Marín, J.M., Gil, A., Reinoso, Ó.: Performing nonsingular transitions between assembly modes in analytic parallel manipulators by enclosing quadruple solutions. ASME J. Mech. Des. 137(12), 122302–122310 (2015)
Peidró, A., Reinoso, Ó., Gil, A., Marín, J.M., Payá, L., Berenguer, Y.: Second-order taylor stability analysis of isolated kinematic singularities of closed-chain mechanisms. In: Proceedings of the 14th International Conference on Informatics in Control, Automation, and Robotics, ICINCO 2017, vol. 2, pp. 351–358 (2017)
Peidró, A., Reinoso, Ó., Gil, A., Marín, J.M., Payá, L.: A simulation tool to study the kinematics and control of 2R PR-PR parallel robots. IFAC-PapersOnLine 49(6), 268–273 (2016)
Peidró, A., Reinoso, O., Gil, A., Marín, J.M., Payá, L.: A virtual laboratory to simulate the control of parallel robots. IFAC-PapersOnLine 48(29), 19–24 (2015)
Petuya, V., Macho, E., Altuzarra, O., Pinto, C., Hernandez, A.: Educational software tools for the kinematic analysis of mechanisms. Comp. Appl. Eng. Educ. 22(1), 72–86 (2014)
Porta, J.M., Ros, L., Bohigas, O., Manubens, M., Rosales, C., Jaillet, L.: The CUIK Suite: analyzing the motion of closed-chain multibody systems. IEEE Robot. Autom. Mag. 21(3), 105–114 (2014)
Thomas, F., Wenger, P.: On the topological characterization of robot singularity loci. a catastrophe-theoretic approach. In: Proceedings of the 2011 IEEE International Conference on Robotics and Automation, pp. 3940–3945. IEEE (2011)
Urízar, M., Petuya, V., Altuzarra, O., Diez, M., Hernández, A.: Non-singular transitions based design methodology for parallel manipulators. Mech. Mach. Theory 91, 168–186 (2015)
Wohlhart, K.: Degrees of shakiness. Mech. Mach. Theory 34(7), 1103–1126 (1999)
Zein, M., Wenger, P., Chablat, D.: Non-singular assembly-mode changing motions for 3-R PR parallel manipulators. Mech. Mach. Theory 43(4), 480–490 (2008)
Acknowledgments
Work supported by the Spanish Ministries of Education (grant No. FPU13/00413) and Economy (project No. DPI 2016-78361-R).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Peidró, A., Reinoso, Ó., Marín, J.M., Gil, A., Payá, L., Berenguer, Y. (2018). A Simulation Tool for Visualizing the Assembly Modes and Singularity Locus of 3RPR Planar Parallel Robots. In: Ollero, A., Sanfeliu, A., Montano, L., Lau, N., Cardeira, C. (eds) ROBOT 2017: Third Iberian Robotics Conference. ROBOT 2017. Advances in Intelligent Systems and Computing, vol 693. Springer, Cham. https://doi.org/10.1007/978-3-319-70833-1_42
Download citation
DOI: https://doi.org/10.1007/978-3-319-70833-1_42
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-70832-4
Online ISBN: 978-3-319-70833-1
eBook Packages: EngineeringEngineering (R0)