Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-22T05:58:42.607Z Has data issue: false hasContentIssue false
  • English
  • Français

Position analysis, singularity loci and workspace of a novel 2PRPU Schoenflies-motion generator

Published online by Cambridge University Press:  10 September 2018

Henrique Simas  and
Raffaele Di Gregorio Open the ORCID record for Raffaele Di Gregorio [Opens in a new window]
Henrique Simas
Affiliation:
Raul Guenther Lab. of Applied Robotics, Department of Mechanical Engineering, Federal University of Santa Catarina, Florianópolis, SC 88040–900, Brazil
Raffaele Di Gregorio*
Affiliation:
Department of Engineering, University of Ferrara, Via Saragat, 1, Ferrara 44100, Italy
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

Pick-and-place applications need to perform rigid body displacements that combine translations along three independent directions and rotations around one fixed direction (Schoenflies motions). Such displacements constitute a four-dimensional (4-D) subgroup (Schoenflies subgroup) of the 6-D displacement group. The four-degrees of freedom (dof) manipulators whose end effector performs only Schoenflies motions are named Schoenflies-motion generators (SMGs). The most known SMGs are the serial robots named SCARA. In the literature, parallel manipulators (PMs) have also been proposed as SMGs. Here, a novel single-loop SMG of type 2PRPU is studied. Its position analysis, singularity loci and workspace are addressed to provide simple analytic and geometric tools that are useful for the design. The proposed single-loop SMG is not overconstrained, its actuators are on or near the base and its end effector can perform a complete rotation. These features solve the main drawbacks that parallel SMG architectures have in general and make the proposed SMG a valid design alternative.

Keywords

Parallel manipulatorsSchoenflies subgroupPosition analysisInstantaneous kinematicsWorkspace
Type
Articles
Information
Robotica , Volume 37 , Issue 1 , January 2019 , pp. 141 - 160
Copyright
Copyright © Cambridge University Press 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Hervé, J. M., “The lie group of rigid body displacements, a fundamental tool for mechanism design,” Mech. Mach. Theory 34, 719–730 (1999).Google Scholar
2. Lee, C.-C. and Hervé, J. M. “Type synthesis of primitive schoenflies-motion generators,” Mech. Mach. Theory 44, 1980–1997 (2009).Google Scholar
3. Lee, C.-C. and Hervé, J. M. “Isoconstrained parallel generators of schoenflies motion,” ASME J. Mech. Rob. 3 (2), 021006-(1–10) (2011).Google Scholar
4. Pierrot, F. and Company, O., “H4: A New Family of 4-DOF Parallel Robots,” Proceedings of the 1999 IEEE/ASME International Conference on Advanced Intelligent Mechatronics AIM'99, Atlanta, Georgia, USA (1999) pp. 508–513.Google Scholar
5. Krut, S., Company, O., Benoit, M., Ota, H. and Pierrot, F., “I4: A New Parallel Mechanism for SCARA Motions,” Proceedings of the 2003 International Conference on Robotics and Automation, Taipei, Taiwan (2003) pp. 1875–1880.Google Scholar
6. Nabat, V., de la O Rodriguez, M., Company, O., Krut, S. and Pierrot, F., “Par4: Very High Speed Parallel Robot for Pick-and-Place,” Proceedings of the 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems (2005) pp. 553–558.Google Scholar
7. Angeles, J., Caro, S., Khan, W. and Morozov, A., “The design and prototyping of an innovative schoenflies motion generator,” Proc. IMechE-Part C: J. Mech. Eng. 220 (C7), 935–944 (2006).Google Scholar
8. Li, Z., Lou, Y., Zhang, Y., Liao, B. and Li, Z., “Type synthesis, kinematic analysis, and optimal design of a novel class of schoenflies-motion parallel manipulators,” IEEE Trans. Aut. Sc. Eng. 10, 674–686 (2013).Google Scholar
9. Kong, X. and Gosselin, C. M., “Type synthesis of 3T1R 4-dof parallel manipulators based on screw theory,” IEEE Trans. Rob. Autom. 20, 181–190 (2004).Google Scholar
10. Company, O., Pierrot, F., Nabat, V. and Rodriguez, M., “Schoenflies Motion Generator: A New Non Redundant Parallel Manipulator with Unlimited Rotation Capability,” Proceedings of the 2005 IEEE International Conference on Robotics and Automation, Barcelona, Spain (2005) pp. 3250–3255.Google Scholar
11. Richard, P.-L., Gosselin, C. M. and Kong, X. “Kinematic analysis and prototyping of a partially decoupled 4-DOF 3T1R parallel manipulator,” ASME J. Mech. Des. 129, 611–616 (2007).Google Scholar
12. ABB, “IRB 360 – FlexPicker: Faster processing, faster payback,” ABB Packaging Magazine, ABB Robotics, Issue: May 2008, p. 25 2008, (https://library.e.abb.com/public/aed4c1b308bc9fc2c1257456004f8734/EN_25_techpages_irb360_korr2_abb_pack_108.pdf).Google Scholar
13. Carricato, M., “Fully isotropic four-degrees-of-freedom parallel mechanisms for Schoenflies motion,” Int. J. Robot. Res. 24 (5), 397–414 (2005).Google Scholar
14. Pierrot, F., Company, O., Krut, S. and Nabat, V., “Four-Dof PKM with Articulated Travelling-Plate,” PKS'06: Parallel Kinematics Seminar, Chemnitz, Germany (2006) pp. 25–26.Google Scholar
15. Ball, R. S. A Treatise on the Theory of Screws (Cambridge University Press, Cambridge, UK, 1900, Reprinted in 1998).Google Scholar
16. Shigley, J. E. and Uicker, J. J., Theory of Machines and Mechanisms,” 2nd ed. (McGraw-Hill, Inc., New York, USA, 1995).Google Scholar
17. Euler, L., “Of a New Method of Resolving Equations of the Fourth Degree,” In: Elements of Algebra, (Springer-Verlag, New York, Reprinted in 1984 from the 5th Edition of the 1st English translation published by Longman, London, UK, 1822) pp. 282–288 ISBN: 978-1-4613-8511-0Google Scholar
18. Zlatanov, D., Bonev, I. A. and Gosselin, C. M., “Constraint Singularities of Parallel Mechanisms,” Proceedings of the 2002 IEEE International Conference on Robotics and Automation ICRA2002, Washington, DC (2002) pp. 496–502.Google Scholar
19. Gosselin, C. M. and Angeles, J., “Singularity analysis of closed-loop kinematic chains,” IEEE Trans. Robot. Autom. 6 (3), 281–290 (1990).Google Scholar
20. Ma, O. and Angeles, J., “Architecture Singularities of Platform Manipulators,” Proceedings of the 1991 IEEE International Conference on Robotics and Automation, Sacramento CA, USA (1991) pp. 1542–1547.Google Scholar
21. Zlatanov, D., Fenton, R. G. and Benhabib, B., “A unifying framework for classification and interpretation of mechanism singularities,” ASME J. Mech. Des. 117 (4), 566–572 (1995).Google Scholar
22. Meyer, C. D., “Matrix analysis and applied linear algebra,” Soc. Ind. Appl. Math. (SIAM, Philadelphia, PA, 2000) ISBN: 978-0-898714-54-8.Google Scholar
23. Siciliano, B., Sciavicco, L., Villani, L. and Oriolo, G., Robotics: Modelling, Planning and Control (Springer-Verlag, London, 2009) p. 85, ISBN: 978-1-84628-641-4.Google Scholar
24. Gosselin, C., “Stiffness mapping for parallel manipulators,” IEEE Trans. Robot. Autom. 6 (3), 377–382 (1990).Google Scholar
25. Wu, G., “Stiffness analysis and optimization of a co-axial spherical parallel manipulator,” Modeling, Identification Control 35 (1), 21–30 (2014).Google Scholar
26. Harada, T. and Angeles, J., “Kinematics and singularity analysis of a CRRHHRRC parallel Schönflies motion generator,” CSME Trans. 38 (2), 173–183 2014.Google Scholar
27. Gosselin, C. and Angeles, J., “A global performance index for the kinematic optimization of robotic manipulators,” J. Mech. Des. 113 (3), 220–226 1991.Google Scholar
28. Angeles, J., “Fundamentals of Robotic Mechanical Systems, (Springer-Verlag, New York, 2014) ISBN: 978-3-319-30762-6.Google Scholar
29. Lou, Y., Liu, G., Chen, N. and Li, Z., “Optimal Design of Parallel Manipulators for Maximum Effective Regular Workspace,” Proceedings of the 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems, Edmonton, Canada (2005) pp. 795–800.Google Scholar
30. Lee, P. and Lee, J., “On the kinematics of a new parallel mechanism with Schoenflies motion,” Robotica 34 (9), 2056–2070 (2016), DOI: 10.1017/S0263574714002732Google Scholar