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

  • Henrique Simas (a1) and Raffaele Di Gregorio (a2)

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.

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1. Hervé, J. M., “The lie group of rigid body displacements, a fundamental tool for mechanism design,” Mech. Mach. Theory 34, 719730 (1999).
2. Lee, C.-C. and Hervé, J. M.Type synthesis of primitive schoenflies-motion generators,” Mech. Mach. Theory 44, 19801997 (2009).
3. Lee, C.-C. and Hervé, J. M.Isoconstrained parallel generators of schoenflies motion,” ASME J. Mech. Rob. 3 (2), 021006-(1–10) (2011).
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.
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.
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.
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), 935944 (2006).
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, 674686 (2013).
9. Kong, X. and Gosselin, C. M., “Type synthesis of 3T1R 4-dof parallel manipulators based on screw theory,” IEEE Trans. Rob. Autom. 20, 181190 (2004).
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.
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, 611616 (2007).
12. ABB, “IRB 360 – FlexPicker: Faster processing, faster payback,” ABB Packaging Magazine, ABB Robotics, Issue: May 2008, p. 25 2008, (
13. Carricato, M., “Fully isotropic four-degrees-of-freedom parallel mechanisms for Schoenflies motion,” Int. J. Robot. Res. 24 (5), 397414 (2005).
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.
15. Ball, R. S. A Treatise on the Theory of Screws (Cambridge University Press, Cambridge, UK, 1900, Reprinted in 1998).
16. Shigley, J. E. and Uicker, J. J., Theory of Machines and Mechanisms,” 2nd ed. (McGraw-Hill, Inc., New York, USA, 1995).
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. 282288 ISBN: 978-1-4613-8511-0
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.
19. Gosselin, C. M. and Angeles, J., “Singularity analysis of closed-loop kinematic chains,” IEEE Trans. Robot. Autom. 6 (3), 281290 (1990).
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.
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), 566572 (1995).
22. Meyer, C. D., “Matrix analysis and applied linear algebra,” Soc. Ind. Appl. Math. (SIAM, Philadelphia, PA, 2000) ISBN: 978-0-898714-54-8.
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.
24. Gosselin, C., “Stiffness mapping for parallel manipulators,” IEEE Trans. Robot. Autom. 6 (3), 377382 (1990).
25. Wu, G., “Stiffness analysis and optimization of a co-axial spherical parallel manipulator,” Modeling, Identification Control 35 (1), 2130 (2014).
26. Harada, T. and Angeles, J., “Kinematics and singularity analysis of a CRRHHRRC parallel Schönflies motion generator,” CSME Trans. 38 (2), 173183 2014.
27. Gosselin, C. and Angeles, J., “A global performance index for the kinematic optimization of robotic manipulators,” J. Mech. Des. 113 (3), 220226 1991.
28. Angeles, J., “Fundamentals of Robotic Mechanical Systems, (Springer-Verlag, New York, 2014) ISBN: 978-3-319-30762-6.
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.
30. Lee, P. and Lee, J., “On the kinematics of a new parallel mechanism with Schoenflies motion,” Robotica 34 (9), 20562070 (2016), DOI: 10.1017/S0263574714002732
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