Classification and Occurrence Conditions of Singularities in Parallel Mechanisms

Research related to singularities of parallel mechanisms is an important step in the synthesis and analysis of such mechanisms. However, this topic is not sufficiently addressed in Russian scientific literature. The first part of this article contains a review of some popular approaches to the classification and analysis of occurrence conditions for singularities in parallel mechanisms, and serves the purpose of showing the basic principles, advantages and disadvantages of these approaches to Russian readers. It is shown that at present there is no universally accepted approach used by all the researchers.  In the second part of this paper an approach to the aforementioned problem based on the screw theory is presented. Although this approach is based on a known technique, it has some important improvements and corrections, which expands its application onto a wider range of possible structures of parallel mechanisms. The differences from the existing approaches and the advantages of the new approach are shown.

References

[1] Merlet J.-P. Parallel Robots. Springer, 2006. 402 p.

[2] Carricato M., Parenti-Castelli V. Singularity-Free Fully-Isotropic Translational Parallel Mechanisms. International Journal of Robotics Research, 2002, no. 21(2), pp. 161–174.

[3] Hunt K.H. Kinematic Geometry of Mechanisms. Clarendon Press, 1978. 465 p.

[4] Gosselin C.M., Angeles J. Singularity Analysis of Closed-Loop Kinematic Chains. IEEE Transactions on Robotics and Automatics, 1990, no. 6(3), pp. 281–290.

[5] Zlatanov D., Bonev I., Gosselin C. Constraint Singularities of Parallel Mechanisms. IEEE International Conference on Robotics and Automation, Washington C.D, May 11–15, 2002, pp. 496–502.

[6] Zlatanov D., Fenton R.G., Benhabib B. A Unifying Framework for Classification and Interpretation of Mechanism Singularities. Journal of Mechanical Design, 1995, no. 117(4), pp. 566–572.

[7] Zlatanov D., Fenton R.G., Benhabib B. Classification and Interpretation of the Singularities of Redundant Mechanisms. ASME Design Engineering Technical Conferences, Atlanta, September 13–16, 1998, pp. 1–11.

[8] Glazunov V.A., Koliskor A.Sh., Krainev A.F. Prostranstvennye mekhanizmy parallel’noi struktury [Spatial mechanisms of parallel structure]. Moscow, Nauka publ., 1991. 95 p.

[9] Glazunov V. A., Arakelian V., Brio S., Rashoian G. V. Skorostnye i silovye kriterii blizosti k singuliarnostiam manipuliatorov parallel’noi struktury [Speed and strength criteria for proximity to the singularities of parallel structure manipulators]. Problemy mashinostroeniia i nadezhnosti mashin [Journal of Machinery Manufacture and Reliability]. 2012, no. 3, pp. 10–17.

[10] Arakelian V., Brio S., Glazunov V.A. Issledovanie osobykh polozhenii manipuliatora s parallel’noi strukturoi «PAMINSA» [The study of specific provisions of the manipulator with parallel structure «PAMINSA»]. Problemy mashinostroeniia i nadezhnosti mashin [Journal of Machinery Manufacture and Reliability]. 2006, no. 1, pp. 80–88.

[11] Briot S., Glazunov V., Arakelian V. Investigation on the Effort Transmission in Planar Parallel Manipulators. Journal of Mechanisms and Robotics, 2013, vol. 5, is. 1, article no. 011011.

[12] Arakelian V., Briot S., Glazunov V. Increase of singularity-free zones in the workspace of parallel manipulators using mechanisms of variable structure. Mechanism and Machine Theory, 2008, vol. 43, no. 9, pp. 1129–1140.

[13] Liu G., Lou Y., Li Z. Singularities of Parallel Manipulators: A Geometric Treatment. IEEE Transactions on Robotics and Automatics, 2003, no. 19(4), pp. 579–594.

[14] Wohlhart K. Degrees of Shakiness. Mechanism and Machine Theory, 1999, no. 34(7), pp. 1103–1126.

[15] Chen I-M., Angeles J., Theingi, Li C.The Management of Parallel-Manipulator Singularities using joint-coupling. IEEE International Conference on Robotics and Automation, Taipei, September 14–19, 2003, pp. 773–778.

[16] Mohamed M.G., Duffy J. A Direct Determination of the Instantaneous Kinematics of Fully Parallel Robot Manipulators. ASME Journal of Mechanisms, Transmissions and Automation in Design, 1985, no. 107(2), pp. 226–229.