On calculation of generalized reactions in parallel mechanisms

Analysis methods utilising screw theory are the main tool for investigating parallel mechanisms. The paper considers the specifics of computing generalised contact forces in these mechanisms featuring less than six degrees of freedom. We show that, in order to calculate the desired contact force magnitude corresponding to a certain wrench of the constraint imposed onto the output link, it is necessary to project the wrenches of the active kinematic pairs in the chain onto a vector space representing an orthogonal complement to the link space of the mechanism. We use a translational guiding mechanism with three degrees of freedom as an example to apply our approach to.

References

[1] Glazunov V.A. Mekhanizmy parallel’noy struktury i ikh primenenie [Parallel mechanisms and their application]. Moscow-Izhevsk, IKI RAN Publ., 2018. 1036 p. (In Russ.).

[2] Gallardo-Alvarado J. Kinematic analysis of parallel manipulators by algebraic screw theory. Springer, 2016. 377 p.

[3] Sugimoto K. Kinematic and dynamic analysis of parallel manipulators by means of motor algebra. J. Mech. Trans. and Automation, 1987, vol. 109, no. 1, pp. 3–7, doi: https://doi.org/10.1115/1.3258783

[4] Glazunov V.A., Kostereva S.D., Danilin P.O. et al. Using theory of screws in modern theory of mechanisms. Vestnik nauchno-tekhnicheskogo razvitiya, 2010, no. 6, pp. 12–17. (In Russ.).

[5] Laryushkin P.A., Rashoyan G.V., Erastova K.G. On the features of applying the theory of screws to the evaluation of proximity to specific positions of the mechanisms of parallel structure. Problemy mashinostroeniya i nadezhnosti mashin, 2017, no. 4, pp. 39–45. (In Russ.) (Eng. version: J. Mach. Manuf. Reliab., 2017, vol. 46, no. 4, pp. 349–355, doi: https://doi.org/10.3103/S1052618817040100)

[6] Gosselin C., Angeles J. Singularity analysis of closed-loop kinematic chains. IEEE Trans. Robot. Autom., 1990, vol. 6, no. 3, pp. 281–290, doi: https://doi.org/10.1109/70.56660

[7] Hunt K. Kinematic geometry of mechanisms. Clarendon Press, 1978. 465 p.

[8] Zlatanov D., Bonev I., Gosselin C. Constraint singularities of parallel mechanisms. Proc. 2002 IEEE Int. Conf. on Robotics and Automation, 2002, vol. 1, pp. 496–502, doi: https://doi.org/10.1109/ROBOT.2002.1013408

[9] Merlet J.-P. Parallel robots. Springer, 2006. 402 p.

[10] Voglewede P., Ebert-Uphoff I. Overarching framework for measuring closeness to singularities of parallel manipulators. IEEE Trans. Robot., 2005, vol. 21, no. 6, pp. 1037–1045, doi: https://doi.org/10.1109/TRO.2005.855993

[11] Glazunov V.A., Arakelyan V., Brio S. et al. Speed and force criteria for the proximity to singularities of parallel structure manipulators. Problemy mashinostroeniya i nadezhnosti mashin, 2012, no. 3, pp. 10–17. (In Russ.). (Eng. version: J. Mach. Manuf. Reliab., 2012, vol. 41, no. 3, pp. 194–199. https://doi.org/10.3103/S1052618812030041)

[12] Hao K., Ding Y. Screw theory and singularity analysis of parallel robot. Int. Conf. Mechatronics and Automation, 2006, pp. 147–152, doi: https://doi.org/10.1109/ICMA.2006.257468

[13] Laryushkin P., Glazunov V., Demidov S. Singularity analysis of 3-DOF translational parallel manipulator. In: Advances on theory and practice of robots and manipulators. Springer, 2014, vol. 22, pp. 47–54.

[14] Laryushkin P.A., Palochkin S.V. Workspace of the parallel structure manipulator with three degrees of freedom. Izvestiya vysshikh uchebnykh zavedeniy. Tekhnologiya tekstil’noy promyshlennosti [Proceedings of Higher Education Institutions. Textile Industry Technology], 2012, no. 3, pp. 92–96. (In Russ.).

[15] Glazunov V.A., Nguen N.Kh., Nguen M.T. Singular configuration analysis of the parallel mechanisms. Mashinostroenie i inzhenernoe obrazovanie, 2009, no. 4, pp. 11–16. (In Russ.).