Solving the working area positioning and studying problem in the kinematically redundant parallel structure mechanism

Parallel structure mechanisms are widely used in various branches of science and technology due to such advantages as high operation speed, accuracy and rigidity, which determines relevance of working to find and analyze new schemes for such mechanisms. Flat mechanism with parallel structure, four kinematic chains of the PRR type and a sliding platform was considered. It was shown that it had kinematic redundancy. For such mechanism, the direct and inverse position problems were analytically solved, and the working area was studied using the iterative approach. Fundamental possibility was demonstrated of using the additional mechanism mobility to avoid special situations.

References

[1] Glazunov V.A. Mekhanizmy parallelnoy struktury i ikh primenenie [Parallel structure mechanisms and their applications]. Moskva-Izhevsk, IKI Publ., 2018. 1036 p. (In Russ.).

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

[3] Pritschow G. Parallel kinematic machines (PKM) — limitations and new solutions. CIRP Annals, 2000, vol. 49, no. 1, pp. 275–280, doi: https://doi.org/10.1016/S0007-8506(07)62945-X

[4] Rosyid A., Stefanini C., El-Khasawneh B. A reconfigurable parallel robot for on-structure machining of large structures. Robotics, 2022, vol. 11, no. 5, art. 110, doi: https://doi.org/10.3390/robotics11050110

[5] Saied H., Chemori A., Michelin M. Et al. A redundant parallel robotic machining tool: design, control and real-time experiments. In: New developments and advances in robot control. Springer, 2019, pp. 39–79, doi: https://doi.org/10.1007/978-981-13-2212-9_3

[6] Rossi P., Simoni R., Carboni A.P. Analysis of a 4-DOF 3T1R parallel robot for machining applications: a stiffness study. In: Advances in industrial machines and mechanisms. Springer, 2021, pp. 161–171, doi: https://doi.org/10.1007/978-981-16-1769-0_15

[7] Briot S., Pashkevich A., Chablat D. Optimal technology-oriented design of parallel robots for high-speed machining applications. 2010 IEEE Int. Conf. on Robotics and Automation, 2010, pp. 1155–1161, doi: https://doi.org/10.1109/ROBOT.2010.5509543

[8] Liu G., Lou Y., Li Z., Singularities of parallel manipulators: a geometric treatment. IEEE Trans. Robot. Autom., 2003, vol. 19, no. 4, pp. 579–594, doi: https://doi.org/10.1109/TRA.2003.814507

[9] Slavutin M., Shai O., Sheffer A. et al. A novel criterion for singularity analysis of parallel mechanisms. Mech. Mach. Theory, 2019, vol. 137, pp. 459–475, doi: https://doi.org/10.1016/j.mechmachtheory.2019.03.001

[10] Mostashiri N., Dhupia J., Xu W. Redundancy in parallel robots: a case study of kinematics of a redundantly actuated parallel chewing robot. In: RITA 2018. Springer, 2019, pp. 65–78, doi: https://doi.org/10.1007/978-981-13-8323-6_6

[11] Erastova K.G., Shikhanova N.V., Komarov R.A. et al. Workspace of a plane lambda mechanism with singularities. Vestnik mashinostroeniya, 2021, no. 3, pp. 36–40. (In Russ.). (Eng. version: Russ. Engin. Res., 2021, vol. 41, no. 6, pp. 498–503, doi: https://doi.org/10.3103/S1068798X21060058)

[12] Laryushkin P.A., Mukabenova L.G., Erastova K.G. et al. Scheme choice and inverse kinematics of a positioning system based on a planar parallel mechanism. Nauka i obrazovanie: nauchnoe izdanie [Science and Education: Scientific Publication], 2017, no. 7. URL: https://www.elibrary.ru/item.asp?id=30585854 (in Russ.).

[13] Reshetov L.N. Konstruirovanie ratsionalnykh mekhanizmov [Designing rational mechanisms]. Moscow, Mashinostroenie Publ., 1972. 256 p. (In Russ.).

[14] 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.).

[15] 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