Certain dynamic features of the “tripod” type parallel structure mechanisms at the singular positions

The paper considers a three degrees of freedom mechanism, which output link is oscillating in vicinity of the singular positions. Various types of the mechanism motion are observed depending on initial conditions, mass of the output link and feedback coefficients of the drives. In particular, transition through a specific position (singularity) could take place. Translational drives of such a mechanism are positioned along the edges of a pyramid formed by the tripod kinematic chains. Axes of the drives converge at one point, i.e. at the output link center. The entire mass is concentrated in the output link (working body). In turn, entire elasticity of this mechanism is determined by the linear actuators. Dependence between the oscillation frequency and the initial conditions could be of interest. By setting the output link initial position closer or farther from the equilibrium point, different laws of the output link motion could be obtained. In particular, the specified link is able to pass through singularity. By changing the output link initial position height, different frequency of the oscillatory process could be received. Thus, there appears a dependence of the oscillation frequency on the amplitude.

References

[1] Ganiev R.F. On the current state and the future prospects of the Institute of Machine Science, Russian Academy of Sciences, and problems of the mechanics of machines and breakthrough technologies. Problemy mashinostroeniya i nadezhnosti mashin, 2014, no. 3, pp. 11–36. (In Russ.). (Eng. version: J. Mach. Manuf. Reliab., 2014, vol. 43, no. 3, pp. 188–210, doi: https://doi.org/10.3103/S1052618814030029)

[2] Veliev E.I., Ganiev R.F., Glazunov V.A. et al. Development and investigation of mechanisms with a constant point of entry of a tool into the working area, intended for surgery and study of the properties of plasma. Problemy mashinostroeniya i nadezhnosti mashin, 2020, no. 6, pp. 3–15. (In Russ.). (Eng. version: J. Mach. Manuf. Reliab., 2020, vol. 49, no. 6, pp. 463–473, https://doi.org/10.3103/S1052618820060096)

[3] Russo M., Ceccarelli M. Dynamics of a humanoid robot with parallel architectures. In: IFToMM WS 2019. Springer, 2019, pp. 1799–1808, doi: https://doi.org/10.1007/978-3-030-20131-9_178

[4] Brinker J., Corves B. A survey on parallel robots with delta-like architecture. 14th IFToMM World Congress, 2015, pp. 407–414, doi: https://doi.org/10.6567/IFToMM.14TH.WC.PS13.003

[5] Laryushkin P., Glazunov V., Erastova K. On the maximization of joint velocities and generalized reactions in the workspace and singularity analysis of parallel mechanisms. Robotica, 2019, vol. 37, no. 4, pp. 675–690, doi: https://doi.org/10.1017/S026357471800125X

[6] Antonov A., Glazunov V. Position, velocity, and workspace analysis of a novel 6-DOF parallel manipulator with “piercing” rods. Mech. Mach. Theory, 2021, vol. 161, art. 104300, doi: https://doi.org/10.1016/j.mechmachtheory.2021.104300

[7] Balchanowski J., Szrek J., Wudarczyk S. Analysis of constraint equations of the parallel mechanisms with 3 DoF in singular configurations. In: IFToMM WC 2019. Springer, 2019, pp. 607–616, doi: https://doi.org/10.1007/978-3-030-20131-9_61

[8] Lu Ya., Aoustin Ya., Arakelian V. Control performance improvement in dynamically decoupled manipulators. In: ROMANSY 2022. Springer, 2022, pp. 199–209, doi: https://doi.org/10.1007/978-3-031-06409-8_21

[9] Guagliumi L., Berti A., Monti E. et al. Design optimization of a 6-DOF cable-driven parallel robot for complex pick-and-place tasks. In: ROMANSY 2022. Springer, pp. 283–291, doi: https://doi.org/10.1007/978-3-031-06409-8_30

[10] Fomin A., Antonov A., Glazunov V. Forward kinematic analysis of a rotary hexapod. In: ROMANSY 2020. Springer, 2021, pp. 486–494, doi: https://doi.org/10.1007/978-3-030-58380-4_58

[11] Laryushkin P., Antonov A., Fomin A. et al. Inverse and forward kinematics of a reconfigurable spherical parallel mechanism with a circular rail. In: ROMANSY 2022. Springer, 2022, pp. 246–254, doi: https://doi.org/10.1007/978-3-031-06409-8_26

[12] Li R., Fan X., Li X. et al. Kinematic Design of a 2-SPS/PU&R 4-DOF hybrid robot for ankle rehabilitation. In: IFToMM WC 2019. Springer, 2019, pp. 1849–1858, doi: https://doi.org/10.1007/978-3-030-20131-9_183

[13] Balderas Hill R., Briot S., Chriette A. et al. Minimizing the energy consumption of a delta robot by exploiting the natural dynamics. In: ROMANSY 2020. Springer, 2020, pp. 213–224, doi: https://doi.org/10.1007/978-3-030-58380-4_26

[14] Geng J., Arakelian V. Balancing of planar 5R symmetrical parallel manipulators taking into account the varying payload. In: ROMANSY 2020. Springer, 2020, pp. 372–379, doi: https://doi.org/10.1007/978-3-030-58380-4_45

[15] Harada T., Kunishige Y. Singularity free mode changes of a redundantly driven two limbs six-dof parallel robot. In: ROMANSY 2020. Springer, 2020, pp. 405–413, doi: https://doi.org/10.1007/978-3-030-58380-4_49

[16] Gebel E.S., Gavrilina L.V., Glazunov V.A. et al. Forming a singularity zone for a one view mechanisms of parallel structure. Problemy mashinostroeniya i avtomatizatsii [Engineering and Automation Problems], 2020, no. 3, pp. 4–10. (In Russ.).

[17] Gebel E., Gavrilina L., Glazunov V. et al. To the analysis of singular zones mechanisms of parallel structure with linear motors. Stankoinstrument, 2021, no. 3, pp. 92–98, doi: https://doi.org/10.22184/2499-9407.2021.24.3.92.98 (in Russ.).

[18] Edakina T.V., Lastochkin A.B., Gavrilina L.V. et al. Structural analysis and construction of the operating area of an isomorphous translational–directional mechanism with a parallel structure. Problemy mashinostroeniya i nadezhnosti mashin, 2022, no. 4, pp. 6–13. (In Russ.). (Eng. version: J. Mach. Manuf. Reliab., 2022, vol. 51, no. 4, pp. 287–293, doi: https://doi.org/10.3103/S1052618822040057)