Kinematics of a Parallel Mechanism Consisting of Rotational Pairs

The article describes one of the possible quantitative approaches to the analysis of kinematics of a parallel mechanism consisting of planar rotational pairs. The mechanism is widespread in robotics. It comprises three parallel branches, each of which includes four rigid bodies and connects the stationary base with the output link. The mechanism has 13 mobile links and 15 pairs of the fifth class, that is, 13×6 – 15×5 = 3 degrees of freedom. Thus, 15 generalized coordinates, angles of rotation of one link relative to the other, are connected by 12 coupling equations. A numerical algorithm for solving the coupling equations is developed. Using three pre-determined angles, this allows the authors to find the others angles, as well as the coordinates and angular position of the output link. The algorithm is implemented using MATLAB software.

References

[1] Artobolevskii I.I. Teoriia mekhanizmov i mashin [Theory of mechanisms and machines]. Moscow, Nauka publ., 1988. 639 p.

[2] Merlet J.-P. Parallel Robots. Kluwer Academic Publishers, 2000. 372 p.

[3] Carricato M., Parenti-Castelli V. On the topological and geometrical synthesis and classification of translational parallel mechanisms. Proc. of the XI World Congress in Mechanism and Machine Science, Tianjin, China, 2004, pp. 1624–1628.

[4] Arsenault M., Boudreau R. The synthesis of three-degree-of-freedom planar parallel mechanisms with revolute joints (3-RRR) for an optimal singularity-free workspace. Journal of Robotic Systems, 2004, no. 21(5), pp. 259–274.

[5] Latest Advances in Robot Kinematics. Ed. Lenarcic J., Husty M. Springer, Dordrecht, Heidelberg, New York, London, 2012, XI, 457 p.

[6] Lee K.-M., Shah D.K. Kinematic analysis of a three-degrees-of freedom in-parallel actuated manipulator. IEEE Journal of Robotics and Automation, 1988, no. 4(3), pp. 354–360.

[7] Glazunov V.A., Lastochkin A.B., Terekhova A.N., Vu Ngok Bik. Ob osobennostiakh ustroistv otnositel’nogo manipulirovaniia [About the peculiarities of the device relative to the manipulation]. Problemy mashinostroeniia i nadezhnosti mashin [Journal of Machinery Manufacture and Reliability]. 2007, no. 2, pp. 77–85.

[8] Glazunov V.A. Struktura prostranstvennykh mekhanizmov. Gruppy vintov i strukturnye gruppy [The structure of spatial mechanisms. Group screws and structural groups]. Spravochnik. Inzhenernyi zhurnal [Handbook. An engineering journal]. 2010, att. no. 3, 24 p.

[9] Lariushkin P.A., Glazunov V.A., Kheilo S.V. Reshenie zadachi o polozheniiakh parallel’nykh manipuliatorov s tremia stepeniami svobody [Kinematics of 3-dof parallel manipulator]. Spravochnik. Inzhenernyi zhurnal [Handbook. An engineering journal]. 2012, no. 2, pp. 16–20.

[10] Huda S., Takeda Y. Dimension Synthesis of 3-URU Pure Rotation Parallel Mechanism with Respect to Singularity and Workspace. 12th IFToMM World Congress, Becasson, 2007, pp. 235–242.