Kinematics and Singularity Analysis of 2 DOF Planar Parallel Manipulators with Symmetrical Parallelogram Chains

Adriyan Adriyan


This paper presented the kinematic and singularity analysis of two degree of freedom planar parallel manipulator or 2DOF PPM, in short, with symmetrical parallelogram chains. There were two configurations of 2DOF PPM that analyzed in this paper, that were 2-ΠΠΠ and 2-ΠΠ. Both PPM were represented on a topology diagram using graphs, respectively. Before conducting a kinematic analysis, 2-ΠΠΠ dan 2-ΠΠ were simplified to an equivalent kinematic chain, which was a well-known 5R kinematic chain. Then, the closed-form solutions for the inverse kinematic and the direct kinematic of the PPM were obtained by using the equivalent kinematic chain. Afterward, the velocity analysis was carried out to acquire Jacobians of the PPM. Hence, the singularity analysis can be performed to investigate singularity conditions that existed on the manipulator using these Jacobians. The singularity analysis showed that three singularity conditions existed on the manipulator, i.e. inverse, direct, and combined kinematic singularity. An insightful schematic was provided to illustrate each singularity condition.


Planar parallel manipulators, parallelogram chains, kinematic analysis, singularity analysis.

Full Text:



S. Cinquemani, H. Giberti, and M. Bassetti, “Optimal design, simulation and experimental tests of an 5R PKM manipulator,” in IEEE International Conference on Mechatronics (ICM), 2013, pp. 430–435.

M. Isaksson, “A Family of Planar Parallel Manipulators,” in IEEE International Conference on Robotics and Automation, 2011, pp. 1–10.

A. Joubair, M. Slamani, and I. A. Bonev, “Kinematic calibration of a five-bar planar parallel robot using all working modes,” Robot. Comput. Integr. Manuf., vol. 29, no. 4, pp. 15–25, 2013, doi: 10.1016/j.rcim.2012.10.002.

M. Z. Huang, “Design of a Planar Parallel Robot for Optimal Workspace and Dexterity,” Int. J. Adv. Robot. Syst., vol. 8, no. 4, pp. 176–183, 2011, doi: 10.5772/45693.

X. Liu, J. Wang, and H. Zheng, “Optimum design of the 5R symmetrical parallel manipulator with a surrounded and good-condition workspace,” Rob. Auton. Syst., vol. 54, pp. 221–233, 2006, doi: 10.1016/j.robot.2005.11.002.

X. Liu, J. Wang, and G. Pritschow, “Performance atlases and optimum design of planar 5R symmetrical parallel mechanisms,” Mech. Mach. Theory, vol. 41, pp. 119–144, 2006, doi: 10.1016/j.mechmachtheory.2005.05.003.

F. A. Lara-Molina, E. H. Koroishi, V. Steffen Jr., and L. A. Martins, “Kinematic performance of planar 5R symmetrical parallel mechanism subjected to clearances and uncertainties,” J. Brazilian Soc. Mech. Sci. Eng., vol. 40, no. 4, pp. 1–15, 2018, doi: 10.1007/s40430-018-1118-4.

X. Liu, J. Li, and Y. Zhou, “Kinematic optimal design of a 2-degree-of-freedom 3-parallelogram planar parallel manipulator,” Mech. Mach. Theory J., vol. 87, pp. 1–17, 2015, doi: 10.1016/j.mechmachtheory.2014.12.014.

T. Huang, S. Liu, J. Mei, and D. G. Chetwynd, “Optimal design of a 2-DOF pick-and-place parallel robot using dynamic performance indices and angular constraints,” Mech. Mach. Theory, vol. 70, pp. 246–253, 2013, doi: 10.1016/j.mechmachtheory.2013.07.014.

O. Company, F. Pierrot, S. Krut, C. Baradat, and V. Nabat, “Par2: A spatial mechanism for fast planar two-degree-of-freedom pick-and-place applications,” in The Second International Workshop on Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators, 2008, pp. 1–10, doi: 10.1007/s11012-010-9413-x.

C. Germain, S. Briot, V. Glazunov, S. Caro, and P. Wenger, “IRSBOT-2: A novel two-DOF parallel robot for high-speed operations,” in Proceedings of the ASME 2011 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, 2011, pp. 1–11, doi: 10.1115/DETC2011-47564.

X. Liu, L. Guan, and J. Wang, “Kinematics and Closed Optimal Design of a Kind of PRRRP Parallel Manipulator,” Mech. Des., vol. 129, no. May, pp. 558–563, 2007, doi: 10.1115/1.2712224.

X. Liu, J. Wang, and G. Pritschow, “Optimal kinematic design of the PRRRP 2-DoF parallel mechanism,” vol. 41, pp. 1111–1130, 2006, doi: 10.1016/j.mechmachtheory.2005.10.008.

L. Kang, J. T. Seo, W. Kim, and B. J. Yi, “Synthesis of new statically balanced parallel mechanisms,” 2014 IEEE Int. Conf. Mechatronics Autom. IEEE ICMA 2014, pp. 1102–1107, 2014, doi: 10.1109/ICMA.2014.6885852.


  • There are currently no refbacks.

Copyright of JTM (p-ISSN: 2089-4880   e-ISSN:2598-8263)