Abstract
This paper presents the kinematics and workspace optimization of the two different 2-DOF (Degrees-of-Freedom) planar parallel mechanisms: one (called 2-RPR mechanism) with translational actuators and the other (called 2-RRR mechanism) with rotational ones. First of all, the inverse kinematics and Jacobian matrix for each mechanism are derived analytically. Then, the workspace including the output-space and the joint-space is systematically analyzed in order to determine the geometric parameters and the operating range of the actuators. Finally, the kinematic optimization of the mechanisms is performed in consideration of their dexterity and rigidity. It is expected that the optimization results can be effectively used as a basic material for the applications of the presented mechanisms to more industrial fields.
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Birglen, L., Gosselin, C., Pouliot, N., Monsarrat, B. and Laliberté, T., 2002, “SHaDe, A New 3-DOF Haptic Device,”IEEE Trans. on Robotics and Automation, Vol. 18, No. 2, pp. 166–175.
Carretero, J. A., Podhorodeski, R. P., Nahon, M. A. and Gosselin, C. M., 2000, “Kinematic Analysis and Optimization of a New Three Degree-of-Freedom Spatial Parallel Manipulator,”ASME J. of Mechanical Design, Vol. 122, pp. 17–24.
Choi, K. B., 2003, “Kinematic Analysis and Optimal Design of 3-PPR Planar Parallel Manipulator,”KSME International Journal, Vol. 17, No. 4, pp. 528–537.
Chung, J.-H., Ko, S.-Y., Kwon, D.-S., Lee, J.,-J., Yoon, Y.-S. and Won, C.-H., 2003, “Robot-Assisted Femoral Stem Implantation Using an Intramedulla Gauge,”IEEE Trans. on Robotics and Automation, Vol. 19, No. 5, pp. 855–892.
Chung, Y.-H. and Lee, J.-W., 2001, “Design of a New 2 DOF Parallel Mechanism,”Proc. of IEEE IASME Int. Conf. on Advanced Intelligent Mechatronics, Como, Italy, pp. 129–134.
Chung, Y.-H., Lee, J.-W., Sung, Y.-G. and Joo, H.-H., 2001, “Dynamics and Control of 2-DOF 5-Bar Parallel Manipulator with Closed Chain,”International Journal of the Korean Society of Precision Engineering, Vol. 2, No. 1, pp. 5–10.
Frisoli, A., Prisco, G. M., Salsedo, F. and Bergamasco, M., 1999, “A Two Degrees-of-Freedom Planar Haptic Interface with High Kinematic Isotropy,”Proc. of IEEE Int. Workshop on Robot and Human Interaction, Pisa, Italy, pp. 297–302.
Gao, F., Liu, X. and Gruver, W. A., 1998, “Performance Evaluation of Two-Degree-of-Freedom Planar Parallel Robots,”Mechanism and Machine Theory, Vol. 33, No. 6, pp. 661–668.
Gregorio, R. D. and Parenti-Castelli, V., 2001, “Position Analysis in Analytical Form of the 3-PSP Mechanism,”ASME J. of Mechanical Design, Vol. 123, pp. 51–57.
Gregorio, R. D., 2002, “Analytic Determination of Workspace and Singularities in a Parallel Pointing System,”J. of Robotic Systems, Vol. 19, pp. 37–43.
Huang, T., Li, M., Li, Z., Chetwynd, D. G. and Whitehouse, D. J., 2004, “Optimal kinematic Design of 2-DOF Parallel Manipulators With Well-Shaped Workspace Bounded by a Specified Conditioning Index,”IEEE Trans. on Robotics and Automation, Vol. 20, No. 3, pp. 538–543.
Joshi, S. and Tsai, L.-W., 2002, “A Comparison Study of Two 3-DOF Parallel Manipulators: One with Three and the Other with Four Supporting Legs,”Proc. IEEE Int. Conf. on Robotics and Automation, DC, pp. 3690–3697.
Kim, H. S. and Tsai, L.-W., 2003, “Kinematic Synthesis of a Spatial 3-RPS Parallel Manipulator,”ASME J. of Mechanical Design, Vol. 125, pp. 92–97.
Liu, X.-J., Tang, X. and Wang, J., 2003, “A Novel 2-DOF Parallel Mechanism Based Design of a New 5-Axis Hybrid Machine Tool,”Proc. of IEEE Int. Conf. on Robotics and Automation, Taipei, Taiwan, pp. 3990–3995.
Liu, X.-J., Wang, J., Gao, F. and Wang, L.-P., 2001, “On the Analysis of a New Spatial Three-Degree-of-Freedom Parallel Manipulator,”IEEE Trans. on Robotics and Automation, Vol. 17, No. 6, pp. 959–968.
Nam, Y.-J., Lee, Y.-H. and Park, M. K., 2005, “Kinematic Analysis and Optimal Design of 2RPR-RP Parallel Manipulator,”Tran. of the Korean Society of Mechanical Engineering (Part A), Vol. 29, No. 11, pp. 1509–1517.
Park, M. K., Lee, M. C., Yoo, K. S., Son, K., Yoo, W. S. and Han, M. C., 2001, “Development of the PNU Vehicle Driving Simulator and Its Performance Evaluation,”Proc. of IEEE Int. Conf. on Robotics and Automation, Seoul, Korea, pp. 2325–2330.
Romdhane, L., Affi, Z. and Fayet, M., 2002, “Design and Singularity Analysis of a 3-Translational-DOF In-Parallel Manipulator,”ASME J. of Mechanical Design, Vol. 124, pp. 419–426.
Stock, M. and Miller, K., 2003, “Optimal Kinematic Design of Spatial Parallel Manipulators: Application to Linear Delta Robot,”ASME J. of Mechanical Design, Vol. 125, pp. 292–301.
Wang, J. and Liu, X.-J., 2003, “Analysis of a Novel Cylindrical 3-DOF Parallel Robot,”Robotics and Autonomous System, Vol. 42, pp. 31–46.
Wolf, A., Ottaviano, E., Shoham, M. and Ceccarelli, M., 2003, “Application of Line Geometry and Linear Complex Approximation to Singularity Analysis of the 3-DOF CaPaMan Parallel Manipulator,”Mechanism and Machine Theory, Vol. 39, pp. 75–95.
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Nam, YJ., Park, MK. Workspace optimization and kinematic performance evaluation of 2-DOF parallel mechanisms. J Mech Sci Technol 20, 1614–1625 (2006). https://doi.org/10.1007/BF02916265
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DOI: https://doi.org/10.1007/BF02916265