This paper introduces an asymmetrical parallel robotic wrist, which can generate a decoupled unlimited-torsion motion and achieve high positioning accuracy. The kinematics, dexterity, and singularities of the manipulator are investigated to visualize the performance contours of the manipulator. Using the method of Lagrange multipliers and considering all the mobile components, the equations of motion of the manipulator are derived to investigate the dynamic characteristics efficiently. The developed dynamic model is numerically illustrated and compared with its simplified formulation to show its computation accuracy. 1. Introduction The parallel typed wrist mechanisms, also called spherical parallel manipulators (SPMs), have found their applications in camera-orientating [1], minimally invasive surgery [2] and wrist joint [3] thanks to their large orientation workspace and high payload capacity. Since the SPM can generate three pure rotations, another potential application is that it can function as a tool head for complicated surface machining. However, the general SPM only can produce a limited torsion motion with a prescribed tilt angle, whereas an unlimited torsion is necessary in some common material processing such as milling. The coaxial input SPM reported in [3] can achieve unlimited torsion, whereas its unique structure introduces a complex input mechanism. Moreover, the general SPMs result in low positioning accuracy [4] without a ball-and-socket joint as the center of rotation. In this paper, an asymmetrical parallel robotic wrist is proposed, which can generate an unlimited-torsion motion with enhanced positioning accuracy. This manipulator adopts a universal joint as the center of rotation supported by an input shaft at the center, which simplifies the manipulator architecture. The SPMs have been extensively studied on many aspects, such as workspace [5, 6], dexterity [7–9], singularity [10], stiffness [4, 11], and type synthesis [12–14]. These performance criteria can be classified into two groups: one relates to the kinematic performance of the manipulator while the other relates to the kinetostatic/dynamic performance of the manipulator [15]. In the kinematic considerations, the quality of the workspace that reflects the shape, size, and presence of singularities is of primary importance in the manipulator design. Another utmost important concern is the dexterity, which is usually evaluated by means of the conditioning number of the kinematic Jacobian matrix. On the other hand, the dynamics of SPMs received relatively less attention.
References
[1]
C. M. Gosselin and J. F. Hamel, “The Agile Eye: a high-performance three-degree-of-freedom camera-orienting device,” in Proceedings of the IEEE International Conference on Robotics and Automation, vol. 1, pp. 781–786, San Diego, Calif, USA, May 1994.
[2]
T. Li and S. Payandeh, “Design of spherical parallel mechanisms for application to laparoscopic surgery,” Robotica, vol. 20, no. 2, pp. 133–138, 2002.
[3]
H. Asada and J. Granito, “Kinematic and static characterization of wrist joints and their optimal design,” in Proceedings of the IEEE International Conference on Robotics and Automation, pp. 244–250, 1985.
[4]
G. Wu, S. Bai, and J. Kepler, “Mobile platform center shift in spherical parallel manipulators with flexible limbs,” Mechanism and Machine Theory, vol. 75, pp. 12–26, 2014.
[5]
C. M. Gosselin and J. Angeles, “The optimum kinematic design of a spherical three-degree-of-freedom parallel manipulator,” Journal of Mechanical Design, vol. 111, no. 2, pp. 202–207, 1989.
[6]
S. Bai, “Optimum design of spherical parallel manipulators for a prescribed workspace,” Mechanism and Machine Theory, vol. 45, no. 2, pp. 200–211, 2010.
[7]
C. Gosselin and J. Angeles, “Global performance index for the kinematic optimization of robotic manipulators,” Journal of Mechanical Design, vol. 113, no. 3, pp. 220–226, 1991.
[8]
S. Bai, M. R. Hansen, and T. O. Andersen, “Modelling of a special class of spherical parallel manipulators with Euler parameters,” Robotica, vol. 27, no. 2, pp. 161–170, 2009.
[9]
G. Wu, “Multiobjective optimum design of a 3-RRR spherical parallel manipulator with kinematic and dynamic dexterities,” Modeling, Identification and Control, vol. 33, no. 3, pp. 111–121, 2012.
[10]
I. A. Bonev and C. M. Gosselin, “Singularity loci of spherical parallel mechanisms,” in Proceedings of the IEEE International Conference on Robotics and Automation, pp. 2957–2962, April 2005.
[11]
F. Bidault, C. P. Teng, and J. Angeles, “Structural optimization of a spherical parallel manipulator using a two-level approach,” in Proceedings of the ASME Design Engineering Technical Conference and Computers and Information in Engineering Conference, pp. 215–224, Pittsburgh, Pa, USA, September 2001.
[12]
X. Kong and C. M. Gosselin, “Type synthesis of three-degree-of-freedom spherical parallel manipulators,” The International Journal of Robotics Research, vol. 23, no. 3, pp. 237–245, 2004.
[13]
G. Gogu, “Fully-isotropic three-degree-of-freedom parallel wrists,” in Proceedings of the IEEE International Conference on Robotics and Automation (ICRA '07), pp. 895–900, Roma, Italy, April 2007.
[14]
M. Karouia and J. M. Hervé, “Asymmetrical 3-dof spherical parallel mechanisms,” European Journal of Mechanics: A/Solids, vol. 24, no. 1, pp. 47–57, 2005.
[15]
S. Caro, D. Chablat, R. Ur-Rehman, and P. Wenger, “Multiobjective design optimization of 3-PRR planar parallel manipulators,” in Global Product Development, A. Bernard, Ed., pp. 373–383, Springer, Berlin, Germany, 2011.
[16]
R. N. Murray, Z. X. Li, and S. S. Sastry, A Mathematical Introduction to Robotic Manipulation, CRC Press, 1994.
[17]
R. Featherstone and D. Orin, “Robot dynamics: equations and algorithms,” in Proceedings of the IEEE International Conference on Robotics and Automation (ICRA '00), pp. 826–834, April 2000.
[18]
J. Angeles, Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms, Springer, New York, NY, USA, 2007.
[19]
S. Staicu, “Recursive modelling in dynamics of Agile Wrist spherical parallel robot,” Robotics and Computer-Integrated Manufacturing, vol. 25, no. 2, pp. 409–416, 2009.
[20]
J. G. de Jalon and E. Bayo, Kinematic and Dynamic Simulation of Multibody Systems: The Real-Time Challenge, Springer, New York, NY, USA, 1994.
[21]
http://en.wikipedia.org/wiki/Universal_joint.
[22]
F. Freudenstein, “Approximate synthesis of four-bar linkages,” Resonance, vol. 15, no. 8, pp. 740–767, 2010.
[23]
R. E. Stamper, L.-W. Tsai, and G. C. Walsh, “Optimization of a three DOF translational platform for well-conditioned workspace,” in Proceedings of the IEEE International Conference on Robotics and Automation, vol. 4, pp. 3250–3255, Albuquerque, NM, USA, 1997.
[24]
X.-J. Liu, J. Wang, K.-K. Oh, and J. Kim, “A new approach to the design of a DELTA robot with a desired workspace,” Journal of Intelligent and Robotic Systems, vol. 39, no. 2, pp. 209–225, 2004.
[25]
P. Wenger and D. Chablat, “Kinematic analysis of a new parallel machine tool: the Orthoglide,” in Advances in Robot Kinematics, J. Lenar？i？ and M. M. Stani？i？, Eds., pp. 305–314, Springer, Amsterdam, The Netherlands, 2000.
