Design and kinematic analysis of a 3-translational-DOF spatial parallel mechanism based on polyhedra

Abstract Because of the high rigidity and high load-capacity, the spatial parallel mechanisms (SPMs) which have coupling chains or consist of loop chains in the limbs are attracting more and more interest. In order to obtain such kind of mechanism, a design strategy inspired by the ground structure method for the topology optimization of trusses is proposed in this paper. Based on the strategy, a new three degree-of-freedom (DOF) translational SPM is found. One characteristic of the proposed mechanism is that each limb of the mechanism consists of a passive planar 6R single-loop closed chain (6RSCC). Then the kinematics is analyzed in detail, including kinematic modeling, Jacobian analysis, singularity analysis, isotropy configuration analysis and workspace analysis. The analysis results further guide the detailed design of the mechanism. Based on the analysis results, a prototype is fabricated to demonstrate the feasibility of the design. At the end of the paper, some conclusions are drawn and future works are discussed.

[1]  Sheng Guo,et al.  Structural synthesis of a class of 2R2T hybrid mechanisms , 2016 .

[2]  Uri Kirsch,et al.  Optimal topologies of truss structures , 1989 .

[3]  Ziming Chen,et al.  Structural synthesis of two-layer and two-loop spatial mechanisms with coupling chains , 2015 .

[4]  Karl Wohlhart,et al.  Double-Ring Polyhedral Linkages , 2012 .

[5]  J. M. Hervé,et al.  Structural synthesis of 'parallel' robots generating spatial translation , 1991, Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments.

[6]  Jumpei Arata,et al.  Development of a haptic device “DELTA-4” using parallel link mechanism , 2009, 2009 IEEE International Conference on Robotics and Automation.

[7]  Q. C. Li,et al.  General Methodology for Type Synthesis of Symmetrical Lower-Mobility Parallel Manipulators and Several Novel Manipulators , 2002, Int. J. Robotics Res..

[8]  F. Park,et al.  Singularity Analysis of Closed Kinematic Chains , 1999 .

[9]  Clément Gosselin,et al.  Construction, Mobility Analysis and Synthesis of Polyhedra With Articulated Faces , 2014 .

[10]  Jian S. Dai,et al.  Mobility and Geometric Analysis of the Hoberman Switch-Pitch Ball and Its Variant , 2010 .

[11]  R. Clavel.  Une nouvelle structure de manipulateur parallèle pour la robotique légère , 1989 .

[12]  Grigore Gogu.  Structural synthesis of parallel robots. , 2008 .

[13]  Jorge Angeles,et al.  Kinematic Isotropy and the Optimum Design of Parallel Manipulators , 1997, Int. J. Robotics Res..

[14]  Thierry Lalibert,et al.  Polyhedra with Articulated Faces , 2007 .

[15]  Gökhan Kiper,et al.  Regular Polygonal and Regular Spherical Polyhedral Linkages Comprising Bennett Loops , 2009 .

[16]  François Pierrot,et al.  DELTA: a simple and efficient parallel robot , 1990, Robotica.

[17]  Rasim Alizade,et al.  Structural synthesis of parallel manipulators , 2004 .

[18]  Clément Gosselin,et al.  Synthesis and design of a one-degree-of-freedom planar deployable mechanism with a large expansion ratio , 2016 .

[19]  Xianwen Kong,et al.  Type Synthesis of Linear Translational Parallel Manipulators , 2002 .

[20]  Yuefa Fang,et al.  Structural synthesis and analysis of serial–parallel hybrid mechanisms with spatial multi-loop kinematic chains , 2012 .

[21]  Zexiang Li,et al.  A Novel 3-DoF Purely Translational Parallel Mechanism , 2006, 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[22]  Gregory Walsh,et al.  Kinematics of a novel three DOF translational platform , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[23]  Clément Gosselin,et al.  Conceptual Design and Dimensional Synthesis of a Novel 2-DOF Translational Parallel Robot for Pick-and-Place Operations , 2004 .

[24]  Xianwen Kong,et al.  A Method for Constructing Reconfigurable Deployable Polyhedral Mechanism , 2016 .

[25]  Robert E. Tarjan,et al.  Depth-First Search and Linear Graph Algorithms , 1972, SIAM J. Comput..

[26]  Harvey J. Greenberg,et al.  Automatic design of optimal structures , 1964 .

[27]  Kornel Ehmann,et al.  Design of parallel hybrid-loop manipulators with kinematotropic property and deployability , 2014 .

[28]  Jian S. Dai,et al.  Numeration and type synthesis of 3-DOF orthogonal translational parallel manipulators , 2008 .

[29]  Curtis L. Collins,et al.  A pantograph linkage parallel platform master hand controller for force-reflection , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[30]  Ridha Kelaiaia,et al.  Multiobjective optimization of a linear Delta parallel robot , 2012 .

[31]  Jürgen Hesselbach,et al.  A type synthesis method for hybrid robot structures , 2008 .

[32]  Florian Ion Tiberiu Petrescu,et al.  Kinematics at the Main Mechanism of a Railbound Forging Manipulator , 2015 .

[33]  Kornel Ehmann,et al.  Design of a Novel 4-DOF Kinematotropic Hybrid Parallel Manipulator , 2011 .

[34]  Jian S. Dai,et al.  A Spatial Eight-Bar Linkage and Its Association With the Deployable Platonic Mechanisms , 2014 .

[35]  R. G. Fenton,et al.  A Unifying Framework for Classification and Interpretation of Mechanism Singularities , 1995 .

[36]  Marco Carricato,et al.  Singularity-Free Fully-Isotropic Translational Parallel Manipulators , 2002 .

[37]  Dominique Deblaise,et al.  Effective geometrical calibration of a delta parallel robot used in neurosurgery , 2005, 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[38]  H. Lipkin,et al.  Mobility of Overconstrained Parallel Mechanisms , 2006 .

[39]  Weimin Li,et al.  A three-DOF translational manipulator with decoupled geometry , 2005, Robotica.

[40]  Lung-Wen Tsai,et al.  Kinematics of A Three-Dof Platform with Three Extensible Limbs , 1996 .

[41]  G. Gogu.  Structural synthesis of fully-isotropic translational parallel robots via theory of linear transformations , 2004 .

[42]  Martin P. Bendsøe,et al.  A New Method for Optimal Truss Topology Design , 1993, SIAM J. Optim..

[43]  Karl Wohlhart,et al.  Irregular Polyhedral Linkages , 2004 .

[44]  Jungwon Yoon,et al.  Design, fabrication, and evaluation of a new haptic device using a parallel mechanism , 2001 .

[45]  Albert A. Rizzo,et al.  Interactive game-based rehabilitation using the Microsoft Kinect , 2012, 2012 IEEE Virtual Reality Workshops (VRW).

[46]  Jean-Pierre Merlet.  Singular Configurations of Parallel Manipulators and Grassmann Geometry , 1989, Int. J. Robotics Res..

[47]  Sunil K. Agrawal,et al.  Polyhedral Single Degree-of-freedom Expanding Structures: Design and Prototypes , 2002 .

[48]  Huiping Shen,et al.  Synthesis and structure analysis of kinematic structures of 6-dof parallel robotic mechanisms , 2005 .

[49]  Takashi Suehiro,et al.  Stiffness Analysis and Design of a Compact Modified Delta Parallel Mechanism , 2004, Robotica.

[50]  Xianwen Kong,et al.  Type Synthesis of 3-DOF Translational Parallel Manipulators Based on Screw Theory , 2004 .

[51]  Han Sung Kim,et al.  Evaluation of a Cartesian Parallel Manipulator , 2002 .

[52]  Damien Chablat,et al.  Architecture optimization of a 3-DOF translational parallel mechanism for machining applications, the orthoglide , 2003, IEEE Trans. Robotics Autom..

[53]  Clément Gosselin,et al.  Singularity analysis of closed-loop kinematic chains , 1990, IEEE Trans. Robotics Autom..

[54]  Vincenzo Parenti-Castelli,et al.  A Translational 3-dof Parallel Manipulator , 1998 .

[55]  Eric Courteille,et al.  Design optimization of a Delta-like parallel robot through global stiffness performance evaluation , 2009, 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[56]  Xin-Jun Liu,et al.  A three translational DoFs parallel cube-manipulator , 2003, Robotica.

[57]  Jian S. Dai,et al.  Synthesis, Mobility, and Multifurcation of Deployable Polyhedral Mechanisms With Radially Reciprocating Motion , 2014 .

[58]  Qingsong Xu,et al.  Dynamic analysis of a modified DELTA parallel robot for cardiopulmonary resuscitation , 2005, 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[59]  Qingsong Xu,et al.  Design and application of a new 3-DOF translational parallel manipulator , 2007, 2007 IEEE Workshop on Advanced Robotics and Its Social Impacts.

[60]  Med Amine Laribi,et al.  Analysis and dimensional synthesis of the DELTA robot for a prescribed workspace , 2007 .

[61]  D. Zlatanov,et al.  On the velocity analysis of interconnected chains mechanisms , 2006 .

[62]  Clément Gosselin,et al.  Expandable Polyhedral Mechanisms Based on Polygonal One-Degree-of-Freedom Faces , 2006 .

[63]  Qinchuan Li,et al.  Theory of Parallel Mechanisms , 2012 .

[64]  Sébastien Briot,et al.  Pantopteron: A New Fully Decoupled 3DOF Translational Parallel Robot for Pick-and-Place , 2009 .