Topological and Geometrical Synthesis of Three-Degree-of-Freedom Fully Parallel Manipulators by Instantaneous Kinematics

This paper presents a new synthesis procedure of fully parallel manipulators (PMs) of three degrees of freedom (DOFs) that could be implemented in a computer-aided synthesis process. Possible designs of PMs are represented by a set of unit joint twists at an initial configuration, called here topological and geometric parameters (TGPs). This makes it possible to represent PMs of all topologies and geometries in an easy and consistent way. The kinematic bond between the end effector (EE) and the base is then formulated as a set of equations involving TGPs, actuated-joint variables, and non-actuated-joint variables (passive joints). To achieve the required type of EE motion, possible topologies are first derived from tangent space analysis, and then the feasible topologies are retained by further displacement analysis. The geometries are determined such that the set of equations should be isoconstrained when passive-joint variables are taken as unknowns. The synthesis procedure of 3DOF PMs is illustrated with three numerical examples: one producing a new architecture of one translation and two rotations, while the other two producing existing architectures of translational PMs.

[1]  J. Denavit,et al.  A kinematic notation for lower pair mechanisms based on matrices , 1955 .

[2]  J. Michael McCarthy,et al.  Introduction to theoretical kinematics , 1990 .

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

[4]  Bernard Roth,et al.  Kinematic analysis of the 6R manipulator of general geometry , 1991 .

[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]  Clément Gosselin,et al.  The agile eye: a high-performance three-degree-of-freedom camera-orienting device , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[7]  Jacques M. Hervé,et al.  The mathematical group structure of the set of displacements , 1994 .

[8]  C. Gosselin,et al.  On the direct kinematics of spherical three-degree-of-freedom parallel manipulators of general architecture , 1994 .

[9]  Jorge Angeles,et al.  Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms , 1995 .

[10]  Jorge Angeles,et al.  The isotropic decoupling of the direct kinematics of parallel manipulators under sensor redundancy , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[11]  Lung-Wen Tsai,et al.  A Parallel Manipulator with Only Translational Degrees of Freedom , 1997 .

[12]  Claude Reboulet,et al.  Design of a 3-DOF parallel translating manipulator with U-P-U joints kinematic chains , 1997, Proceedings of the 1997 IEEE/RSJ International Conference on Intelligent Robot and Systems. Innovative Robotics for Real-World Applications. IROS '97.

[13]  Jorge Angeles,et al.  Contributions to the estimation of rigid-body motion under sensor redundancy , 1997 .

[14]  J. M. Hervé.  The Lie group of rigid body displacements, a fundamental tool for mechanism design , 1999 .

[15]  Guilin Yang,et al.  Design and kinematic analysis of modular reconfigurable parallel robots , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[16]  Feng Gao,et al.  On the analysis of a new spatial three-degrees-of-freedom parallel manipulator , 2001, IEEE Trans. Robotics Autom..

[17]  Jorge Angeles,et al.  Singularity analysis of three-legged parallel robots based on passive-joint velocities , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

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

[19]  S. Stramigioli,et al.  On the geometry of rigid-body motions: The relation between Lie groups and screws , 2002 .

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

[21]  Lung-Wen Tsai,et al.  Kinematic Analysis of 3-DOF Position Mechanisms for Use in Hybrid Kinematic Machines , 2002 .

[22]  J. M. Hervé,et al.  A Family of Novel Orientational 3-DOF Parallel Robots , 2002 .

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

[24]  L. Baron,et al.  Kinematic Modelling and Isotropic Conditions of a Family of Translational Parallel Manipulators , 2003, 2003 4th International Conference on Control and Automation Proceedings.

[25]  Clément Gosselin,et al.  A fully decoupled 3-DOF translational parallel mechanism , 2004 .

[26]  Paul J. Zsombor-Murray,et al.  Unified Kinematic Analysis of General Planar Parallel Manipulators , 2004 .

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

[28]  J. Angeles.  The Qualitative Synthesis of Parallel Manipulators , 2004 .

[29]  M. J. D. Hayes,et al.  ATLAS: A NOVEL KINEMATIC ARCHITECTURE FOR SIX DOF MOTION PLATFORMS , 2005 .

[30]  J. M. Hervé,et al.  Translational parallel manipulators with doubly planar limbs , 2006 .

[31]  Xin-Jun Liu,et al.  Determination of the Link Lengths for a Spatial 3-DOF Parallel , 2006 .

[32]  Raffaele Di Gregorio.  Analytic Form Solution of the Direct Position Analysis of a Wide Family of Three-Legged Parallel Manipulators , 2006 .

[33]  Qingsong Xu,et al.  Kinematic analysis and design of a new 3-DOF translational parallel manipulator , 2006 .

[34]  Damien Chablat,et al.  Kinematic Analysis of a New Parallel Machine Tool: the Orthoglide , 2007, ArXiv.

[35]  Farhad Tahmasebi.  Kinematics of a New High-Precision Three-Degree-of-Freedom Parallel Manipulator , 2007 .

[36]  J-P. Merlet,et al.  Still a long way to go on the road for parallel mechanisms , 2009 .