Type synthesis of 4-DOF SP-equivalent parallel manipulators : A virtual chain approach

Abstract SP-equivalent parallel mechanisms are the parallel counterparts of the 4-DOF SP serial manipulators, which are composed of one S (spherical) and one P (prismatic) joint. Using the virtual chain approach that we proposed elsewhere for the type synthesis of parallel mechanisms, this paper deals with the type synthesis of this class of 4-DOF parallel mechanisms. First, the application of the principle of virtual chain to the type synthesis of parallel mechanisms is recalled. Then, the type synthesis of 4-DOF SP-equivalent parallel mechanisms is performed in four steps, namely, the decomposition of the wrench system of an SP-equivalent parallel kinematic chain, the type synthesis of legs of SP-equivalent parallel kinematic chains, the generation of SP-equivalent parallel kinematic chains and the selection of actuated joints. SP-equivalent parallel kinematic chains with and without inactive joints are synthesized. The main characteristic of the proposed approach is that the type synthesis of legs for SP-equivalent parallel kinematic chains is reduced to the type synthesis of 4-DOF single-loop kinematic chains and thus easy to perform. The validity condition of actuated joints of SP-equivalent parallel mechanisms is reduced to the computation of a 4 × 4 determinant. In addition to all the 4-DOF SP-equivalent parallel kinematic chains and 4-DOF SP-equivalent parallel mechanisms proposed in the literature, a number of new 4-DOF SP-equivalent parallel kinematic chains and 4-DOF SP-equivalent parallel mechanisms are identified.

[1]  Yuefa Fang,et al.  Analytical Identification of Limb Structures for Translational Parallel Manipulators , 2004 .

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

[3]  Marco Carricato,et al.  A Family of 3-DOF Translational Parallel Manipulators , 2003 .

[4]  C. Gosselin,et al.  Type Synthesis of 3-DOF Spherical Parallel Manipulators Based on Screw Theory , 2004 .

[5]  Clément Gosselin,et al.  Type synthesis of 3T1R 4-DOF parallel manipulators based on screw theory , 2004, IEEE Transactions on Robotics and Automation.

[6]  L. W. Tsai,et al.  Robot Analysis: The Mechanics of Serial and Parallel Ma-nipulators , 1999 .

[7]  Antonio Frisoli,et al.  SYNTHESIS BY SCREW ALGEBRA OF TRANSLATING IN-PARALLEL ACTUATED MECHANISMS , 2000 .

[8]  W. Chung,et al.  Kinematic condition analysis of three-DOF pure translational parallel manipulators , 2003 .

[9]  K. H. Hunt,et al.  Kinematic geometry of mechanisms , 1978 .

[10]  Xianwen Kong,et al.  Type Synthesis of 3-DOF PPR Parallel Manipulators Based on Screw Theory and the Concept of Virtual Chain , 2004 .

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

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

[13]  Clément Gosselin,et al.  Kinematics and Singularity Analysis of a Novel Type of 3-CRR 3-DOF Translational Parallel Manipulator , 2002, Int. J. Robotics Res..

[14]  Raffaele Di Gregorio.  Translational Parallel Manipulators: New Proposals , 2002, J. Field Robotics.

[15]  Tieshi Zhao.  THEORY AND APPLICATION OF SELECTING ACTUATING COMPONENTS OF SPATIAL PARALLEL MECHANISMS , 2000 .

[16]  J. Dai,et al.  Geometric Analysis of Overconstrained Parallel Manipulators with Three and Four Degrees of Freedom , 2002 .

[17]  Jadran Lenarčič,et al.  Advances in Robot Kinematics , 2000 .

[18]  Joseph K. Davidson,et al.  Robots and Screw Theory: Applications of Kinematics and Statics to Robotics , 2004 .

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

[20]  K. H. Hunt.  Constant-Velocity Shaft Couplings: A General Theory , 1973 .

[21]  Xianwen Kong,et al.  Type Synthesis of 3-DOF PPR-Equivalent Parallel Manipulators Based on Screw Theory and the Concept of Virtual Chain , 2005 .

[22]  Jean-Pierre Merlet,et al.  Parallel Robots , 2000 .

[23]  Clément Gosselin,et al.  Analytical kinematics models and special geometries of a class of 4-DOF parallel mechanisms , 2005, IEEE Transactions on Robotics.

[24]  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..

[25]  Xianwen Kong,et al.  Type synthesis of 5-DOF parallel manipulators based on screw theory , 2005 .

[26]  Qiong Jin,et al.  Theory for Topology Synthesis of Parallel Manipulators and Its Application to Three-Dimension-Translation Parallel Manipulators , 2004 .