Analytical determination of the workspace of symmetrical spherical parallel mechanisms

This paper presents a methodology for the analytical determination and representation of the workspace boundaries of symmetrical spherical parallel mechanisms (SPMs). The methodology is based on an intuitive orientation representation which, while not well known, has proven to be very useful for the analysis of symmetrical parallel mechanisms. The latter, previously introduced as "tilt-and-torsion angles," are briefly described. Then, relatively simple analytical expressions are found for the workspace boundaries of general symmetrical SPMs. Next, using these expressions and a simple numerical procedure, a fast algorithm is proposed for representing the so-called constant-torsion workspace. Finally, several examples are provided

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

[2]  Mircea Badescu,et al.  Workspace Optimization of 3-Legged UPU and UPS Parallel Platforms With Joint Constraints , 2004 .

[3]  Jeha Ryu,et al.  Orientation workspace analysis of 6-DOF parallel manipulators , 1999 .

[4]  Clément Gosselin,et al.  Development and Experimentation of a Fast 3-DOF Camera-Orienting Device , 1997, Int. J. Robotics Res..

[5]  C. Gosselin,et al.  The optimum kinematic design of a spherical three-degree-of-freedom parallel manipulator , 1988 .

[6]  James U. Korein,et al.  A geometric investigation of reach , 1985 .

[7]  G. Yamaguchi,et al.  A new technique for determining 3-D joint angles: the tilt/twist method. , 1999, Clinical biomechanics.

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

[9]  Raffaele Di Gregorio,et al.  A new parallel wrist using only revolute pairs: the 3-RUU wrist , 2001, Robotica.

[10]  Marco Ceccarelli,et al.  Optimal design of CaPaMan (Cassino Parallel Manipulator) with a specified orientation workspace , 2002, Robotica.

[11]  C. Peter Keller,et al.  Map Projections: A Reference Manual , 1996 .

[12]  C. Gosselin,et al.  Singularity Loci of a Special Class of Spherical 3-DOF Parallel Mechanisms With Prismatic Actuators , 2004 .

[13]  H. Harry Asada,et al.  Kinematic and static characterization of wrist joints and their optimal design , 1985, Proceedings. 1985 IEEE International Conference on Robotics and Automation.

[14]  Jinsong Wang,et al.  Closed Form Solution to Workspace of Hexapod-Based Virtual Axis Machine Tools , 1999 .

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

[16]  Vincenzo Parenti-Castelli,et al.  Echelon form solution of direct kinematics for the general fully-parallel spherical wrist , 1993 .

[17]  C. Gosselin,et al.  Advantages of the modified Euler angles in the design and control of PKMs , 2002 .

[18]  J. Sefrioui.  Etude et representation des lieux de singularite des manipulateurs parallelles spheriques a trois degres de liberte avec actionneurs prismatiquesDetermination of the singularity loci of spherical three-degree-of-freedom parallel manipulators , 1994 .

[19]  Ilian A. Bonev,et al.  Working and assembly modes of the agile eye , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[20]  Bijan Shirinzadeh,et al.  Loci of singular configurations of a 3-DOF spherical parallel manipulator , 2004, Robotics Auton. Syst..

[21]  Clément Gosselin,et al.  Singularity Loci of Spherical Parallel Mechanisms , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[22]  Shahram Payandeh,et al.  Design of spherical parallel mechanisms for application to laparoscopic surgery , 2002, Robotica.

[23]  H. Funabashi,et al.  Development of a spherical in-parallel actuated mechanism with three degrees of freedom with large working space and high motion transmissibility : Evaluation of motion transmissibility and analysis of working space , 1996 .

[24]  Raffaele Di Gregorio,et al.  Kinematics of a new spherical parallel manipulator with three equal legs: The 3-URC wrist , 2001, J. Field Robotics.

[25]  Jean-Pierre Merlet,et al.  Determination of the orientation workspace of parallel manipulators , 1995, J. Intell. Robotic Syst..