Inverse and Forward Kinematic Analysis of a 6-DOF Parallel Manipulator Utilizing a Circular Guide

The proposed study focuses on the inverse and forward kinematic analysis of a novel 6-DOF parallel manipulator with a circular guide. In comparison with the known schemes of such manipulators, the structure of the proposed one excludes the collision of carriages when they move along the circular guide. This is achieved by using cranks (links that provide an unlimited rotational angle) in the manipulator kinematic chains. In this case, all drives stay fixed on the base. The kinematic analysis provides analytical relationships between the end-effector coordinates and six controlled movements in drives (driven coordinates). Examples demonstrate the implementation of the suggested algorithms. For the inverse kinematics, the solution is found given the position and orientation of the end-effector. For the forward kinematics, various assembly modes of the manipulator are obtained for the same given values of the driven coordinates. The study also discusses how to choose the links lengths to maximize the rotational capabilities of the end-effector and provides a calculation of such capabilities for the chosen manipulator design.

[1]  Victor Glazunov,et al.  Kinematic analysis of a spatial parallel structure mechanism with a circular guide , 2015 .

[2]  Amir Rezaei,et al.  Implementing the homotopy continuation method in a hybrid approach to solve the kinematics problem of spatial parallel robots , 2017, Intell. Serv. Robotics.

[3]  Clément Gosselin,et al.  Evaluation and Representation of the Theoretical Orientation Workspace of the Gough–Stewart Platform , 2009 .

[4]  P. Dietmaier,et al.  The Stewart-Gough Platform of General Geometry can have 40 Real Postures , 1998 .

[5]  Andrew J. Newell,et al.  BertiniLab: A MATLAB interface for solving systems of polynomial equations , 2015, Numerical Algorithms.

[6]  Ilian A. Bonev,et al.  A new rotary hexapod for micropositioning , 2013, 2013 IEEE International Conference on Robotics and Automation.

[7]  Huimin Dong,et al.  A 3-RRR Spherical Parallel Manipulator Reconfigured with Four-bar Linkages , 2018 .

[8]  Jae Kyung Shim,et al.  Forward kinematics of the general 6–6 Stewart platform using algebraic elimination , 2001 .

[9]  Chin-Hsing Kuo,et al.  Gravity compensation design of Delta parallel robots using gear-spring modules , 2020 .

[10]  I.A. Bonev,et al.  XY-Theta Positioning Table with Parallel Kinematics and Unlimited Theta Rotation , 2006, 2006 IEEE International Symposium on Industrial Electronics.

[11]  Beno Benhabib,et al.  Comparative analysis of a new 3×PPRS parallel kinematic mechanism , 2014 .

[12]  S. Bai.  Optimum design of spherical parallel manipulators for a prescribed workspace , 2010 .

[13]  Beno Benhabib,et al.  An Emulator-Based Prediction of Dynamic Stiffness for Redundant Parallel Kinematic Mechanisms , 2016 .

[14]  Jean-Pierre Merlet,et al.  Solving the Forward Kinematics of a Gough-Type Parallel Manipulator with Interval Analysis , 2004, Int. J. Robotics Res..

[15]  H. Lipkin,et al.  Characteristic tetrahedron of wrench singularities for parallel manipulators with three legs , 2002 .

[16]  C. B. García,et al.  On the Number of Solutions to Polynomial Systems of Equations , 1980 .

[17]  Feng Gao,et al.  Mechanism design of a simplified 6-DOF 6-RUS parallel manipulator , 2002, Robotica.

[18]  Hiroaki Funabashi,et al.  Development of Spatial Parallel Manipulators with Six Degrees of Freedom , 1991 .

[19]  Katia Bertoldi,et al.  Harnessing transition waves to realize deployable structures , 2020, Proceedings of the National Academy of Sciences.

[20]  Arash Rahmani,et al.  Application of a Novel Elimination Algorithm with Developed Continuation Method for Nonlinear Forward Kinematics Solution of Modular Hybrid Manipulators , 2020, Robotica.

[21]  Zheng Zhang,et al.  An Efficient Numerical Method for Forward Kinematics of Parallel Robots , 2019, IEEE Access.

[22]  M. Husty.  An algorithm for solving the direct kinematics of general Stewart-Gough platforms , 1996 .

[23]  François Pierrot,et al.  Towards a fully-parallel 6 DOF robot for high-speed applications , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[24]  Marco Ceccarelli,et al.  Parallel Architectures for Humanoid Robots , 2020, Robotics.

[25]  Luc Rolland,et al.  Certified solving of the forward kinematics problem with an exact algebraic method for the general parallel manipulator , 2005, Adv. Robotics.

[26]  Lluís Ros,et al.  A unified method for computing position and orientation workspaces of general Stewart platforms , 2011 .

[27]  Victor Glazunov,et al.  Development of a Novel Rotary Hexapod with Single Drive , 2019 .

[28]  Kevin Cleary,et al.  Kinematic analysis of a novel 6-DOF parallel manipulator , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[29]  Lluís Ros,et al.  Singularities of Robot Mechanisms , 2017 .

[30]  D. Tesar,et al.  Analysis of a fully-parallel six degree-of-freedom micromanipulator , 1991, Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments.

[31]  Offer Shai,et al.  Infinitesimal displacement analysis of a parallel manipulator with circular guide via the differentiation of constraint equations , 2016 .

[32]  Vladimir Pavlovsky,et al.  Singularity Analysis of a Wall-Mounted Parallel Robot with SCARA MotionsLower Limb Exoskeleton with Hybrid Pneumaticaly Assisted Electric Drive for Neuroreabilitation , 2017 .