A numerical procedure to solve non‐linear kinematic problems in spatial mechanisms

This paper presents a numerical method to solve the forward position problem in spatial mechanisms. The method may be incorporated in a software for the kinematic analysis of mechanisms, where the procedure is systematic and can be easily implemented, achieving a high degree of automation in simulation. The procedure presents high computational efficiency, enabling its incorporation in the control loop to solve the forward position problem in the case of a velocity control scheme. Also, in this paper preliminary results on the convergence of the proposed procedure are shown, and efficiency results of the method applied to representative spatial mechanisms are presented. Copyright © 2007 John Wiley & Sons, Ltd.

[1]  R. Clavel,et al.  A Fast Robot with Parallel Geometry , 1988 .

[2]  T. Shiau,et al.  Direct kinematic analysis of a 3-PRS parallel mechanism , 2003 .

[3]  Jorge Angeles,et al.  The kinematic decoupling of parallel manipulators using joint-sensor data , 2000, IEEE Trans. Robotics Autom..

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

[5]  Kah Bin Lim,et al.  Forward kinematics solution of Stewart platform using neural networks , 1997, Neurocomputing.

[6]  Xiaoqiang Tang,et al.  On the analysis of active reflector supporting manipulator for the large spherical radio telescope , 2004 .

[7]  Carme Torras,et al.  A branch-and-prune solver for distance constraints , 2005, IEEE Transactions on Robotics.

[8]  Pratik J. Parikh,et al.  A hybrid strategy to solve the forward kinematics problem in parallel manipulators , 2005, IEEE Transactions on Robotics.

[9]  S. V. Sreenivasan,et al.  A Study of the Solvability of the Position Problem for Multi-Circuit Mechanisms by Way of Example of the Double Butterfly Linkage , 1996 .

[10]  E. Amezua,et al.  A method for the solution of the forward position problems of planar mechanisms with prismatic and revolute joints , 2001 .

[11]  A. N. Almadi,et al.  A Gröbner-Sylvester Hybrid Method for Closed-Form Displacement Analysis of Mechanisms , 2000 .

[12]  A. Morgan,et al.  Numerical Continuation Methods for Solving Polynomial Systems Arising in Kinematics , 1990 .

[13]  Eric Walter,et al.  Guaranteed solution of direct kinematic problems for general configurations of parallel manipulators , 1998, IEEE Trans. Robotics Autom..

[14]  M. A. Chace,et al.  A Sparsity-Oriented Approach to the Dynamic Analysis and Design of Mechanical Systems—Part 1 , 1977 .

[15]  Charles Pinto,et al.  A practical procedure to analyze singular configurations in closed kinematic chains , 2004, IEEE Transactions on Robotics.

[16]  B. Roth,et al.  Solving Polynomial Systems for the Kinematic Analysis and Synthesis of Mechanisms and Robot Manipulators , 1995 .

[17]  Fengfeng Xi,et al.  Development of a sliding-leg tripod as an add-on device for manufacturing , 2001, Robotica.

[18]  Tatsuo Arai,et al.  Optimal sensor placement for forward kinematics evaluation of a 6-DOF parallel link manipulator , 1991, Proceedings IROS '91:IEEE/RSJ International Workshop on Intelligent Robots and Systems '91.

[19]  Oscar Altuzarra,et al.  Point-based Jacobian formulation for computational kinematics of manipulators , 2006 .

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

[21]  Alfonso Hernández,et al.  Position analysis of planar mechanisms with R-pairs using a geometrical–iterative method , 2004 .

[22]  Sunan Huang,et al.  Combined PID and adaptive nonlinear control for servo mechanical systems , 2004 .