Forward/Reverse Velocity and Acceleration Analysis for a Class of Lower-Mobility Parallel Mechanisms

This paper proposes a novel kinematic analysis method for a class of lower-mobility mechanisms whose degree-of-freedom (DoF) equal the number of single-DoF kinematic pairs in each kinematic limb if all multi-DoF kinematic pairs are substituted by the single one. For such an N-DoF (N < 6) mechanism, this method can build a square (N X N) Jacobian matrix and cubic (N X N X N) Hessian matrix. The formulas in this method for different parallel mechanisms have unified forms and consequently the method is convenient for programming. The more complicated the mechanism is (for instance, the mechanism has more kinematic limbs or pairs), the more effective the method is. In the rear part of the paper, mechanisms 5-DoF 3-R(CRR) and 5-DoF 3-(RRR)(RR) are analyzed as examples.

[1]  Yuefa Fang,et al.  Structure Synthesis of a Class of 4-DoF and 5-DoF Parallel Manipulators with Identical Limb Structures , 2002, Int. J. Robotics Res..

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

[3]  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..

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

[5]  Oscar Altuzarra,et al.  Kinematic analysis of mechanisms via a velocity equation based in a geometric matrix , 2003 .

[6]  Qinchuan Li,et al.  Type synthesis of 3R2T 5-DOF parallel mechanisms using the Lie group of displacements , 2004, IEEE Transactions on Robotics and Automation.

[7]  K. H. Hunt,et al.  Structural Kinematics of In-Parallel-Actuated Robot-Arms , 1983 .

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

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

[10]  Robert J. Schilling,et al.  Fundamentals of robotics - analysis and control , 1990 .

[11]  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..

[12]  Z. Huang,et al.  Type Synthesis of Symmetrical Lower-Mobility Parallel Mechanisms Using the Constraint-Synthesis Method , 2003, Int. J. Robotics Res..

[13]  Yi Lu.  Using CAD variation geometry for solving velocity and acceleration of parallel manipulators with 3-, 4-, 5-linearly driving limbs , 2006 .

[14]  Delbert Tesar,et al.  Dynamic modeling of serial manipulator arms , 1982 .

[15]  Shin-Min Song,et al.  A Study of Reactional Force Compensation Based on Three-Degree-of Freedom Parallel Platforms , 1995, J. Field Robotics.

[16]  Zhen Huang,et al.  Forward/Reverse Velocity and Acceleration Analyses for a Class of Lower-Mobility Parallel Mechanisms , 2005 .

[17]  Raffaele Di Gregorio.  The 3-RRS Wrist: A New, Very Simple and Not Over-Constrained Spherical Parallel Manipulator , 2002 .

[18]  Fumiki Tanaka,et al.  A Method to Solve Inverse Kinematics Problems Using Lie Algebra and Its Application to Robot Spray Painting Simulation , 2004, DAC 2004.

[19]  Yuefa Fang,et al.  Inverse Velocity and Singularity Analysis of Low-DOF Serial Manipulators , 2003, J. Field Robotics.

[20]  Raffaele Di Gregorio.  Kinematics of the 3-UPU wrist , 2003 .