Constraint and Singularity Analysis of Lower-Mobility Parallel Manipulators With Parallelogram Joints

This paper presents a general approach to analyze the singularities of lower-mobility parallel manipulators with parallelogram joints. Using screw theory, the concept of twist graph is introduced and the twist graphs of two types of parallelogram joints are established in order to simplify the constraint analysis of the manipulators under study. Using Grassmann-Cayley Algebra, the geometric conditions associated with the dependency of six Plucker vectors of finite and infinite lines in the 3 -dimensional projective space are reformulated in the superbracket in order to derive the geometric conditions for parallel singularities. The methodology is applied to three lower-mobility parallel manipulators with parallelogram joints: the Delta-linear robot, the Orthoglide robot and the H4 robot. The geometric interpretations of the singularities of these robots are given.Copyright © 2010 by ASME

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

[2]  Joseph Duffy,et al.  A Direct Determination of the Instantaneous Kinematics of Fully Parallel Robot Manipulators , 1985 .

[3]  C. Barus.  A treatise on the theory of screws , 1998 .

[4]  O. Company,et al.  H4: a new family of 4-DOF parallel robots , 1999, 1999 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (Cat. No.99TH8399).

[5]  François Pierrot,et al.  H4 parallel robot: modeling, design and preliminary experiments , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[6]  Clément Gosselin,et al.  Constraint singularities of parallel mechanisms , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

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

[8]  Atsushi Konno,et al.  SINGULARITY ANALYSIS OF A NOVEL 4-DOFS PARALLEL ROBOT H4 BY USING SCREW THEORY , 2003, DAC 2003.

[9]  Xianwen Kong,et al.  Mobility Analysis of Parallel Mechanisms Based on Screw Theory and the Concept of Equivalent Serial Kinematic Chain , 2005 .

[10]  Neil White,et al.  Grassmann-Cayley Algebra and Robotics Applications , 2005 .

[11]  Youlun Xiong,et al.  Singularity analysis of a novel 4-dof parallel manipulator H4 , 2006 .

[12]  Xianwen Kong,et al.  Type Synthesis of Parallel Mechanisms , 2010, Springer Tracts in Advanced Robotics.

[13]  Moshe Shoham,et al.  Application of Grassmann—Cayley Algebra to Geometrical Interpretation of Parallel Robot Singularities , 2009, Int. J. Robotics Res..

[14]  Damien Chablat,et al.  Singularity Analysis of Lower Mobility Parallel Manipulators Using Grassmann–Cayley Algebra , 2009, IEEE Transactions on Robotics.