On the duality of twist/wrench distributions in serial and parallel chain robot manipulators

Duality and reciprocity between twist and wrench systems is the essence of screw theory. The power of these concepts lies in the idea that once a result is obtained for one type of system it can immediately be applied to the dual system provided the appropriate physical interpretation is also translated. The interrelation between serial and parallel mechanisms is a consequence of this twist/wrench duality. The purpose of this investigation is to focus on some fundamental configurations of serial and parallel robot manipulators in an attempt to further elucidate the various correspondences that exist between their geometries and their kinematic equations. The focus is on zero-pitch screw systems, namely revolute joints for serial manipulators and force producing sub-chains in parallel manipulators. Solutions for twist/wrench distributions will be discussed for both proper and redundant systems.

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

[2]  Vijay R. Kumar,et al.  Force distribution in closed kinematic chains , 1988, IEEE J. Robotics Autom..

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

[4]  Vijay Kumar,et al.  A Compact Inverse Velocity Solution for Redundant Robots , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[5]  Yasuyuki Funahashi,et al.  A new analytical system applying 6 DOF parallel link manipulator for evaluating motion sensation , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[6]  Kenneth J. Waldron,et al.  Series-Parallel Dualities in Actively Coordinated Mechanisms , 1988, Int. J. Robotics Res..

[7]  Joongseon Joh,et al.  Lagrangian wrench distribution for cooperating robotic mechanisms , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[8]  Vijay Kumar,et al.  Instantaneous Kinematics of Parallel-Chain Robotic Mechanisms , 1992 .

[9]  Tom Brock,et al.  The Industrial Robot , 1983 .

[10]  Adi Ben-Israel,et al.  Generalized inverses: theory and applications , 1974 .

[11]  Russell H. Taylor,et al.  A telerobotic assistant for laparoscopic surgery , 1995 .

[12]  Charles A. Klein,et al.  Review of pseudoinverse control for use with kinematically redundant manipulators , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[13]  Kenneth H. Hunt,et al.  Special configurations of robot-arms via screw theory , 1986, Robotica.

[14]  D. Stewart,et al.  A Platform with Six Degrees of Freedom , 1965 .

[15]  Kenneth H. Hunt.  Special configurations of robot-arms via screw theory , 1986, Robotica.

[16]  Jean-Pierre Merlet,et al.  Singular Configurations of Parallel Manipulators and Grassmann Geometry , 1988, Int. J. Robotics Res..

[17]  Gerd Hirzinger,et al.  Automatic tracking of laparoscopic instruments by color coding , 1997, CVRMed.

[18]  D. John Sanger,et al.  Redundant grasps, redundant manipulators, and their dual relationships , 1992, J. Field Robotics.