Reciprocity-Based Singular Value Decomposition for Inverse Kinematic Analysis of the Metamorphic Multifingered Hand

With a new type of multifingered hand that raises a new philosophy in the construction and study of a multifingered hand, this paper is a follow-on study of the kinematics of the metamorphic multifingered robotic hand by proposing the finger-constraint equations. The finger-constraint equations lead to a comprehensive mathematical model of the hand with a reconfigurable palm which integrates all finger motions with the additional palm motion. Singular values of the partitioned Jacobian matrix in their analytical form are derived and applied to obtaining analytical solution to inverse kinematics of a complete robotic hand. The paper for the first time solves this integrated motion and the multifingered hand model with the singular value decomposition and extra degrees of freedom are examined with the singular value analysis to avoid the singularities. The work identifies finger displacement and velocity with effect from the articulated palm and presents a new way of analyzing a multifingered robotic hand.

[1]  Juan A. Carretero,et al.  Overall Motion Planning for Kinematically Redundant Parallel Manipulators , 2012 .

[2]  Charles L. Lawson,et al.  Solving least squares problems , 1976, Classics in applied mathematics.

[3]  Clément Gosselin,et al.  Conceptual Design and Static Analysis of Novel Planar Spring-Loaded Cable-Loop-Driven Parallel Mechanisms , 2012 .

[4]  Ian D. Walker,et al.  Minimum effort inverse kinematics for redundant manipulators , 1997, IEEE Trans. Robotics Autom..

[5]  Scott B. Nokleby,et al.  Reciprocity-based resolution of velocity degeneracies (singularities) for redundant manipulators , 2001 .

[6]  Kazuhiro Kosuge,et al.  Analytical Inverse Kinematic Computation for 7-DOF Redundant Manipulators With Joint Limits and Its Application to Redundancy Resolution , 2008, IEEE Transactions on Robotics.

[7]  Clément Gosselin,et al.  Forward Displacement Analysis of a Linearly Actuated Quadratic Spherical Parallel Manipulator , 2010 .

[8]  Jian S. Dai,et al.  Editorial preface in Reconfigurable Mechanisms and Robots , 2009 .

[9]  J. Dai,et al.  Mobility in Metamorphic Mechanisms of Foldable/Erectable Kinds , 1998 .

[10]  Ashitava Ghosal,et al.  A New Approach for Kinematic Resolution of Redundancy , 1988, Int. J. Robotics Res..

[11]  Jian S. Dai,et al.  Posture, Workspace, and Manipulability of the Metamorphic Multifingered Hand With an Articulated Palm , 2011 .

[12]  J. Dai,et al.  Actuation schemes of a spatial 3-PPRR parallel mechanism , 2012 .

[13]  Jian S. Dai,et al.  Structure Synthesis of Single-Driven Metamorphic Mechanisms Based on the Augmented Assur Groups , 2012 .

[14]  Q. Ge,et al.  Interactive Dimensional Synthesis and Motion Design of Planar 6R Single-Loop Closed Chains via Constraint Manifold Modification , 2010 .

[15]  Andrew A. Goldenberg,et al.  A Null-Space Solution of the Inverse Kinematics of Redundant Manipulators Based on a Decomposition of Screws , 1993 .

[16]  Sunil K. Agrawal,et al.  On the Design of Adaptive Cable-Driven Systems , 2011 .

[17]  Jian S. Dai,et al.  Orientation and Workspace Analysis of the Multifingered Metamorphic Hand—Metahand , 2009, IEEE Transactions on Robotics.

[18]  Philippe Cardou,et al.  Classifying the Boundaries of the Wrench-Closure Workspace of Planar Parallel Cable-Driven Mechanisms by Visual Inspection , 2012 .

[19]  Jian S. Dai,et al.  A Darboux-Frame-Based Formulation of Spin-Rolling Motion of Rigid Objects With Point Contact , 2010, IEEE Transactions on Robotics.

[20]  Kamal K. Gupta,et al.  The kinematic roadmap: a motion planning based global approach for inverse kinematics of redundant robots , 1999, IEEE Trans. Robotics Autom..

[21]  Joseph Duffy,et al.  Kinestatic Analysis of Multifingered Hands , 1990, Int. J. Robotics Res..

[22]  Maurizio Ruggiu.  Kinematic and Dynamic Analysis of a Two-Degree-of-Freedom Spherical Wrist , 2010 .

[23]  Jian S. Dai,et al.  Inverse-kinematics-based control of a redundantly actuated platform for rehabilitation , 2009 .

[24]  Manja V. Kircanski,et al.  Symbolic Singular Value Decomposition for Simple Redundant Manipulators and Its Application to Robot Control , 1995, Int. J. Robotics Res..

[25]  Myung Jin Chung,et al.  Evaluation of dexterity measures for a 3-link planar redundant manipulator using constraint locus , 1995, IEEE Trans. Robotics Autom..

[26]  J. R. Jones,et al.  Null–space construction using cofactors from a screw–algebra context , 2002, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[27]  Jian S. Dai,et al.  Geometry and Constraint Analysis of the Three-Spherical Kinematic Chain Based Parallel Mechanism , 2010 .

[28]  K. H. Hunt.  Robot Kinematics—A Compact Analytic Inverse Solution for Velocities , 1987 .

[29]  Jian S. Dai,et al.  Topology and Constraint Analysis of Phase Change in the Metamorphic Chain and Its Evolved Mechanism , 2010 .

[31]  Jian S. Dai,et al.  Interrelationship between screw systems and corresponding reciprocal systems and applications , 2001 .

[32]  Jonghoon Park,et al.  Characteristics of optimal solutions in kinematic resolutions of redundancy , 1996, IEEE Trans. Robotics Autom..

[33]  Bernard Roth,et al.  Analysis of Multifingered Hands , 1986 .

[34]  Jian S. Dai,et al.  Axis Constraint Analysis and Its Resultant 6R Double-Centered Overconstrained Mechanisms , 2011 .

[35]  Nikolaos G. Tsagarakis,et al.  A High-performance Redundantly Actuated Parallel Mechanism for Ankle Rehabilitation , 2009, Int. J. Robotics Res..

[36]  Charles A. Klein,et al.  A new formulation of the extended Jacobian method and its use in mapping algorithmic singularities for kinematically redundant manipulators , 1995, IEEE Trans. Robotics Autom..

[37]  Scott B. Nokleby,et al.  Identifying multi-DOF-loss velocity degeneracies in kinematically-redundant manipulators , 2004 .

[38]  D. Nenchev.  Restricted Jacobian Matrices of Redundant Manipulators in Constrained Motion Tasks , 1992 .

[39]  J. Michael McCarthy,et al.  21st Century Kinematics: Synthesis, Compliance, and Tensegrity , 2011 .

[40]  Larry L. Howell,et al.  A Pseudo-Rigid-Body Model of the Human Spine to Predict Implant-Induced Changes on Motion , 2011 .

[41]  Ian A. Gravagne,et al.  On the structure of minimum effort solutions with application to kinematic redundancy resolution , 2000, IEEE Trans. Robotics Autom..