Solving active wrench of limited-degree of freedom parallel manipulators based on translational/rotational Jacobian matrices

Abstract A methodology is proposed for unified solving active wrench of the limited-degree of freedom (DOF) parallel manipulators (PMs). First, the geometric constraints and the inverse displacement kinematics are analysed. Second, the formulae for unified solving the inverse/forward velocity and the translational/rotational Jacobian matrices and inverse/forward Jacobian matrices are derived. Third, the analytic formulae for unified solving the active wrench of limited-DOF PMs are derived based on the principle of virtual work. Finally, a 3-DOF PM with linear/rotational active legs is presented to illustrate the use of the methodology.

[1]  Bhaskar Dasgupta,et al.  A Newton-Euler Formulation for the Inverse Dynamics of the Stewart Platform Manipulator , 1998 .

[2]  Fengfeng Xi,et al.  Static balancing of parallel robots , 2005 .

[3]  S. Jack Hu,et al.  Dynamic Formulation and Performance Comparison of the 3-DOF Modules of Two Reconfigurable PKM—the Tricept and the TriVariant , 2005 .

[4]  C. Gosselin,et al.  Kinetostatic Modeling of N-DOF Parallel Mechanisms With a Passive Constraining Leg and Prismatic Actuators , 2001 .

[5]  Bodo Heimann,et al.  Computational efficient inverse dynamics of 6-DOF fully parallel manipulators by using the Lagrangian formalism , 2009 .

[6]  Dimitar Chakarov.  Study of the passive compliance of parallel manipulators , 1999 .

[7]  C. Gosselin,et al.  Kinetostatic modeling of parallel mechanisms with a passive constraining leg and revolute actuators , 2002 .

[8]  Yi Lu,et al.  Unification and simplification of velocity/acceleration of limited-dof parallel manipulators with linear active legs , 2008 .

[9]  M. Bergamasco,et al.  Dynamics of parallel manipulators by means of screw theory , 2003 .

[10]  K. Miller,et al.  Optimal kinematic design of spatial parallel manipulators: Application to Linear Delta robot , 2003 .

[11]  Jian S. Dai,et al.  A six-component contact force measurement device based on the Stewart platform , 2000 .

[12]  Y Shi,et al.  Solving reachable workspace of some parallel manipulators by computer-aided design variation geometry , 2008 .

[13]  L. Tsai.  Solving the Inverse Dynamics of a Stewart-Gough Manipulator by the Principle of Virtual Work , 2000 .

[14]  Yi Lu,et al.  Using virtual work theory and CAD functionalities for solving active force and passive force of spatial parallel manipulators , 2007 .

[15]  A. Fattah,et al.  Kinematics and dynamics of a parallel manipulator with a new architecture , 2000, Robotica.

[16]  Bo Hu,et al.  Kinematics/statics analysis of some limited-dof parallel manipulators by a block diagram modelling system , 2008, Int. J. Comput. Aided Eng. Technol..

[17]  L. Tsai,et al.  Jacobian Analysis of Limited-DOF Parallel Manipulators , 2002 .

[18]  B. Shirinzadeh,et al.  Topology optimisation and singularity analysis of a 3-SPS parallel manipulator with a passive constraining spherical joint , 2004 .

[19]  Karol Miller,et al.  Optimal Design and Modeling of Spatial Parallel Manipulators , 2004, Int. J. Robotics Res..