Analysis of stiffness and elastic deformation for a four-degree-of-freedom 4SPS + SP parallel manipulator with a SP passive constrained leg

Abstract The total stiffness matrix and elastic deformation of a four-degree-of-freedom (4-dof) four-spherical joint—active prismatic joint—spherical joint plus spherical joint—prismatic joint (4SPS + SP) parallel kinematic machine (PKM) with a passive constrained leg are studied systematically. First, the workspace of this PKM is constructed, and the poses of the active/constrained forces are determined. Second, based on the poses of active/constrained forces, the formulae are derived for solving the kinematics/statics, and some singularities of this PKM are determined. Third, a stiffness matrix of four spherical joint—active prismatic joint—spherical joint (SPS) active legs and one spherical joint—prismatic joint (SP) passive constrained leg is established. Finally, a total stiffness matrix and the elastic deformation of this PKM are solved and analysed based on the kinematics/statics formulae, the stiffness matrix of legs, and the principle of virtual work.

[1]  Chunping Sui.  STATICS AND STIFFNESS STUDY ON A 3-DOF PARALLEL WIRE DRIVEN FLEXIBLE MANIPULATOR , 2006 .

[2]  Z. Huang,et al.  The Singularity Principle and Property of Stewart Parallel Manipulator , 2003, J. Field Robotics.

[3]  Yi Lu,et al.  Analyzing kinematics and solving active/constrained forces of a 3SPU + UPR parallel manipulator , 2007 .

[4]  S J Zhang,et al.  A general method for the stiffness analysis of manipulator mechanisms , 2000 .

[5]  Y. Fang,et al.  Kinematics of a three-degree-of-freedom in-parallel actuated manipulator mechanism☆ , 1997 .

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

[7]  Tian Huang,et al.  Stiffness estimation of a tripod-based parallel kinematic machine , 2002, IEEE Trans. Robotics Autom..

[8]  Y Lu,et al.  A unified method to find active forces and passive wrench of some parallel manipulators with n SPS active legs and a passive leg , 2007 .

[9]  Saeed Behzadipour,et al.  Stiffness of Cable-based Parallel Manipulators With Application to Stability Analysis , 2006 .

[10]  I-Ming Chen,et al.  Stiffness modeling of flexure parallel mechanism , 2005 .

[11]  Dan Zhang,et al.  Stiffness modeling for a class of reconfigurable PKMs with three to five degrees of freedom , 2004 .

[12]  Qingsong Xu,et al.  Stiffness analysis for a 3-PUU parallel kinematic machine , 2008 .

[13]  Yanwen Li.  Study of regularity of general-linear-complex singularity of 3/6-Stewart mechanism , 2003 .

[14]  M. Ceccarelli,et al.  A stiffness analysis for CaPaMan (Cassino Parallel Manipulator) , 2002 .

[15]  Xin-Jun Liu,et al.  On the optimal kinematic design of the PRRRP 2-DoF parallel mechanism , 2006 .

[16]  Shuguang Huang,et al.  Minimal realizations of spatial stiffnesses with parallel or serial mechanisms having concurrent axes , 2001, J. Field Robotics.

[17]  Takashi Suehiro,et al.  Stiffness Analysis and Design of a Compact Modified Delta Parallel Mechanism , 2004, Robotica.

[18]  Marco Ceccarelli,et al.  A stiffness analysis for a hybrid parallel-serial manipulator , 2004, Robotica.

[19]  C. Gosselin,et al.  Kinematic analysis and singularity representation of spatial five‐degree‐of‐freedom parallel mechanisms , 1997 .