Stiffness modeling of a family of 6-DoF parallel mechanisms with three limbs based on screw theory

Abstract

The stiffness modeling of a family of six degrees of freedom (DoF) parallel mechanisms with configurations of 3-RUPU is presented. The mobility of the mechanisms is firstly analyzed, and then the stiffness analysis and modeling of the family of mechanisms is developed by a novel screw-theory based method. The method employs screw theory as a tool for force analysis and deformation analysis. Based on the developed stiffness model, two global flexibility indices, which refer to the maximum and minimum singular values of compliance matrix, are introduced to evaluate the compliance of parallel mechanisms. Finally, a case study is presented to demonstrate the effectiveness of the method in analyzing and evaluating the stiffness behavior of the presented parallel mechanisms.

Design and analysis of a 6-DOF mobile parallel robot with 3 limbs

“…should be adjusted to the equal heights of the points 1 A , 2 A and 3 A , respectively. Based on Eq.…”

“…Based on Eq. (12), the heights of 1 a′ , 2 a′ and 3 a′ of the points 1 A′ , 2 A′ and 3 A′ can be obtained, and the relative height differences can be given as follows: …”

“…Recently, parallel robots have become the focus of intensive research; it is well known that parallel robots have many advantages over traditional serial robots, such as high speed, high stiffness, high load capability, etc. [1][2][3][4][5]. As each limb of a parallel robot is fixed to the base, this will limit the mobility of the robot.…”

“…O x y z − can be obtained by rotating 1 1 1 O x y z − about axis 1 y with an angle β . So 3 3 3 O x y z − can be obtained by rotating 2 2 2 O x y z − about axis 2 z with an angle γ .…”

Compliance analysis of a 3-SPR parallel mechanism with consideration of gravity

“…The difference is that the generalized Jacobian considers the theoretically inaccessible instantaneous motions between the joint space and operation space, which is an important issue in the stiffness and accuracy analysis. Based upon the overall and generalized Jacobians, the stiffness analyses of a number of lower mobility parallel manipulators have been investigated [17][18][19][20][21][22][23][24][25][26]. The advantages of the screw theory based approach is that it enables the Cartesian stiffness matrix to be decomposed into two meaningful components associated respectively with actuations and constraints, providing designers with clear and useful guidelines for taking appropriate measures to improve static performance of the system.…”