Stiffness analysis of a planar parallel manipulator with variable platforms

Author(s):  
Xiaoyong Wu ◽  
Yujin Wang ◽  
Zhaowei Xiang ◽  
Ran Yan ◽  
Rulong Tan ◽  
...  
2014 ◽  
Vol 592-594 ◽  
pp. 2303-2307
Author(s):  
M. Ganesh ◽  
R. Karthikeyan ◽  
Anjan Kumar Dash ◽  
M. Vikramadityan ◽  
R. Gopalachary

This paper presents a new design of a 3-RRR planar manipulator with non-planar legs. In contrast to the conventional 3-RRR planar parallel mechanism, the links are not planar. They are elevated above the X-Y plane and non planar legs are constructed. The kinematics of this model is realized on a common projected plane and traced back to its elevated position. The moment of inertia for the inclined links is computed. A stiffness model is established for the proposed design of 3-RRR manipulator and compared with a conventional 3-RRR planar manipulator. The analysis shows how the proposed design has better stiffness along all the three directions of motion.


Author(s):  
J Wu ◽  
J-S Wang ◽  
L-P Wang ◽  
T-M Li

The current paper deals with the dexterity and stiffness of a three-degree of freedom (DOF) planar parallel manipulator with actuation redundancy, which is a subpart of a four-DOF-hybrid machine tool. Based on the kinematics, the dexterity is analysed. The stiffness indices, which are the maximum deflection of the moving platform under the action of a unit force and the minimum eigenvalue of the stiffness matrix of the manipulator, are presented for investigating the stiffness. According to the minimum eigenvalue index, it is proved that actuation redundancy can improve the stiffness of the parallel manipulator. Moreover, the relationship between the singular configuration and the stiffness of the parallel manipulator is discussed. Compared with the corresponding non-redundant parallel manipulator without the redundant link, the redundantly actuated parallel manipulator has better dexterity and higher stiffness.


Author(s):  
Guanglei Wu ◽  
Shaoping Bai ◽  
Jørgen A. Kepler

In this paper, the stiffness of 3-PPR planar parallel manipulator (PPM) is analyzed with the consideration of nonlinear actuation compliance. The characteristics of the stiffness matrix pertaining to the planar parallel manipulators are analyzed and discussed. Graphic representation of the stiffness characteristics by means of translational and rotational stiffness mapping is developed. The developed method is illustrated with an unsymmetrical 3-PPR PPM, being compared with its structure-symmetrical counterpart.


Author(s):  
Zhengsheng Chen ◽  
Minxiu Kong

To obtain excellent comprehensive performances of the planar parallel manipulator for the high-speed application, an integrated optimal design method, which integrated dimensional synthesis, motors/reducers selection, and control parameters tuning, is proposed, and the 3RRR parallel manipulator was taken as the example. The kinematic and dynamic performances of condition number, velocity index, acceleration capability, and low-order frequency are taken into accounts for the dimensional synthesis. Then, to match motors/reducers parameters and keep an economical cost, the constraint equations and the parameters library are built, and the cost is chosen as one of the optimization objectives. Also, to get high tracking accuracy, the dynamic forward plus proportional–derivative control scheme is introduced, and the tracking error is chosen as one of the optimization objectives. Hence, the optimization model including dimensional synthesis, motors/reducers selection and controller parameters tuning is established, which is solved by the genetic algorithm II (NSGA-II). The result shows that comprehensive performances can be effectively promoted through the proposed integrated optimal design, and the prototype was constructed according to the Pareto-optimal front.


Author(s):  
Ethan Stump ◽  
Vijay Kumar

While there is extensive literature available on parallel manipulators in general, there has been much less attention given to cable-driven parallel manipulators. In this paper, we address the problem of analyzing the reachable workspace using the tools of semi-definite programming. We build on earlier work [1, 2] done using similar techniques by deriving limiting conditions that allow us to compute analytic expressions for the boundary of the reachable workspace. We illustrate this computation for a planar parallel manipulator with four actuators.


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