Dynamic balancing methodology of planar parallel manipulator using a constrained optimisation procedure

2015 ◽  
Vol 2 (3/4) ◽  
pp. 214
Author(s):  
K.V. Varalakshmi ◽  
J. Srinivas
Robotica ◽  
2004 ◽  
Vol 22 (1) ◽  
pp. 97-108 ◽  
Author(s):  
Gürsel Alıcı ◽  
Bijan Shirinzadeh

This paper deals with an optimum synthesis of planar parallel manipulators using two constrained optimisation procedures based on the minimization of: (i) the overall deviation of the condition number of manipulator Jacobian matrix from the ideal/isotropic condition number, and (ii) bearing forces throughout the manipulator workspace for force balancing. A revolute jointed planar parallel manipulator is used as an example to demonstrate the methodology. The parameters describing the manipulator geometry are obtained from the first optimisation procedure, and subsequently, the mass distribution parameters of the manipulator are determined from the second optimisation procedure based on force balancing. Optimisation results indicate that the proposed optimisation approach is systematic, versatile and easy to implement for the optimum synthesis of the parallel manipulator and other kinematic chains. This work contributes to previously published work from the point of view of being a systematic approach to the optimum synthesis of parallel manipulators, which is currently lacking in the literature.


Author(s):  
Xiaoyong Wu ◽  
Yujin Wang ◽  
Zhaowei Xiang ◽  
Ran Yan ◽  
Rulong Tan ◽  
...  

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.


Author(s):  
S Kemal Ider

In planar parallel robots, limitations occur in the functional workspace because of interference of the legs with each other and because of drive singularities where the actuators lose control of the moving platform and the actuator forces grow without bounds. A 2-RPR (revolute, prismatic, revolute joints) planar parallel manipulator with two legs that minimizes the interference of the mechanical components is considered. Avoidance of the drive singularities is in general not desirable since it reduces the functional workspace. An inverse dynamics algorithm with singularity robustness is formulated allowing full utilization of the workspace. It is shown that if the trajectory is planned to satisfy certain conditions related to the consistency of the dynamic equations, the manipulator can pass through the drive singularities while the actuator forces remain stable. Furthermore, for finding the actuator forces in the vicinity of the singular positions a full rank modification of the dynamic equations is developed. A deployment motion is analysed to illustrate the proposed approach.


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