Kinematic Optimization of a Redundantly Actuated Parallel Mechanism for Maximizing Active Stiffness and Workspace Using Taguchi Method

2009 ◽  
Author(s):  
Hyunpyo Shin ◽  
SungCheul Lee ◽  
Woosung In ◽  
Jay I. Jeong ◽  
Jongwon Kim
Keyword(s):  
Taguchi Method ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Virtual Work ◽  
Optimization Procedure ◽  
Kinematic Parameter ◽  
Response Analysis ◽  
Stiffness Analysis ◽  
Redundantly Actuated ◽  
The Relationship

We present an optimization procedure that uses the Taguchi method to optimize the mean stiffness and workspace of a redundantly actuated parallel mechanism. The kinematic parameters of a planar 2-DOF parallel manipulator are optimized to maximize the manipulator’s workspace and mean stiffness at the same time. Kinematic analysis is performed to obtain a constraint Jacobian and forward Jacobian. And stiffness analysis of the redundantly actuated parallel manipulator is performed based on the virtual work theorem. The Taguchi method is applied to separate the more influential and controllable variables from the less influential ones in the optimization procedure. In the first stage of optimization, the number of experimental variables is reduced by response analysis. And after the response analysis, quasi-optimal kinematic parameter group is obtained in the second stage of optimization. The optimization procedure was used to investigate the optimal kinematic parameter groups and the relationship between the length and the stiffness of the link.

Kinematic Optimization of a Redundantly Actuated Parallel Mechanism for Maximizing Stiffness and Workspace Using Taguchi Method

2010 ◽  
Vol 6 (1) ◽  
Author(s):  
Hyunpyo Shin ◽  
Sungchul Lee ◽  
Woosung In ◽  
Jay I. Jeong ◽  
Jongwon Kim
Keyword(s):  
Taguchi Method ◽  
Parallel Mechanism ◽  
Optimization Procedure ◽  
Kinematic Parameter ◽  
Response Analysis ◽  
Kinematic Parameters ◽  
Stiffness Analysis ◽  
Second Stage ◽  
Workspace Analysis ◽  
Redundantly Actuated

We present an optimization procedure that uses the Taguchi method to maximize the mean stiffness and workspace of a redundantly actuated parallel mechanism at the same time. The Taguchi method is used to separate the more influential and controllable variables from the less influential ones among kinematic parameters in workspace analysis and stiffness analysis. In the first stage of optimization, the number of experimental variables is reduced by the response analysis. Quasi-optimal kinematic parameter group is obtained in the second stage of optimization after the response analysis. As a validation of the suggested procedure, the kinematic parameters of a planar 2-DOF parallel manipulator are optimized, which optimization procedure is used to investigate the optimal kinematic parameter groups between the length of the link and the stiffness.

Optimal dimensioning of redundantly actuated mechanism for maximizing energy efficiency and workspace via Taguchi method

2016 ◽  
Vol 231 (2) ◽  
pp. 326-340 ◽  
Author(s):  
Sumin Park ◽  
Jehyeok Kim ◽  
Jay I Jeong ◽  
Jongwon Kim ◽  
Giuk Lee
Keyword(s):  
Energy Efficiency ◽  
Taguchi Method ◽  
Performance Index ◽  
Parallel Mechanism ◽  
Response Analysis ◽  
Parallel Mechanisms ◽  
End Effector ◽  
Controllable Factors ◽  
Redundantly Actuated ◽  
A Chain

A kinematic optimization of a redundantly actuated parallel mechanism is developed via the Taguchi method to maximize the sum of energy efficiency and workspace. In the optimization process, the energy consumption in a representative pathway of a predefined workspace is used as the performance index of the energy efficiency. The horizontal reach and stroke, and the vertical reach of mechanism, are used for the performance index of the workspace. The kinematic parameters of a chain that was added to the proposed non-redundantly actuated parallel mechanism as an extension to achieve redundant actuation are selected as the controllable factors. The velocity of the end-effector is considered to be a noise factor. Because the Taguchi method was originally used for robust optimization, we can improve the energy efficiency and workspace under various velocities for the end-effector. In the first stage of optimization, the number of controllable factors is reduced, and their correlations are eliminated using a response analysis. Quasi-optimized results are derived after the second stage of optimization. The optimized redundantly actuated parallel mechanism result is validated by comparing the energy efficiencies and workspaces of the original and optimal redundantly actuated parallel mechanisms.

Kineto Static Design and Stiffness Analysis of a New Kind of 3-RRR Planar Parallel Manipulator

2014 ◽  
Vol 592-594 ◽  
pp. 2303-2307
Author(s):  
M. Ganesh ◽  
R. Karthikeyan ◽  
Anjan Kumar Dash ◽  
M. Vikramadityan ◽  
R. Gopalachary
Keyword(s):  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Moment Of Inertia ◽  
Stiffness Analysis ◽  
Stiffness Model ◽  
Planar Parallel Manipulator ◽  
The Moment

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.

Static Stiffness Analysis of a Novel Parallel Manipulator

2012 ◽  
Vol 522 ◽  
pp. 703-707
Author(s):  
Yun Feng Li ◽  
Chang Feng Li ◽  
Dong Sheng Qu ◽  
Ling Zou
Keyword(s):  
Parallel Manipulator ◽  
Virtual Work ◽  
Elastic Model ◽  
Static Stiffness ◽  
Single Chain ◽  
Stiffness Analysis ◽  
Stiffness Properties ◽  
Maximum Stiffness ◽  
Stiffness Model ◽  
Spatial Architecture

One novel 6-DOF parallel manipulator with hooke hinges is presented to provide precision positioning in this paper. The geometric parameters and spatial architecture of kinematic pairs will influence the system stiffness directly, which impact indirectly the characteristics such as supporting capacity, driving burden and so on. The elastic model of the single chain based on the stiffness equation is presented and the stiffness model of the whole structure is constructed via the principle of virtual work. The static stiffness properties of the manipulator are discussed and the problem of finding the minimum and maximum stiffness and the directions in which they occur for a manipulator in a given posture is addressed. An example is given and the results show that static stiffness properties can be used to guide the optimal design of the structure.

Geometry and Kinematic Analysis of a Redundantly Actuated Parallel Mechanism for Rehabilitation

2007 ◽  
Author(s):  
Jody A. Saglia ◽  
Jian S. Dai
Keyword(s):  
Control System ◽  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Forward Kinematics ◽  
Control System Design ◽  
Ankle Rehabilitation ◽  
Redundantly Actuated ◽  
Moving Platform

This paper presents the geometry and the kinematic analysis of a parallel manipulator developed for ankle rehabilitation, as the beginning of a control system design process. First the geometry of the parallel mechanism is described, secondly the equations for the inverse and the forward kinematics are obtained, then the forward kinematics is analyzed in order to define all the possible configurations of the moving platform. Finally the Jacobian matrix of the rig is obtained by differentiating the position equations and the singularities are investigated, comparing the non-redundant and redundant type of mechanism.

Stiffness modelling and comparison of the 5-UPS/PRPU parallel machine tool with its non-redundant counterpart

2016 ◽  
Vol 231 (9) ◽  
pp. 1646-1657 ◽  
Author(s):  
Xin Zhou ◽  
Yundou Xu ◽  
Jiantao Yao ◽  
Kuijing Zheng ◽  
Yongsheng Zhao
Keyword(s):  
Machine Tool ◽  
Stiffness Matrix ◽  
Parallel Mechanism ◽  
Screw Theory ◽  
Virtual Work ◽  
Matrix Decomposition ◽  
Parallel Machine ◽  
Stiffness Model ◽  
Redundantly Actuated ◽  
Parallel Machine Tool

This article presents a derivation of the stiffness matrix of a general redundantly actuated parallel mechanism based on the overall Jacobian. The Jacobian of the constraints and actuations is derived using reciprocal screw theory. Based on the mapping relationship between constraint, actuated and external forces combined with the principle of virtual work, a compatibility equation for the deformation of all of the limbs is achieved, and the stiffness model of the general redundantly actuated parallel mechanism is derived. The 5-UPS/PRPU redundantly actuated parallel machine tool is used to illustrate this method. The parallel machine tool comprehensively reveals the effect of the elastic deformation of active–passive joints and some basic transmission parts. The stiffness model is further validated by experimental data. Moreover, the global stiffness matrix of the general redundantly actuated parallel mechanism can be separated into two parts via matrix decomposition. The first part is the stiffness matrix of the corresponding non-redundant parallel mechanism, and the second part is the stiffness matrix of the redundantly actuated limbs (actuators). The redundantly actuated 5-UPS/PRPU parallel machine tool is also investigated for further analysis. The different stiffness characteristics of the machine tool and its corresponding non-redundant 5-UPS/PRPU parallel machine tool are compared. Actuation redundancy is found to improve the stiffness performance of the machine tool efficiently.

Optimal trajectory planning considering optimal torque distribution of redundantly actuated parallel mechanism

2018 ◽  
Vol 232 (23) ◽  
pp. 4410-4419 ◽  
Author(s):  
Sumin Park ◽  
Jongwon Kim ◽  
Giuk Lee
Keyword(s):  
Parallel Mechanism ◽  
Optimization Procedure ◽  
Optimal Operation ◽  
Operation Planning ◽  
Parallel Mechanisms ◽  
Planning Stage ◽  
End Effector ◽  
Torque Distribution ◽  
Redundantly Actuated ◽  
Two Stages

Previous studies on the optimal operation planning of redundantly actuated parallel mechanisms have focused on optimal torque distribution for a predefined trajectory. However, the optimized result obtained for a predefined trajectory cannot guarantee an optimal operation plan, because the torque distribution ability of a redundantly actuated parallel mechanism is highly dependent on the shape of the end-effector trajectory. Therefore, we can expect the redundantly actuated parallel mechanism performance to be enhanced when both the trajectory and torque distribution are optimized during the optimal operation planning stage. We propose a novel redundantly actuated parallel mechanism optimization procedure that can optimize both the end-effector trajectory and torque distribution. The proposed procedure is composed of two stages of optimizers, i.e. upper- and lower-level optimizers that generate the end-effector trajectory and distribute the torques along the generated trajectory, respectively. Composition of these two stages of the optimization procedure allows optimization of both the trajectory and torque distribution, despite the correlation between them. The proposed optimization procedure is simulated using two types of cost functions. All the simulation results show that the proposed procedure facilitates optimization of the end-effector trajectory and the torque distribution concurrently. Also, the cost function value is minimized to a greater extent than in the result with the optimal torque distribution along the initial trajectory.

scholarly journals Kinematics Performance and Dynamics Analysis of a Novel Parallel Perfusion Manipulator with Passive Link

2018 ◽  
Vol 2018 ◽  
pp. 1-18 ◽  
Author(s):  
Hui Yang ◽  
Hairong Fang ◽  
Yuefa Fang ◽  
Haibo Qu
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Thermal Protection ◽  
Virtual Work ◽  
Kinematics And Dynamics ◽  
Main Body ◽  
Perfusion System ◽  
Dynamics Models ◽  
The Relationship

In order to solve the problem of the honeycombs perfusion in the thermal protection system of the spacecraft, this paper presents a novel parallel perfusion manipulator with one translational and two rotational (1T2R) degrees of freedom (DOFs), which can be used to construct a 5-DOF hybrid perfusion system for the perfusion of the honeycombs. The proposed 3PSS&PU parallel perfusion manipulator is mainly utilized as the main body of the hybrid perfusion system. The inverse kinematics and the Jacobian matrix of the proposed parallel manipulator are obtained. The analysis of kinematics performance for the proposed parallel manipulator including workspace, singularity, dexterity, and stiffness is conducted. Based on the virtual work principle and the link Jacobian matrix, the dynamic model of the parallel perfusion manipulator is carried out. With reference to dynamic equations, the relationship between the driving force and the mechanism parameters can be derived. In order to verify the correctness of the kinematics and dynamics model, the comparison of theoretical and simulation curves of the motion parameters related to the driving sliders is performed. Corresponding analyses illustrate that the proposed parallel perfusion possesses good kinematics performance and could satisfy the perfusion requirements of the honeycombs. The correctness of the established kinematics and dynamics models is proved, which has great significance for the experimental research of the perfusion system.

Workspace and singularity analysis of a 3-DOF planar parallel manipulator with actuation redundancy

Robotica ◽  
2009 ◽  
Vol 27 (1) ◽  
pp. 51-57 ◽  
Author(s):  
Jinsong Wang ◽  
Jun Wu ◽  
Tiemin Li ◽  
Xinjun Liu
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Actuation Redundancy ◽  
Hybrid Machine Tool ◽  
Planar Parallel Manipulator ◽  
Redundantly Actuated ◽  
Value Decomposition ◽  
The Relationship ◽  
Orientation Workspace

SUMMARYThis paper deals with the position workspace, orientation workspace, and singularity of a 3-degree-of-freedom (DOF) planar parallel manipulator with actuation redundancy, which is created by introducing a redundant link with active actuator to a 3-DOF nonredundant parallel manipulator. Based on the kinematic analysis, the position workspace and orientation workspace of the redundantly actuated parallel manipulator and its corresponding nonredundant parallel manipulator are analyzed, respectively. In the singularity analysis phase, the relationship between the generalized input velocity and the generalized output velocity is researched on the basis of the theory of singular value decomposition. Then a method to investigate the singularity of parallel manipulators is presented, which is used to determine the singularity of the redundantly actuated parallel manipulator. In contrast to the corresponding nonredundant parallel manipulator, the redundant one has larger orientation workspace and less singular configurations. The redundantly actuated parallel manipulator is incorporated into a 4-DOF hybrid machine tool which also includes a feed worktable to demonstrate its applicability.

Kinematic Calibration for Redundantly Actuated Parallel Mechanisms: Theory and Application for 2-DOF Mechanism

2004 ◽  
Author(s):  
Jay il Jeong ◽  
Dongsoo Kang ◽  
Jongwon Kim
Keyword(s):  
Optimization Algorithm ◽  
Parallel Mechanism ◽  
Kinematic Calibration ◽  
Parallel Mechanisms ◽  
Angle Error ◽  
Calibration Algorithm ◽  
Redundantly Actuated ◽  
Relationship Of ◽  
The Relationship

We present a new kinematic calibration algorithm for redundantly actuated parallel mechanisms. The calibration algorithm for a non-redundant case does not apply for a redundantly actuated parallel mechanism, because the angle error of the actuating joint varies with position and the geometrical constraint fails to be consistent. Such change of joint angle error comes from constraint torque variation with each kinematic pose. To calibrate a redundant parallel mechanism, one therefore has to consider constraint torque equilibrium and the relationship of constraint torque to torsional deflection, in addition to geometric constraint. In this paper, we develop the calibration algorithm for a redundantly actuated parallel mechanism using these three relationships, and formulate cost functions for an optimization algorithm. As a case study, we executed the calibration of a 2-degree of freedom (DOF) parallel mechanism with three actuators using the developed algorithm. Coordinate values of tool plate were measured using a laser ball bar and the actual kinematic parameters were identified with a new cost function of the optimization algorithm. Experimental results showed that the accuracy of the tool plate improved by 82% after kinematic calibration in a redundant actuation case.

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