scholarly journals Calibration Method for a Parallel Mechanism Type Machine Tool by Response Surface Methodology –Consideration via Simulation on a Stewart Platform Mechanism–

2010 ◽  
Vol 4 (4) ◽  
pp. 355-363 ◽  
Author(s):  
Hiroshi Yachi ◽  
◽  
Hiroshi Tachiya
Keyword(s):  
Response Surface Methodology ◽  
Response Surface ◽  
Parallel Mechanism ◽  
Measurement Data ◽  
Calibration Method ◽  
Stewart Platform ◽  
Parallel Mechanisms ◽  
Data Set ◽  
Efficient Data ◽  
Efficient Measurement

This paper proposes a calibration method for parallel mechanisms usingResponse Surface Methodology. This method is a statistical approach to estimating an unknown input-output relationship using a small set of efficient data collected on an intended system. Although identifying locations causing positional errors in a parallel mechanism and precisely measuring the position and posture of the output point are difficult, the proposed calibration method based onResponse Surface Methodologyaims to compensate for positional and postural errors, without indentifying the locations causing these errors, by using a small yet efficient measurement data set. This study analyzes the effectiveness of the method we propose by applying it to a Stewart platform, which is a typical spatial 6-DOF parallel mechanism.

scholarly journals Sensitivity Analysis of Reliability of Low-Mobility Parallel Mechanisms Based on a Response Surface Method

2021 ◽  
Vol 11 (19) ◽  
pp. 9002
Author(s):  
Qiang Yang ◽  
Hongkun Ma ◽  
Jiaocheng Ma ◽  
Zhili Sun ◽  
Cuiling Li
Keyword(s):  
Sensitivity Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Error Component ◽  
Parallel Mechanisms ◽  
Kinematic Accuracy ◽  
Surface Method ◽  
Input Error

Kinematic accuracy is a crucial indicator for evaluating the performance of mechanisms. Low-mobility parallel mechanisms are examples of parallel robots that have been successfully employed in many industrial fields. Previous studies analyzing the kinematic accuracy analysis of parallel mechanisms typically ignore the randomness of each component of input error, leading to imprecise conclusions. In this paper, we use homogeneous transforms to develop the inverse kinematics models of an improved Delta parallel mechanism. Based on the inverse kinematics and the first-order Taylor approximation, a model is presented considering errors from the kinematic parameters describing the mechanism’s geometry, clearance errors associated with revolute joints and driving errors associated with actuators. The response surface method is employed to build an explicit limit state function for describing position errors of the end-effector in the combined direction. As a result, a mathematical model of kinematic reliability of the improved Delta mechanism is derived considering the randomness of every input error component. And then, reliability sensitivity of the improved Delta parallel mechanism is analyzed, and the influences of the randomness of each input error component on the kinematic reliability of the mechanism are quantitatively calculated. The kinematic reliability and proposed sensitivity analysis provide a theoretical reference for the synthesis and optimum design of parallel mechanisms for kinematic accuracy.

scholarly journals Collision-free workspace of parallel mechanisms based on an interval analysis approach

Robotica ◽  
2016 ◽  
Vol 35 (8) ◽  
pp. 1747-1760 ◽  
Author(s):  
MohammadHadi FarzanehKaloorazi ◽  
Mehdi Tale Masouleh ◽  
Stéphane Caro
Keyword(s):  
Interval Analysis ◽  
Parallel Mechanism ◽  
Spherical Shape ◽  
Stewart Platform ◽  
Analysis Approach ◽  
Parallel Mechanisms ◽  
Planar Case ◽  
End Effector ◽  
Mechanical Interference

SUMMARYThis paper proposes an interval-based approach in order to obtain the obstacle-free workspace of parallel mechanisms containing one prismatic actuated joint per limb, which connects the base to the end-effector. This approach is represented through two cases studies, namely a 3-RPR planar parallel mechanism and the so-called 6-DOF Gough–Stewart platform. Three main features of the obstacle-free workspace are taken into account: mechanical stroke of actuators, collision between limbs and obstacles and limb interference. In this paper, a circle(planar case)/spherical(spatial case) shaped obstacle is considered and its mechanical interference with limbs and edges of the end-effector is analyzed. It should be noted that considering a circle/spherical shape would not degrade the generality of the problem, since any kind of obstacle could be replaced by its circumscribed circle/sphere. Two illustrative examples are given to highlight the contributions of the paper.

The Maximal Singularity-Free Workspace of the Gough–Stewart Platform for a Given Orientation

2008 ◽  
Vol 130 (11) ◽  
Author(s):  
Qimi Jiang ◽  
Clément M. Gosselin
Keyword(s):  
Case Studies ◽  
Parallel Mechanism ◽  
Stewart Platform ◽  
Parallel Robots ◽  
Analytic Method ◽  
Robot Design ◽  
Parallel Mechanisms ◽  
Leg Length ◽  
Maximal Singularity ◽  
The Relationship

The maximal singularity-free workspace of parallel mechanisms is a desirable criterion in robot design. However, for a 6DOF parallel mechanism, it is very difficult to find an analytic method to determine the maximal singularity-free workspace around a prescribed point for a given orientation. Hence, a numerical algorithm is presented in this paper to compute the maximal singularity-free workspace as well as the corresponding leg length ranges of the Gough–Stewart platform. This algorithm is based on the relationship between the maximal singularity-free workspace and the singularity surface. Case studies with different orientations are performed to demonstrate the presented algorithm. The obtained results can be applied to the geometric design or parameter (leg length) setup of this type of parallel robots.

The Realization of Desired Stiffness of Parallel Mechanism by Adding Redundantly-Actuated Limbs

2017 ◽  
Author(s):  
Shunzhou Huang ◽  
Jue Yu ◽  
Hao Wang ◽  
Yong Zhao ◽  
Xinmin Lai
Keyword(s):  
Parallel Mechanism ◽  
Parallel Manipulators ◽  
Stewart Platform ◽  
Industrial Applications ◽  
Parallel Mechanisms ◽  
Normal Stiffness ◽  
Stiffness Properties ◽  
Mirror Milling ◽  
Redundantly Actuated ◽  
Mapping Models

Stiffness performance is of importance for the use of parallel manipulators in the industrial applications. For this consideration, this paper proposes to realize the desired stiffness properties of parallel mechanism by adding redundantly-actuated limbs. Based on the stiffness mapping models of both the full-DOF and limited-DOF parallel mechanisms, the stiffness variation rules when redundant limbs is introduced into the mechanism are discussed. Moreover, an algorithm for designing the types and configurations of redundant limbs is studied. Two cases are investigated to validate the presented approach. One is about the stiffness decoupling of the Stewart platform, the other is focused on the enhancement of normal stiffness of a Tricept supporting mechanism used in a mirror milling machine designed by us. The result shows that the stiffness performance of Stewart platform can be decoupled when adding six redundantly-actuated limbs that are symmetric with the original active limbs. Besides, the normal stiffness of Tricept mechanism can be enhanced significantly by transforming the passive UP chain to be a redundant actuated chain.

Decolorization of reactive dye Remazol Brilliant Blue R by zirconium oxychloride as a novel coagulant: optimization through response surface methodology

2018 ◽  
Vol 78 (2) ◽  
pp. 379-389 ◽  
Author(s):  
Sonalika Sonal ◽  
Astha Singh ◽  
Brijesh Kumar Mishra
Keyword(s):  
Response Surface Methodology ◽  
Response Surface ◽  
Oxygen Demand ◽  
Zirconium Oxychloride ◽  
Reactive Dye ◽  
Cod Removal ◽  
Interactive Effects ◽  
Data Set ◽  
Operational Variables ◽  
The Individual

Abstract The aim of the present study was to investigate the performance of a novel coagulant, i.e. ZrOCl2, for the removal of anthraquinone-based reactive dye from aqueous solution. An ideal experimental setup was designed based on central composite design using response surface methodology to determine the individual and interactive effects of different operational variables (i.e. pH, coagulant dose and dye concentration) on treatment performance in terms of dye and chemical oxygen demand (COD) removal efficiencies. Total 92.58% dye and 85.33% COD removal were experimentally attained at optimized conditions at low coagulant dose, i.e. 156.67 mg/L for the dye concentration of 105.67 mg/L at pH 2. To validate the working pH of the metal coagulant, the static charge of ZrOCl2 was measured using Eh value. The performance of the coagulant was validated with experimental and predicted values in the selected data set, and R2 values for both responses were found to be 0.99 and 0.95 respectively, which shows the reliability of the experimental design. Further, the toxicity of the coagulant was assessed and no such toxicity was found even up to the concentration of 500 mg/L, proclaiming the disposal of sludge may not exhibit any threat to humans. Experimental results suggested that the ZrOCl2 could be used as an eco-friendly coagulant for dye wastewater treatment.

A Study on Regression Model Using Response Surface Methodology

2014 ◽  
Vol 666 ◽  
pp. 235-239 ◽  
Author(s):  
Ahmad Nooraziah ◽  
V. Janahiraman Tiagrajah
Keyword(s):  
Response Surface Methodology ◽  
Regression Model ◽  
Response Surface ◽  
Polynomial Equation ◽  
Second Order ◽  
Statistical Regression ◽  
Data Set ◽  
Best Response ◽  
Statistical Regression Method ◽  
The Given

Response Surface Methodology (RSM) mostly employs statistical regression method as it is practical, economical and relatively easy to use. The first and second order polynomial equation was developed using RSM. This polynomial model usually refers as a regression model. In this research, the objective is to find the best response surface method to model three factors and three levels parameters in machining. From the study, the Box-Behnken Design can develop a good regression model rather than Central Composite Design or Full Factorial Design. While, the second order regression model has proved to be more effective in predicting the performance of the given data set.

Closed-Form Direct Position Analysis of a 5–5 Parallel Mechanism

1993 ◽  
Vol 115 (3) ◽  
pp. 515-521 ◽  
Author(s):  
C. Innocenti ◽  
V. Parenti-Castelli
Keyword(s):  
Closed Form ◽  
Parallel Mechanism ◽  
General Feature ◽  
Polynomial Equation ◽  
Stewart Platform ◽  
Parallel Mechanisms ◽  
Complex Field ◽  
Output Link ◽  
Degree Polynomial ◽  
Displacement Analysis

The paper presents the closed form direct displacement analysis for a class of Stewart platform-type parallel mechanisms whose general feature consists of six legs which meet five distinct points both in the base and in the movable output link. Out of the two possible arrangements, only one is here analyzed in detail. Given a set of actuator displacements the analysis provides all the possible locations of the platform relative to the base. The analysis results in a 40th degree polynomial equation in one unknown. The roots of the equation provide in the complex field forty closures of the mechanism. This new result has been numerically verified by the inverse displacement analysis.

Sign in / Sign up

Export Citation Format

Share Document