Global Conditioning Index Research Articles

Multi-Objective Optimization of a Three Degree-of-Freedom Translational Parallel Kinematic Machine with Coplanar Rails

Several advancements in the field of parallel manipulators have taken place in recent days as they offer many advantages over serial manipulators in terms of accuracy, agility, stiffness, speed, etc. The Parallel Kinematic Machines (PKMs) with lower Degree of Freedom (DoF) joints are being explored for a variety of industrial applications and, in particular, machining applications as these offer more accuracy, high machining capability, and more stiffness. This research work focuses on the modeling, kinematics, workspace and dexterity analyses of a 3DoF Translational PKM having coplanar rails along the Cartesian axes: -X, +X, +Y. Actuation of sliders, independently along the respective rails, offer the tool platform pure translational motion. Fixed length links are used to connect the sliders and tool platform. The PKM under study is modeled in CATIA. Inverse kinematics and workspace analysis are carried out using the performance indices, namely, Workspace Volume Index (WVI) and Global Condition Index (GCI). Attempts are also made to find the optimal dimensions of the PKM through multi-objective optimization using Genetic Algorithms in MATLAB. The methodology presented is helpful to predict the PKM's performance capability while the results obtained are helpful for the development of a physical prototype necessary for further experimental investigations.

Dimensional Optimization of a Modular Robot Manipulator

The mechanism parameters of the manipulator not only have a great influence on the size of the working space but also affect flexible performance distribution. Aimed at obtaining a 6 DOF modular manipulator, mechanism parameters were optimized in order to explore the effect of upper arm and forearm dimensions on the end dexterity of the manipulator. First, forward kinematic equations were derived using the DH method, and the Jacobian matrix of the manipulator was solved. Second, three indicators, including the condition number index, structural length index, and global conditioning index, were employed as optimization indicators for the mechanism parameters of the manipulator, and an orthogonal experiment was designed based on the Grey–Taguchi method and robot toolbox. Third, the grey relational analysis method was used to process the experimental results, and the grey relational grade for each group was solved. Last, the variation curve between the grey relational grade and the parameter level of each mechanism was drawn, and optimized mechanical arm mechanism parameters were derived. It was found that although the overall dimension of the manipulator was slightly decreased, as determined via comparing the original and optimized manipulator length, the performance indexes were improved. The results not only verified the correctness of the proposed optimization method but also laid a foundation for subsequent research on the dynamic performance of modular robot systems.

Analysis and Optimization of a 6-DoF 3-RRPS Parallel Mechanism for Robot-Assisted Long-Bone Fracture Surgery

Abstract Robot-assisted femur repair has been of increased interest in recent literature due to the success of robot-assisted surgeries and current reoperation rates for femur fracture surgeries. The current limitation of robot-assisted femur fracture surgery is the lack of large force generation and sufficient workspace size in traditional mechanisms. To address these challenges, our group has created a 3-RRPS parallel mechanism, Robossis, which maintains the strength of parallel mechanisms while improving the translational and rotational workspace volume. In this paper, an optimal design methodology of parallel mechanisms for application to robot-assisted femur fracture surgery using a single-objective genetic algorithm is proposed. The genetic algorithm will use a single-objective function to evaluate the various configurations based on the clinical and mechanical design criteria for femur fracture surgery as well as the global conditioning index. The objective function is composed of the desired translational and rotational workspaces based on the design criteria, dynamic load-carrying capacity, and the homogeneous Jacobian global conditioning index. Lastly, experimental results of Robossis were obtained to validate the kinematic solution and the mechanism itself; Robossis had an average error of 0.31 mm during experimental force testing.

Global economic uncertainty and the Chinese stock market: Assessing the impacts of global indicators

We comparatively assess the influence of global economic uncertainty measures on Chinese stock market volatility. Using a model based on generalized autoregressive conditional heteroskedasticity and mixed-data sampling, the results show that the global economic policy uncertainty index, the geopolitical risk index, and the global economic condition index all significantly influence the long-term volatility of China’s equity market. We highlight which of these measures has the most explanatory power under differing contexts. As uncertainty measures have wide applicability, investors, policymakers, and academicians will be quite interested in our results.

Design Optimization of 3-DOF Hybrid Manipulator

Studies related to reachable workspace, inverse kinematics, and best dimensions of 3-DOF Hybrid Manipulator (HM) are presented in this paper. This mechanism possesses both serial and parallel links. A third revolute joint is added in the five-linkage structure having two actuated revolute joints. The third revolute joint is added in such a way that its axis should pass through the axes of the two actuated revolute joints. This produces a structure called a hybrid mechanism consisting of parallel and serial links. The inverse kinematics analysis is implemented for obtaining the joint positions of the HM. The reachable workspace of the manipulator is found using inverse kinematic equations, and finally, the Global Conditioning Index (GCI) is used for optimization to find the optimal dimensions of the HM. The corresponding dimensions obtained based on the optimization by considering maximum GCI as an objective gives the best dimensions that are free from singularities. Here optimization is carried using Genetic Algorithms (GAs).

Global economic conditions index and oil price predictability

The numerous academics rely on exogenous drivers to improve the accuracy of oil price forecasting. This study mainly explores whether a new indicator of global economic conditions proposed by Baumeister et al. (2020) can successfully predict the oil price. Our empirical results reveal that the global economic conditions index can extremely improve the accuracy in forecasting oil price in terms of univariate and bivariate analysis. In addition, compared with 14 traditional macroeconomic variables, global economic conditions index exhibits incremental predictive content in forecasting oil price. The longer forecasting horizons analysis confirms the superior forecasting performance of the global economic condition index for short-term (h = 2 and h = 3). Our findings can provide important implications to market participants in crude oil market.

Kinematic Optimization of 6DOF Serial Robot Arms by Bio-Inspired Algorithms

Robotic systems are essential to technological development in the industrial, medical, and aerospace sectors. Nevertheless, their use in different applications requires that the robot have the best possible execution efficiency. For this, a robot with specific optimized characteristics is necessary to impact the performance of the specific task. Different techniques have been used in robot optimization, the most widely used being genetic algorithms (GA) and particle swarm optimization (PSO). However, there are optimization algorithms with high convergence speeds inspired by animal behavior, whose application in robot optimization has not been reported. In this work, bio-inspired algorithms Harris hawks optimization (HHO) and Grey wolf optimizer (GWO) are applied to a six-degree-of-freedom (6DOF) robot arm design through kinematic optimization. The lengths of the main robot links are optimized to improve the workspace volume and obtain a better-conditioned robot using the structural length index (SLI) and global condition index (GCI) as objective functions. A comparison is made between the proposed algorithms and GA and PSO regarding convergence speed, computational load, and optimality. Similar behavior has been found for HHO, GWO, and PSO compared to GA for both indexes. For the GCI problem, an average improvement of 14% was found when optimizing an industrial robot arm. Furthermore, multiple runs experiment is performed to test the robustness of the algorithms. The results show that HHO is the best technique to obtain an optimal robot design because it needs less than ten iterations to provide a better result despite its computational load.

Sintesis Dimensi Manipulator Paralel Bidang Dua Derajat Kebebasan Dengan Rantai Kinematik Paralelogram Simetris

The paper discussed the process to find the optimum dimension for the kinematic constants of a two-degree of freedom planar parallel manipulator. This manipulator itself was constructed by symmetric three parallelogram chains. An optimization process using non-sorted dominated genetic algorithm II (NSGA-II) was carried out for maximization of ( i ) r MIC (the radius of the maximum inscribed circle) and GCI (global conditioning index), and (ii) r MIC and GTI (global transmission index). Here, GCI and GTI were evaluated on the useful workspace. Instead of using atlases of performance indices, a grid search evaluation was applied to obtain a region in PDS near the optimum values for both maximization cases. This region gave a small bound for NSGA-II to start searching the optimum values of the kinematic constants. For simplification, a python framework for the multi-objective optimization called pymoo was applied to solve the optimization problem. Henceforth, the maximization for two cases yielded an insignificant difference of results in terms of optimum kinematic constants, r MIC , GCI, GTI, area of useful workspace, area of good condition workspace (GCW), area of good transmission workspace (GTW), and the area ratio of GCW and GTW to the useful workspace.

Optimal design of tricept parallel manipulator with particle swarm optimization using performance parameters

The parallel manipulators are skilled for their precision manufacturing but need optimized design to get maximum dexterity that will lead towards better industrial production rates. The 3-DOF tricept is chosen to utilize its maximum capabilities for its functionality. Three performance parameters conditioning index, workspace volume, and global conditioning index are used to obtain optimum design variables of tricept mechanism. With a view to compare them in terms of processing effort, particle swarm optimization (PSO) is applied here. Finally, multiobjective optimization with two strategies weighted and epsilon constraint is performed to control the different parameters simultaneously and also to give validation of previously obtained GA based optimum design values of tricept mechanism.

Effect of Spherical Joint Symmetry Axis Orientation on the Kinematic Performance of Lower Mobility Parallel Manipulators

Parallel manipulators (PMs) are often used as parallel kinematic machines (PKMs), which are more accurate and have more payload capacity compared to their serial counterparts. Spherical joints are frequently used in the construction of PKMs; however, spherical joints have a unique physical constraint, known as cone angle limit, around their axis of symmetry. The present work investigates the effect of changing the orientation of the spherical joint symmetry axis (SJSA) on the kinematic performance of PMs. Workspace index, global conditioning index, kinematic conditioning index and global stiffness index are chosen as performance indices. It is found that changing the orientation of SJSA has a remarkable impact on the kinematic performance of PMs. Also, it is shown that considering the cone angle limits considerably affect the kinematic performance of PMs. To demonstrate the results, two PMs, namely 3-PRS (P, R, and S denote prismatic, revolute, and spherical joints, respectively) and 3-RPS manipulators with spherical joints with adjustable axis of symmetry orientation, are used. The effect of changing SJSA orientation on various performance indices is carried out, and optimal orientation values are determined. Genetic algorithm (GA) optimization technique and traditional method are used. The results obtained using the two methods matched very well. It is found that orientation of the SJSA is one of the important PMs optimization parameters that should be considered during the design process.

Functional Design of a 6-DOF Platform for Micro-Positioning

Parallel kinematic machines (PKMs) have demonstrated their potential in many applications when high stiffness and accuracy are needed, even at micro- and nanoscales. The present paper is focused on the functional design of a parallel platform providing high accuracy and repeatability in full spatial motion. The hexaglide architecture with 6-PSS kinematics was demonstrated as the best solution according to the specifications provided by an important Italian company active in the field of micro-positioning, particularly in vacuum applications. All the steps needed to prove the applicability of such kinematics at the microscale and their inherent advantages are presented. First, the kinematic model of the manipulator based on the study’s parametrization is provided. A global conditioning index (GCI) is proposed in order to optimize the kinetostatic performance of the robot, so that precise positioning in the required platform workspace is guaranteed avoiding singular configurations. Some numerical simulations demonstrate the effectiveness of the study. Finally, some details about the realization of a physical prototype are given.

Diseño cinemático de un robot paralelo 2-PRR

In civil construction Abstract— This paper presents a dimensional synthesis for a 2-PRR planar parallel robot with a structural plane of symmetry. This robot can achieve the translation of the moving platform without changing the orientation, being useful for applications that require controlled positions with high rigidity. Because the performance of parallel robots is highly sensitive to their geometric parameters, many methodologies to state the dimensional synthesis has been developed. We used the method of Parameter - Finiteness Normalization Method (PFNM) to state the dimensional synthesis using Global Condition Index (GCI) and workspace ( ) design atlases. For the two, GCI and , designed atlases, it is not possible to maximize one of the indexes without diminishing the other one, which represents a design compromise. Also, we remark singular configurations that are coming from specific geometry or limit positions. The complete dimensional synthesis is also presented.

Comparison of Pavement Performance Models for Urban Road Management System

The key factors for effective pavement management system (PMS) are timely preservation and rehabilitation activities, which provide benefit in terms of drivers’ safety, comfort, budget and impact on the environment. In order to reasonably plan the preservation and rehabilitation activities, the pavement performance models are used. The pavement performance models are usually based on damage and distress observations of rural roads, and can be applied to forecast the performance of urban roads. However, the adjustment of the parameters related to traffic volume, speed and load, climate conditions, and maintenance has to be made before adding them to PMS for urban roads. The main objective of this study is to identify the performance indicators and to suggest pavement condition establishment methodology of urban roads in Vilnius. To achieve the objective, the distresses (rut depth and cracks), bearing capacity, and international roughness index (IRI) were measured for fifteen urban roads in service within a two-year period. The distresses, rut depth and IRI were collected with the Road Surface Tester (RST) and bearing capacity of pavement structures were measured with a Falling Weight Deflectometer (FWD). The measured distresses were compared to the threshold values identified in the research. According to the measured data, the combined pavement condition indices using two methodologies were determined, as well as a global condition index for each road. The analysed roads were prioritized for maintenance and rehabilitation in respect to these criteria. Based on the research findings, the recommendations for further pavement condition monitoring and pavement performance model implementation to PMS were highlighted.

Integrating Dynamics into Design and Motion Optimization of a 3-PRR Planar Parallel Manipulator with Discrete Time Transfer Matrix Method

This paper presents a novel method of dynamic modeling and design optimization integrated with dynamics for parallel robot manipulators. Firstly, a computationally efficient modeling method, the discrete time transfer matrix method (DT-TMM), is proposed to establish the dynamic model of a 3-PRR planar parallel manipulator (PPM) for the first time. The numerical simulations are performed with both the proposed DT-TMM dynamic modeling and the ADAMS modeling. The applicability and effectiveness of DT-TMM in parallel manipulators are verified by comparing the numerical results. Secondly, the design parameters of the 3-PRR parallel manipulator are optimized using the kinematic performance indices, such as global workspace conditioning index (GWCI), global condition index (GCI), and global gradient index (GGI). Finally, a dynamic performance index, namely, driving force index (DFI), is proposed based on the established dynamic model. The described motion trajectory of the moving platform is placed into the optimized workspace and the initial position is determined to finalize the end-effector trajectory of the parallel manipulator by the further optimization with the integrated kinematic and dynamic performance indices. The novelty of this work includes (1) developing a new dynamic model method with high computation efficiency for parallel robot manipulators using DT-TMM and (2) proposing a new dynamic performance index and integrating the dynamic index into the motion and design optimization of parallel robot manipulators.

Dynamic Performance Optimization of a Novel 8-SPU Parallel Walking Mechanism

Abstract Dynamic performance as one of the important properties of the parallel mechanism cannot be ignored, which is usually illustrated through dynamic performance analysis with the aid of index. Therefore, to develop reasonable dynamic performance indices is of great theoretical and practical significance for the parallel mechanism. In this paper, the above issues are discussed by taking the parallel mechanism designed by our research group as a study object. First, on the basis of considering the driving motor, kinematics dexterity and dynamic dexterity based on the global kinematics condition index and the global dynamic condition index are analyzed, respectively, in the workspace. Second, a novel diagonally dominant index (DDI) is presented in terms of the equivalent inertia parameter in joint space, and the proposed approach gives full consideration to minimize the inter-chain coupling effects. Furthermore, the parallel mechanism is optimized by means of taking the volume of the workspace, the global kinematics condition index, the global dynamic condition index, and the diagonally dominant index as objective functions. The optimization result shows that the larger workspace, higher dexterity, and smaller DDI are obtained to further improve the work capability and dynamic property of the mechanism. Finally, a real and novel 8-SPU (spherical pair, prismatic pair, and universal pair) parallel walking mechanism is manufactured in terms of the optimized architecture parameters.

Unified motion reliability analysis and comparison study of planar parallel manipulators with interval joint clearance variables

Motion reliability is a significant performance index for manipulators with uncertainties. This paper presents a unified motion reliability analysis method for general planar parallel manipulators (PPMs) with interval clearance variables of revolute and prismatic joints. The uncertainties of manufacturing and inputs are also considered and assumed to follow normal distributions. Two typical types of PPMs, 3RRR PPM and 3PRR PPM, are analyzed as examples to demonstrate the effectiveness of the method. For the purpose of a relatively fair comparison, the two PPMs are designed to have the same sizes of base platforms and moving platforms by using a traditional kinematic optimization based on the global conditioning index (GCI). Then, the comparison studies of the two PPMs are made with respect to performance indices of GCI, LCI (local conditioning index) and motion reliability. Furthermore, the index comparison between LCI and motion reliability is also carried out in detail through the two PPMs. The numerical analysis results indicate that: (i) the presented method could achieve a higher confidence estimate compared with the traditional probability method; (ii) the 3PRR PPM exhibits better motion reliability performance than the 3RRR PPM at the same uncertainty levels; and (iii) the traditional optimization based on the GCI cannot guarantee the good motion reliability performance of the PPM. This study provides support for the design and control of PPMs in terms of accuracy and motion reliability.

Design Optimisation of a 6-RSS Parallel Manipulator via Surrogate Modelling

Parallel manipulators are robots with the capability to perform motion up to six degrees of freedom. This work presents a surrogate-based optimisation process for designing a 6-RSS parallel manipulator that is driven by six rotary actuators; the kinematic performance of the manipulator is defined by the volume of the total orientation workspace and the global conditioning index. The surrogate modelling technique was demonstrated by simulation to be highly beneficial in exploring the design landscape thoroughly even for a high-dimensional case with six design variables. Computational expense in the optimisation process was reduced by sequentially searching the surrogate models instead of the original performance indices. One platform geometry with the best compromise between the two contradicting indices was obtained in accordance with the weighted-sum function. Despite the fact that this work considers a small-scale 6-RSS parallel manipulator, the presented surrogate-based optimal design framework is generic and can be applied to different types of manipulators.

SQP Optimization of 6dof 3x3 UPU Parallel Robotic System for Singularity Free and Maximized Reachable Workspace

The determination of kinematic parameters for a parallel robotic system (PRS) is an important and a critical phase to maximize reachable workspace while avoiding singular configurations. Stewart Platform (SP) mechanism is one of the widely known PRS and it is used to demonstrate the proposed technique. In the related literature, GCI (Global Condition Index) and LCI (Local Condition Index) are the commonly used performance indexes which give a measure about the dexterity of a mechanism. In this work, Sequential Quadratic Programming (SQP) method is used to optimize kinematic parameters of a 6dof 3x3 UPU SP in order to reach maximum workspace satisfying small condition numbers. The radius of mobile and base platforms and the lengths of the legs used in the platform are chosen as kinematic parameters to be optimized in a multiobjective optimization problem. Optimization is performed at different stages and the number of optimized kinematic parameters is increased at each level. In conclusion, optimizing selected kinematic parameters at once by using SQP technique presents the best results for the PRS.

Performance-Based Design of the CRS-RRC Schoenflies-Motion Generator

Rigid-body displacements obtained by combining spatial translations and rotations around axes whose direction is fixed in the space are named Shoenflies’ motions. They constitute a 4-dimensional (4-D) subgroup, named Shoenflies’ subgroup, of the 6-D displacement group. Since the set of rotation-axis’ directions is a bi-dimensional space, the set of Shoenflies’ subgroups is a bi-dimensional space, too. Many industrial manipulations (e.g., pick-and-place on a conveyor belt) require displacements that belong to only one Schoenflies’ subgroup and can be accomplished by particular 4-degrees-of-freedom (4-DOF) manipulators (Shoenflies-motion generators (SMGs)). The first author has recently proposed a novel parallel SMG of type CRS-RRC1. Such SMG features a single-loop architecture with actuators on the base and a simple decoupled kinematics. Here, firstly, an organic review of the previous results on this SMG is presented; then, its design is addressed by considering its kinetostatic performances. The adopted design procedure optimizes two objective functions, one (global conditioning index (GCI)) that measures the global performance and the other (CImin) that evaluates the worst local performance in the useful workspace. The results of this optimization procedure are the geometric parameters’ values that make the studied SMG have performances comparable with those of commercial SMGs. In addition, a realistic 3D model that solves all the manufacturing doubts with simple and cheap solutions is presented.

Kinematic performance evaluation of 2-degree-of-freedom parallel mechanism applied in multilayer garage

In this article, our recent work on a kind of 2-degree-of-freedom lower-mobility parallel mechanism, which has one rotation degree of freedom and one translational degree of freedom, used in multilayer garage is presented. It has the following characteristics: lower-mobility, non-symmetric structure but can realize symmetric movement and a good compatibility for different kinds of lifting work. Kinematic performance should be considered in the first of designing a new kind of mechanism, the optimal kinematic design and analysis of this lower-mobility parallel mechanism are primarily investigated. In process of study, the global conditioning index over workspace is adopted, we establish a new evaluation method for the lower-mobility parallel mechanism, called global symmetry index and simulation results are shown. In addition, the flexible workspace of this lower-mobility parallel mechanism is also proposed. The evaluation index can be also applied on other lower-mobility parallel mechanism, which needs steady and symmetric movement.