Robust optimization of constrained mechanical system with joint clearance and random parameters using multi-objective particle swarm optimization

Joint clearance and uncertainty are inevitable in mechanical systems due to design tolerance, abrasion, manufacture error, assembly error and imperfections. In this study, kinematic analysis and robust optimization of constrained mechanical systems with joint clearance and random parameters were performed. Joint clearance was modeled by Lankarani-Nikravesh contact force model, and probability space was applied for characterizing uncertain parameters. A kinematic analysis method based on Baumgarte approach and confidence region method was presented to predict kinematic error of the mechanical system. Slider-crank mechanism, an illustrative example was presented to show the influence of clearance and uncertainty on the kinematic accuracy. Then, a novel multi-objective robust optimization methodology was presented for kinematic accuracy robust optimization design of the constrained mechanical system. In this approach, a multi-objective robust optimization model derived from 95% confidence region is constructed to reduce the effects of clearance and parameter uncertainty on 95% confidence region of kinematic error. The robust optimization model is a double-loop process. A multi-objective robust optimization strategy, combing Kriging surrogate model, multi-objective particle swarm optimization, confidence region and Monte Carlo methods, was proposed to search the design variables for minimizing the optimization objectives derived from confidence region while balancing computational accuracy and efficiency of the optimization process. The optimal results of the slider-crank mechanism demonstrated the validity and feasibility of the proposed robust optimization method.     

Natural coordinates for the computer analysis of multibody systems

In this paper we will describe a new method for the computer kinematic and dynamic analysis of a wide range of three-dimensional mechanisms or multibody systems. This method is based on a new system of non-independent coordinates that use Cartesian coordinates of points and Cartesian components of unitary vectors in order to describe the position and the motion of the system. Angular coordinates are not used. The kinematic constraint equation comes in two ways, from the rigid-body condition for each element and from the joints or kinematic pairs. The consideration of unitary vectors facilitates considerably the formulation of pair constraints when the pair is associated with a particular direction, as is the case with revolute (R), cylindrical (C), or prismatic (P) pairs. The constraint equations are quadratic in the problem coordinates and they never involve transcendental functions. The dynamic differential equations are obtained in a very simple and effective way from the theorem of virtual power. Finally, two examples will be presented.     

Translational Parallel Manipulators: New Proposals

Translational parallel manipulators are parallel manipulators wherein the end‐effector performs only spatial translations. This paper presents a new family of translational parallel manipulators. The manipulators of this family are independent constraint manipulators. They have three limbs that are topologically identical and have no rotation singularity. The limbs of these manipulators feature five one‐degree‐of‐freedom kinematic pairs in series. Four joints are revolute pairs and the remaining one, called T‐pair, is a kinematic pair that can be manufactured in different ways. In each limb, three adjacent revolute pairs have parallel axes and the remaining revolute pair has an axis that is not parallel to the axes of the other revolute pairs. The mobility analysis of the manipulators of this new family is addressed by taking into account two different choices for the actuated pairs. One of the results of this analysis is that the geometry of a translational parallel manipulator free from singularities can be defined for a particular choice of the actuated pairs. © 2002 Wiley Periodicals, Inc.     

基于激光位移传感器的小转角测量方法研究

针对结构刚度测试中的转角测量问题,提出了一种新的小转角测量方法。采用激光位移传感器测量待测物体的切向线位移值,再通过几何关系将其转换成转角值。建立了包含4个因素的误差数学模型,分析了±1°的测量范围内各误差因素分别对测量结果的影响,结果表明：光斑距刻线标志偏距Δl对误差的影响较大。应用本方法,针对一异形构件进行了扭转刚度测试,当Δl上下限为±1 mm时,测量误差在2%左右,验证了本方法的有效性和准确性。     

A Novel Parallel Manipulator Architecture for Manufacturing Applications

This paper proposes a new type of a six-degree-of-freedom parallelmanipulator with six prismatic legs for manufacturing applications. Eachleg is connected to a base by universal and prismatic joints, and to amoving platform by spherical joints. Based on the complete kinematicsmodel developed in this paper, analytical expressions are derived forthe displacement, velocity and accelerations. The dynamic equations ofthe manipulator are obtained from the kinematic model using the NOCmethod. The implementation of the model in an algorithm is shown throughsimulations to compute the required actuator forces for a sampletrajectory.     

Conceptual development of an enhanced tripod mechanism for machine tool

In this paper, a spatial three degrees of freedom parallel mechanism enhanced by a passive leg is proposed. The proposed parallel mechanism can be used in several applications, e.g. motion simulator, micromanipulator and machine tools. First, the geometric model of the three degrees of freedom parallel mechanism is addressed, in which a fourth kinematic link—a passive link connecting the base center to the platform center—is introduced. This last link is used to constrain the motion of the platform to only three degrees of freedom, i.e. the degree of freedom of the mechanism depends on the passive leg. The passive leg also enhances the global stiffness of the structure and distributes the torque from machining. Second, the kinematic analysis with the consideration of link flexibility is conducted. A kinetostatic model of the three degrees of freedom parallel mechanism with a passive link is then established and analyzed using lumped-parameter model. With the proposed method, a significant effect of the link flexibility on the mechanism's precision has been demonstrated. The influence of the change of structure parameters, including material properties, on the system behavior is discussed. Compliance mapping is also illustrated. The kinetostatic model proposed in the paper can be extended for optimal design and control of parallel kinematic machines. Finally, design optimization is conducted using genetic algorithms and some design guideline is given.     

Improving the absolute positioning accuracy of robot manipulators

The absolute positioning accuracy of robot manipulator can be increased substantially by updating the nominal link parameters in the control software. This paper presents a general method to estimate the link parameter errors for any serial link manipulator (i.e., n links, and any combination of revolute and prismatic joints). The parameters are estimated through a linear kinematic model which relates the link bias errors to the end-effector positioning error. Only end-effector measurements are required instead of individual link measurements to implement this method.     

Analysis of parallel kinematic machine with kinetostatic modelling method

A new method, called Kinetostatic Modelling Method is proposed for analysis of parallel kinematic machines (PKMs) in the paper. First, system modelling includes mobility study, kinematic model and inverse kinematic is conducted. Then, kinetostatic modelling is presented. It includes a complete compliant model developed for the analysis of the PKMs with fixed-length legs, with the model, two global compliance indices are introduced to provide a new mean of measuring the PKM's compliance over the workspace. These two global indices are the mean value and the standard deviation of the trace of the generalized compliance matrix. The mean value represents the average compliance of the PKM over the workspace, while the standard deviation indicates the compliance fluctuation relative to the mean value. The effect of three types of compliance is investigated in order to identify a dominant factor. The proposed method is implemented to analyze the compliance of the Tripod-based PKM prototype built at the Integrated Manufacturing Technologies Institute of the National Research Council of Canada. It is shown that the proposed method is an effective means for evaluating the kinetostatic behaviour of PKMs globally.     

Numerical inverse kinematics for modular reconfigurable robots

The inverse kinematics solutions of a reconfigurable robot system built upon a collection of standardized components is difficult to obtain because of its varying configurations. This article addresses the formulation of a generic numerical inverse kinematics model and automatic generation of the model for arbitrary robot geometry including serial and tree‐typed geometries. Both revolute and prismatic types of joints are considered. The inverse kinematics is obtained through the differential kinematics equations based on the product‐of‐exponential (POE) formulas. The Newton–Raphson iteration method is employed for solution. The automated model generation is accomplished by using the kinematic graph representation of a modular robot assembly configuration and the related accessibility matrix and path matrix. Examples of the inverse kinematics solutions for different types of modular robots are given to demonstrate the applicability and effectiveness of the proposed algorithm. ©1999 John Wiley & Sons, Inc.     

PKM capabilities and applications exploration in a collaborative virtual environment

This paper introduces an integrated validation system that consists of the following modular components: kinematic/dynamic analysis module, kinetostatic model, CAD module, FEM module, CAM module, optimization module and virtual environment for remote control. In this paper, authors focus mainly on the modules of kinetostatic modeling, dynamic modeling, PKM design optimization and remote control realization. The prototype of a 3-dof Parallel Kinematic Machine (PKM) developed at the Integrated Manufacturing Technologies Institute of National Research Council of Canada (NRC-IMTI) is used as an example throughout this paper.     

Modeling errors for dimensional inspection using active vision

In active vision inspection, errors in dimensional measurements are often due to displacement of the sensor and image digitization effects. Using a model of error in linear measurements based on a normally distributed sensor displacement, uniform image digitization and geometric approximation, the accuracy of measurements from a particular sensor setting can be assessed. In comparison with experimental measurements, this error model demonstrates a high predictive ability. Related experiments demonstrate a procedure for assessing the accuracy of sensor settings providing insight into what sensor settings lead to lower measurement variances and thus higher measurement reliability.     

Determination of the dynamic angle of the bearing's rolling element location and of its influence on the loads and rolling friction

A model for determination and analysis of bearing external radial and axial load distributions per individual rolling elements and a model for determination of the resistance to motion of rolling friction, accounting for rolling element locations during the bearing track motion with respect to the direction the bearing radial load resultant vector acts, are presented. A dynamic angle of the rolling element location has been defined as well. The models have been developed to determine values of bearing load distribution parameters, individual rolling element loads, and resistances to rolling motion of bearings and rolling bearing systems, as well as to analyze distributions and values of the radial and axial stiffness of rolling elements, bearings, and kinematic pairs as a function of the bearing rolling element distribution and the direction along which the bearing radial load resultant vector acts. The proposed models have been built to carry out analysis of the resistance to motion of rolling kinematic pairs of industrial robot manipulators. Slow‐speed and short‐period motions of rolling bearings have been assumed as a characteristic type of motion of rolling kinematic pairs in manipulators. © 2000 John Wiley & Sons, Inc.     

Virtual joint method for kinematic modeling of wheeled mobile manipulators

In this paper, we propose a virtual joint method that better utilizes quasi-velocities for the kinematic modeling of wheeled mobile manipulators. By identifying quasi-velocities as motions of imaginary revolute and prismatic kinematic pairs, our method enables one to regard a mobile manipulator as an ordinary articulated manipulator for the purposes of velocity analysis. We also propose an inverse kinematic scheme for the mobile manipulators along the line with the virtual joint based kinematic framework. Details are worked out for mobile manipulators with representative differential-drive and car-like mobile platforms.     

基于SIFT特征的多帧图像超分辨重建

精确的亚像素级图像配准是图像超分辨重建中的关键问题.在图像超分辨重建中广泛使用的基于像素特征的光流法,对于大幅度运动场的计算很难做到精确的亚像素级配准.本文考虑了一种基于SIFT(scale invariant feature transform)特征的鲁棒性多帧图像超分辨重建算法.首先提取输入的低分辨待匹配图像对的SIFT关键点及其特征矢量.随后选取候选匹配关键点对,通过RANSAC(random sample consensus)鲁棒方法去除奇异值,并根据假设的平移性几何约束模型,获得图像对的平移运动配准参数,然后选取视场中心对应的或指定的图像帧为初始参考帧,再使用传统的超分辨重建框架获得最终的重建结果.仿真实验结果表明,提出的基于SIFT特征的图像超分辨重建方案是有效的,超分辨重建的图像质量在主观评价和客观指标上都获得了优于经典算法的效果.     

An Improved Elasto-Kinematic Model of the Human Forearm for Biofidelic Medical Diagnosis

Described in this paper is a new kinetostatic model of the forearm axial motion, i.e., from supination (palm up) to pronation (palm down) and vice versa. The model features an elastokinematic coupling between axial displacement and lateral swaying of the humero-ulnar (elbow) articulation. Such an evasive axial and swaying motion of the ulna has been observed by various authors using magnetic resonance imaging (MRI). In this paper, a two-degree-of-freedom model is presented in which the swaying and axial motion of the ulna is controlled by static equilibrium via two corresponding virtual springs. The spring stiffnesses are identified from geometric measurements, such that the observed motions correspond to the simulated ones. This model can be later used for biofidelic computer-oriented surgery planning. The paper presents the basic kinematic and static relationships of the model as well as an implementation featuring on-line 3D rendering of the motion of the bones.     

基于灰度塔评分的匹配模型构建在无人机网络视频拼接中的应用

对于复杂非配合情况下，视频拼接中特征匹配对的数目和特征匹配准确率无法同时达到后续稳像和拼接的要求这一问题，提出一种基于灰度塔对特征点进行评分后构建匹配模型来进行精准特征匹配的方法。首先，利用灰度级压缩后相近灰度级合并这一现象，建立灰度塔来实现对特征点的评分；而后，选取评分高的特征点建立基于位置信息的匹配模型；最后，依据匹配模型的定位进行区域分块匹配来避免全局特征点的干扰和大误差噪点匹配，选择误差最小的特征匹配对作为最终结果匹配对。另外，在运动的视频流中，可通过前后帧信息建立掩模进行区域特征提取，匹配模型也可选择性遗传给后帧以节约算法时间。实验结果表明，在运用了基于灰度塔评分的匹配模型后，特征匹配对准确率在95%左右。相同帧特征匹配对的数目相较于随机采样一致性有近10倍的提升，在兼顾匹配数目和匹配准确率的同时且无大误差匹配结果，对于环境和光照有较好的鲁棒性。     

Redundant Control of a Planar Snake Robot with Prismatic Joints

This paper presents a control method of a planar snake robot with prismatic joints. The kinematic model is derived considering velocity constraints caused by passive wheels. The proposed control method based on the model allows the robot to track a target trajectory by appropriately changing its link length using prismatic joints. The degrees of freedom of prismatic joints are represented as kinematic redundancy in the model and are used in realizing subtasks such as singularity avoidance and obstacle avoidance. In addition, the link length is below its limit when introducing a sigmoid function into the kinematic model. Simulations are carried out to demonstrate the effectiveness of the proposed method and show a novel motion that avoids singular configurations through changes in link lengths.

     

Multiobjective Optimization of 6-dof UPS Parallel Manipulators

The optimal design of parallel kinematic machines goes through two fundamental stages. The first one concerns the structural synthesis. It enables, a priori, to determine the choice of families of the most adapted architectures according to the desired applications such as flight simulators, machine-tools, medical applications, etc. This can be done by applying several techniques such as: screw theory, Lie groups, graph theory, finite element method, etc. The second one concerns the dimensional synthesis and aims to determine the dimensions of the architecture that has been selected during the structural synthesis. This stage remains a major task because the criteria of performance of a given architecture are strongly dependent on its sizing. In this paper, we present a dimensioning methodology of the architectural parameters of the 6-dof UPS (U: universal joint, P: prismatic joint, and S: ball-and-socket joint) parallel manipulators (the positions of the attachment points of the actuators on the base and mobile plate as well as the radius of the base and the mobile plate). The problem will be formulated as a multiobjective optimization problem (MOOP) by taking into account simultaneously several criteria of performance such as the workspace, kinetostatic performances, stiffness, and dynamic dexterity. The SPEA-II genetic algorithm is adopted to solve this type of MOOP.     

A constrained assumed modes method for dynamics of a flexible planar serial robot with prismatic joints

In the present study, for the first time, flexible multibody dynamics for a three-link serial robot with two flexible links having active prismatic joints is presented using an approximate analytical method. Transverse vibrations of flexible links/beams with prismatic joints have complicated differential equations. This complexity is mostly due to axial motion of the links. In this study, first, vibration analysis of a flexible link sliding through an active prismatic joint having translational motion is considered. A rigid-body coordinate system is used, which aids in obtaining a new and rather simple form of the kinematic differential equation without the loss of generality. Next, the analysis is extended to include dynamic forces for a three-link planar serial robot called PPP (Prismatic, Prismatic, Prismatic), in which all joints are prismatic and active. The robot has a rigid first link but flexible second and third links. To model the prismatic joint, time-variant constraints are written, and a motion equation in a form of virtual displacement and virtual work of forces/moments is obtained. Finally, an approximate analytical method called the “constrained assumed modes method” is presented for solving the motion equations. For a numerical case study, approximate analytical results are compared with finite element results, which show that the two solutions closely follow each other.     

Kinematic Reasoning with Spatial Decompositions

This paper examines the application of hierarchical discrete spatial representations to the kinematic analysis and synthesis of the higher pairs. Two instances of hierarchical representation are investigated, a global decomposition in the form of quadtrees, and an object-centered, multi-level molecular decomposition. Kinematic reasoning with both representations relies upon the rapid evaluation of the single occupancy constraint. For both representations we present algorithms that allow the rapid detection of intersection between two objects, the analysis of higher pair mechanisms, and a restricted class of kinematic synthesis.