Modeling and Optimal Design of Planar Linkage Mechanism of Coupled Joint Clearances for Manufacturing

The uncertainty of the mechanism motion error is mostly caused by the manufacturing process,so the motion error cannot be effectively predicted at the design phase.The problems of manufacturing complexity and the relationship between design and manufacturing are analyzed,and the influence of dimensional tolerance and fit tolerance on the motion accuracy of the system is considered in the design process.Then based on the Monte Carlo simulation,an optimal design model of planar linkage mechanism is set up.A typical offset slider-crank mechanism is used as an illustrative example to carry out the optimal design.Compared with the result of typical robustness design,the similar variation characteristics of the mean value and the standard deviation can be found,so the proposed method is effective.The method is furthermore applied in the optimization of the schemes with different fit tolerances and the prediction of motion errors in the design phase is achieved.A set of quantitative evaluation system for mechanism optimal design is provided.Finally,a basic strategy is presented to balance the motion precision and manufacturing cost.

CALCULATION OF ELASTIC ERROR OF PLANAR MECHANISM—AN EQUIVALENT METHOD

In rigid mechanism dynamic analysis, the equivalence theorem is often used due to its simplicity and perceivability. Based on conjugation and duality between inertia energy storing element and elastic energy storing element, the equivalence theorem is used in elastic error analysis of planar mechanism. A set of calculation formula of elastic error is introduced, and these equations are similar in expression form to the rigid dynamic equation. To demonstrate the method developed, a computation example is given.

Kinematic Solution of Spherical Stephenson-Ⅲ Six-bar Mechanism

A closed-form solution can be obtained for kinematic analysis of spatial mechanisms by using analytical method.However,extra solutions would occur when solving the constraint equations of mechanism kinematics unless the constraint equations are established with a proper method and the solving approach is appropriate.In order to obtain a kinematic solution of the spherical Stephenson-III six-bar mechanism,spherical analytical theory is employed to construct the constraint equations.Firstly,the mechanism is divided into a four-bar loop and a two-bar unit.On the basis of the decomposition,vectors of the mechanism nodes are derived according to spherical analytical theory and the principle of coordinate transformation.Secondly,the structural constraint equations are constructed by applying cosine formula of spherical triangles to the top platform of the mechanism.Thirdly,the constraint equations are solved by using Bezout’ s elimination method for forward analysis and Sylvester’ s resultant elimination method for inverse kinematics respectively.By the aid of computer symbolic systems,Mathematica and Maple,symbolic closed-form solution of forward and inverse displacement analysis of spherical Stephenson-III six-bar mechanism are obtained.Finally,numerical examples of forward and inverse analysis are presented to illustrate the proposed approach.The results indicate that the constraint equations established with the proposed method are much simpler than those reported by previous literature,and can be readily eliminated and solved.

Analytical expression of non steady-state concentration profiles at planar electrode for the CE mechanism

The analytical solutions of the non-steady-state concentrations of species at a planar microelectrode are presented. These simple new approximate expressions of concentrations are valid for all values of time and possible values of rate constants. Analytical equations are given to describe the current when the homogeneous equilibrium position lies heavily in favour of the electroinactive species. Working surfaces are presented for the variation of limiting current with a homogeneous kinetic parameter and equilibrium constant. Moreover, in this work we employ the Homotopy perturbation method to solve the boundary value problem.

Mechanism of amorphous Ge_2Sb_2Te_5 removal during chemical mechanical planarization in acidic H_2O_2 slurry

In this paper, chemical mechanical planarization （CMP） of amorphous Ge2Sb2Te5 （a-GST） in acidic H2O2 slurry is investigated. It was found that the removal rate of a-GST is strongly dependent on H2O2 concentration and gradually increases with the increase in H2O2 concentration, but the static etch rate first increases and then slowly decreases with the increase in H2O2 concentration. To understand the chemical reaction behavior of H2O2 on the a-GST surface, the potentiodynamic polarization curve, surface morphology and cross-section of a-GST immersed in acidic slurry are measured and the results reveal that a-GST exhibits a from active to passive behavior for from low to high concentration of H2O2. Finally, a possible removal mechanism of a-GST in different concentrations of H2O2 in the acidic slurry is described.

Biped 4R2C Six-bar Mechanism with Inner and Outer Feet

Most current biped robots are equipped with two feet arranged in the right and left which inspired by the human body system. Different from the existing configurations, a novel biped robot with inner and outer feet based on a spatial six-bar 4R2C（R and C denote revolute and cylindric joints, respectively） mechanism is proposed. It can move along a line or a curve by three walking modes that are dwell adjustment mode, limit position adjustment mode and any position adjustment mode. Kinematic, gait planning and stability analyses are performed respectively, and a prototype is developed. Lastly, a potential application is considered and two manipulating modes（sphere and cylinder manipulating modes） are carried out. This interesting mechanism feathering its single dosed-chain structure and unique work performance is expected to motivate the configuration creation of biped robots.

A quantitative analysis method for contact force of mechanism with a clearance joint based on entropy weight and its application in a six-bar mechanism

Contact force in a clearance joint affects the dynamic characteristics and leads to nonlinear response of the mechanism.It is necessary to assess the nonlinearity of contact force quantitatively.Therefore,a new method named contact-force entropy weight is proposed in this paper.This method presents a comprehensive description of the judgment matrix in the X,Y,and Z directions.To assess the influence degrees of different clearances and angular velocities on the contact force,the method is applied to numerical calculation and simulation of a six-bar mechanism with a clearance joint to illustrate its application and investigate the influence degree of angular velocity and clearance on the contact force.By combining the simulation results and theoretical calculations,the influence degrees of different clearances and angular velocities on the contact-force entropy weight of the six-bar mechanism with a clearance joint are revealed.It is found that the angular velocity has a significant influence on the contact force entropy weight of the clearance joint,showing that the contact-force entropy weight is a feasible new method of assessing non-linearity of contact force quantitatively.The method gives a theoretical reference for quantitatively analyzing the nonlinear dynamics.

Dynamics Response and Non⁃linear Characteristics Analysis of Complex Planar 2⁃DOF Mechanism with Revolute Clearances

There are clearances in mechanism because of manufacture and assembly error,which reduces operation life and working accuracy of mechanism and has a great impact on dynamical responses.At the moment,research in this area mainly focuses on single degree⁃of⁃freedom mechanism considering one clearance,while research of multi⁃DOF mechanism considering multi⁃clearance is less.With the purpose of studying the dynamical characteristics of complex multi⁃DOF mechanism with multi⁃clearances,a dynamic model was developed.The dynamic responses of 2⁃DOF mechanism with two clearances under different positions,values,and numbers of clearance were analyzed.The displacement,velocity,acceleration,collision force,and the axis trajectory at clearance were then given.In addition,there is a limited amount of literature on chaotic phenomena,which mainly focuses on the chaotic phenomena of end⁃effector of mechanism.But in this paper,the non⁃linear characteristics were analyzed by chaotic phenomenon of clearance joint,then chaotic phenomenon was identified by Poincarémappings and phase diagrams.Bifurcation diagrams were given.The results will offer a reliable technical support for the study of dynamical responses of planar mechanisms and the analysis of chaotic phenomena.

A Method for Automatically Establishing a Mathematical Model of Kinematic Analysis to a Planar Mechanism with a Multiple Joint and Prismatic Pair

A method for automatically establishing a mathematical model of kinematic analysis to a planar mechanism with multiple joint and prismatic pair is presented. The breadth （ or depth ） first search spanning tree can be obtained based on an adjacency matrix of the mechanism. Then the kinematic chain （or mechanism）＇s basic loops can be obtained. On the basis of these basic loops, a mathematical model of kinematic analysis can be established and solved automatically. In the sense of a calculative mechanism, structural analysis of the kinematic chain relates to the kinematic analysis of a mechanism. Thus, an effective way is supplied to the given mechanism＇s kinematic analysis for automatic modeling and solving, and a method is supplied to the structural type to optimize kinematic synthesis.

VELOCITY ANALYSIS OF A PLANAR MECHANISM USING A METHOD FROM STATICS

A new method for solving the velocity analysis of a mechanism is presented. Central to the method is how to convert the probem of velocity analysis of a mechanism to one of static analysis. Application of the method to certain practical problems has advantages compared to conventional methods for both graphical and analytical solutions. For brevity an example of a planar mechanism only is presented.

用Pro/Mechanism实现复杂凸轮机构的设计及运动分析

针对复杂平面运动从动件盘形凸轮机构设计的困难,介绍1种利用Pro/Mechanism的强大功能实现复杂凸轮机构的创新设计、运动仿真及运动分析。这种创新方法可以使复杂凸轮机构设计变的快捷、便利。

Effect of inter-cycle heat treatment in accumulative roll-bonding(ARB)process on planar isotropy of mechanical properties of AA1050 sheets

The accumulative roll-bonding(ARB)process was applied on the strips of aluminum alloy 1050 in two processing conditions:cold ARB and warm ARB.The results of tensile tests and microhardness measurement show that the warm ARB process exhibits the lower tensile strength and microhardness,more homogeneous distribution of the microhardness,higher elongation,and especially superior planar isotropy of the tensile properties in comparison to the cold ARB,because of the intermediate heat treatment as well as the elevated temperature rolling in the warm ARB process.Furthermore,with increasing the cycles of both processes,the planar isotropy decreases progressively.

TWO STEPS CHEMICAL-MECHANICAL POLISHING OF RIGID DISK SUBSTRATE TO GET ATOM-SCALE PLANARIZATION SURFACE

In order to get atomic smooth rigid disk substrate surface, ultra-fined alumina slurry and nanometer silica slurry are prepared, and two steps chemical-mechanical polishing （CMP） of rigid disk substrate in the two slurries are studied. The results show that, during the first step CMP in the alumina slurry, a high material removal rate is reached, and the average roughness （Ra） and the average waviness （Wa） of the polished surfaces can be decreased from previous 1.4 nm and 1.6 nm to about 0.6 nm and 0.7 nm, respectively. By using the nanometer silica slurry and optimized polishing process parameters in the second step CMP, the Ra and the Wa of the polished surfaces can be further reduced to 0.038 nm and 0.06 am, respectively. Atom force microscopy （AFM） analysis shows that the final polished surfaces are ultra-smooth without micro-defects.

CALCULATION OF NATURAL FREQUENCIES FOR THE PLANAR SIX-BAR LINKAGE OF WATT TYPE

By using transfer matrix,the lower-order natural frequencies of the Watt type planar six-barlinkage are calculated in this paper.The experiment of the modal analysis is done with the SignalProcessor 7T17S,and the experiment results agree with the calculated ones.This method only re-quires calculation of lower-order transfer matrix and determinant values,so that, it can be done ona minicomputer such as IBM/PC.The method adopted in this paper is also suitable for vibrationanalysis of other types of linkages.

Quantitative analysis of the morphing wing mechanism of raptors:Morphing kinematics of Falco peregrinus wing

Raptors are getting more attention from researchers because of their excellent flight abilities.And the excellent wing morphing ability is critical for raptors to achieve high maneuvering flight,which can be a good bionic inspiration for unmanned aerial vehicles(UAV)design.However,morphing wing motions of Falco peregrinus with multi postures cannot be consulted since such a motion database was nonexistent.This study aimed to provide data reference for future research in wing morphing kinetics.We used the computed tomography(CT)approach to obtain nine critical postures of the Falco peregrinus wing skeleton,followed with motion analysis of each joint and bone.Based on the obtained motion database,a six-bar kinematic model was proposed to regenerate wing motions with a high fidelity.

A new passive transfemoral prosthesis mechanism based on 3R36 knee and ESAR foot providing walking and squatting

Researchers have proposed various linkage mechanisms to connect knee and ankle joints for above-knee prosthe-ses,but most of them only offer natural walking.However,studies have shown that people assume a squatting posture during daily activities.This paper introduces a novel mechanism that connects the knee joint with the foot-ankle joint to enable both squatting and walking.The prosthetic knee used is the well-known 3R36,while the energy storing and return(ESAR)prosthetic foot is used for the ankle-foot joint.To coordinate knee and ankle joint movements,a six-bar linkage mechanism structure is proposed.Simulation results demonstrate that the proposed modular transfemoral prosthesis accurately mimics the motion patterns of a natural human leg during walking and squatting.For instance,the prosthesis allows a total knee flexion of more than 140°during squatting.The new prosthesis design also incorporates energy-storing mechanisms to reduce energy expenditure during walking for amputees.

The Analysis of Link Mechanism and Its Programming Realization

This paper introduces realization method of kinematics analysis for the planar four bar mechanism based on the MFC. A mathematicat model is established by a simple and effective method, using the computer simulation technology can the dynamic demonstration mechanism taotion and automatic drawing trajectory curve of arbitrary point on the connecting rod, and can output various motion displacement, speed and acceleration diagram. The paper provides a simple way for motion analysis of planar four link.

基于SimMechanics和iSIGHT的平面四杆机构的运动仿真和优化

以平面四杆机构为典型算例,应用MATLAB/SIMULINK中的SimMechanics模块建立机构运动模型,并进行仿真分析。应用iSIGHT对模型进行预订轨迹的尺度优化设计,为机构仿真和优化提供了一种高效、直观的仿真手段,为其他机构的仿真和优化提供了借鉴。

Numerical and experimental study on seismic behavior of concrete-filled T-section steel tubular columns and steel beam planar frames

The seismic behavior of planar frames with concrete-filled T-section columns to steel beam was experimentally and numerically studied. A finite element analysis （FEA） model was developed to investigate the engineering properties of the planar frames. Two 1：2.5 reduced-scale specimens of T-section concrete-filled steel tubular column and steel beam of single-story and single-bay plane frames were designed and fabricated based on the design principles of strong-column, weak-beam and stronger-joint. One three-dimensional entity model of the investigated frame structure was built using a large-scale nonlinear finite-element analysis software ABAQUS. Experimental results show that the axial compression ratio has no effect on the failure mode of the structure, while with the increase of axial compression ratio and the dissipated energy ability increasing, the structural ductility decreased. The results from both experiments and simulations agree with each other, which verifies the validity and accuracy of the developed finite element model. Furthermore, the developed finite element model helps to reflect the detailed stress status of the investigated frame at different time and different positions.