用快速傅里叶变换进行球面四杆机构连杆轨迹综合

根据给出的球面四杆机构连杆轨迹的数学模型,借助傅里叶级数这一数学工具,对连杆轨迹的谐波成分进行理论分析,发现连杆轨迹的谐波成分与其相应转角函数谐波特征参数和机构尺寸参数的内在联系。确定球面四杆机构的基本尺寸型,在此基础上建立包含600余万组机构基本尺寸型的球面四杆机构连杆轨迹的谐波特征参数数值图谱库。利用傅里叶级数理论建立球面四杆机构处于空间任意位置时连杆曲线的数学方程,推导出计算机构的实际安装尺寸、连杆上点的位置和机构安装尺寸参数的理论计算公式。利用建立的谐波特征参数数值图谱和推导的理论公式解决了球面四杆机构的轨迹综合问题,最后给出算例证明本方法的可行性。     

球面四杆机构近似函数综合的自适应方法

给出了球面运动刚体上具有二次鞍点意义的近似圆点的定义,提出了球面曲线的自适应圆弧拟合方法,把实现给定函数关系的球面机构综合转化为球面上曲线的自适应圆弧拟合逼近问题,建立了球面运动近似函数综合的数学模型和鞍点规划求解方法,由此在理论上阐明了球面四杆机构近似运动综合问题存在最优近似解和收敛性算法。为了克服初始值选取和获得全局最优解等困难,采用了遗传算法的思想,算例表明可行有效。     

球面四杆机构的空间模型及尺寸型

基于特征球面四杆机构的概念，将球面四杆机构分为三类，并建立机构的尺寸型空间模型。每个空间模型可划分为若干个子区间，每个子区间都对应着一族球面四杆机构。按本文提出的尺寸型表示方法，可在全封闭图面内表示球面四杆机构的尺寸型，并在其上绘制出有工程应用价值的机构性能图谱。     

Complete Real Solution of the Five-orientation Motion Generation Problem for a Spherical Four-bar Linkage

For a spherical four-bar linkage,the maximum number of the spherical RR dyad(R:revolute joint)of five-orientation motion generation can be at most 6.However,complete real solution of this problem has seldom been studied.In order to obtain six real RR dyads,based on Strum’s theorem,the relationships between the design parameters are derived from a 6th-degree univariate polynomial equation that is deduced from the constraint equations of the spherical RR dyad by using Dixon resultant method.Moreover,the Grashof condition and the circuit defect condition are taken into account.Given the relationships between the design parameters and the aforementioned two conditions,two objective functions are constructed and optimized by the adaptive genetic algorithm(AGA).Two examples with six real spherical RR dyads are obtained by optimization,and the results verify the feasibility of the proposed method.The paper provides a method to synthesize the complete real solution of the five-orientation motion generation,which is also applicable to the problem that deduces to a univariate polynomial equation and requires the generation of as many as real roots.     

球面四杆机构函数综合精确点选择新方法

讨论了球面四杆机构函数综合中精确点的选择问题,以减小最大综合误差为目标,提出了一种新的精确点优化选择方法。利用球面四杆机构函数综合的封闭形式解,通过引入比例系数,推导了结构偏差的方程式,并构造了精确点选择的优化数学模型。利用数值插值的方法对结构偏差方程式进行了分析,给出了优化模型的初始解,并采用分形算法求得了全局最优解。通过对数值实例的计算和对结果的分析,验证了新方法的有效性。     

A new type of spherical flexure joint based on tetrahedron elements

In this paper we present two new designs of spherical flexure joints, which are the compliant equivalent of a traditional ball-and-socket joint. The designs are formed by tetrahedron-shaped elements, each composed of three blade flexures with a trapezoidal shape, that are connected in series without intermediate bodies. This is new with respect to the designs currently found in literature and helps to increase the range of motion. We also present two planar (x-y-${\theta }_z$) flexure joint designs which were derived as special versions of the spherical designs. In these designs the tetrahedron elements have degenerated to a triangular prisms. For detailed investigation we developed equivalent representations of the tetrahedron and triangular prism elements and proved that three of the four constraint stiffness terms depend solely on the properties of the main blade flexure. Furthermore, we derived equations for these stiffness terms which are compared to finite-element simulations, showing a good correspondence for the prism element with a Normalized Mean Absolute Error (NMAE) of 1.9%. For the tetrahedron element, the equations showed to only capture the qualitative behaviour with a NMAE of 34.9%. Also, we derived an equation for the optimal width of the prism element regarding rotational stiffness.     

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.     

转向装置球面四杆机构的综合

提出了采用球面四杆机构作为转向机构与方向盘之间的运动传递 ,并建立了车辆转向曲率与转向机构输入构件转角的关系。在此基础上获得了球面四杆机构输入—输出关系和机构优化综合数学模型 ,最后绘出误差曲线 ,以验证所提出方法的有效性。     

空间第一组机构连杆扭角和回路的关系研究

从球面三角理论出发 ,对球面四杆机构构件扭角和机构回路的关系进行分析 ;通过球面 4R机构中最大扭角和最小扭角进行定义 ,给出了其所满足的三个条件与球面 4R机构的四种回路特性之间的联系 ,最后阐述了将此结论应用于第一组空间单环机构的方法。这对于机构分析与综合有重要的参考价值。     

On the coupler-great-circle envelopes of spherical four-bar linkages

With use of the techniques developed for coupler-point curves, the tangential equation is derived for the envelope of a great circle attached to the coupler of a general spherical four-bar linkage in the motion of this mechanism. The class of this envelope is determined to be 8. The dual relationships between the coupler-point curve and the coupler-great-circle envelope are discussed. With this concept, the techniques for designing a spherical four-bar coupler-great-circle envelope generator are introduced.     

球开蜗杆砂轮的磨齿原理及其球基螺旋面参数

提出用球开蜗杆砂轮连续分度展成磨削内齿轮的概念,阐述了其磨齿原理.建立了砂轮的球基渐开螺旋面议程和分度球面螺旋线方程,给出螺旋运动参数,螺旋线导程,螺旋升角的定义及计算式.     

3PSS-S型并联机构的奇异轨迹研究

针对一种3PSS-S球面并联机构,建立了该并联机构的位置反解数学模型,推导了并联机构速度方程和雅可比矩阵的解析表达式。基于机构的雅可比矩阵,应用等高线方法绘制了并联机构的奇异轨迹曲线,并讨论了固定平台结构参数对并联机构奇异轨迹的影响。     

THEORY OF HELICOID OF SPHERICAL HOB

ＴＨＥＯＲＹＯＦＨＥＬＩＣＯＩＤＯＦＳＰＨＥＲＩＣＡＬＨＯＢＴＨＥＯＲＹＯＦＨＥＬＩＣＯＩＤＯＦＳＰＨＥＲＩＣＡＬＨＯＢＣｕｉｙｕｎｑｉ；ＨｕＺｈａｎｑｉ（ＹａｎｓｈａｎＵｎｉｖｅｒｓｉｔｙ）ＡｂｓｔｒａｃｔＴｈｅｍｅｃｈａｎｉｓｍｏｆｓｐｈｅｒｉｃ...     

球面3自由度并联机构的正解分析新方法

机构的正解在并联机器人研究域是一个具有挑战性的问题,长期以来人们在这方面做了很多的研究。球面3自由度并联机构是一种有重要应用的机构,如同一般并联机构,其反解容易而正解困难。利用两点间距离在不同坐标系下不变的原理作为约束条件建立约束方程,对球面3自由度并联机构进行位置正解分析,得出了正解的封闭解形式,因为引入了一次半角公式,所以其最终方程是最高次数为16的一元多项式。运用反解的方式对其进行了数值验证,证明该正解分析是正确的。     

Design of Spherical Spiral Groove Bearings for a High-Speed Air-Lubricated Gyroscope

A spherical spiral groove gas bearing has the ability to not only support radial and axial loads simultaneously but also tolerate extensive misalignment. Thus, this bearing type is considered suitable as a supporting and lubrication component of inertial components such as gyroscopes in the fields of aerospace and navigation. In this study, we propose a numerical method for predicting static and dynamic characteristics and conduct a parametric analysis of an aerodynamic spherical bearing with rotating spiral grooves. The finite difference method and the perturbation method are used to calculate the Reynolds equation to obtain the force coefficients. Given the complicated groove distribution, as well as film discontinuity and compressibility, solving the equations numerically in the spherical coordinates system is difficult. Parameter transformation and oblique coordinate transformation are thus applied in this study to modify the Reynolds equation into the planar oblique coordinate system. An eight-point method is also utilized to deal with film thickness discontinuity. The predictions of this proposed method show good agreement with the available experimental data. Parametric studies on nominal clearance, eccentricity ratio, rotating speed, groove depth, groove angle, and perturbation frequency are then conducted to determine optimum design parameters. The results show that these factors significantly affect bearing characteristics in both the radial and axial directions.     

Reducible compositions of spherical four-bar linkages with a spherical coupler component

We use the output angle of a spherical four-bar linkage C as the input angle of a second four-bar linkage D where the two frame links are assumed in aligned position as well as the follower of C and the input link of D. We determine all cases where the relation between the input angle of the input link of C and the output angle of the follower of D is reducible and where additionally at least one of these components produces a transmission which equals that of a single spherical coupler. The problem under consideration is of importance for the classification of flexible 3 × 3 complexes and for the determination of all flexible octahedra in the projective extension of the Euclidean 3-space.     

On a computationally efficient microcomputer kinematic analysis of the basic linkage mechanisms

Based on the algebraic correspondence between the displacement equations of the plane, spherical and skew four-bar linkages and the plane and skew slider-crank mechanisms, a highly compact, computationally efficient procedure has been developed for a microcomputer kinetmatic analysis of these linkages.     

Computer-aided kinematic analysis of basic spatial mechanisms

Using the spherical coordinate system in conjunction with the principle of algebraic correspondence between the displacement equations of the plane, spherical and spatial four-bar mechanisms and the plane and spatial slider-crank mechanisms, an efficacious procedure has been developed to carry out kinematic analysis for the coupler and output link of the mechanisms. The iteration-free nature of the procedure precludes any non-convergence problem and the inherent complexity of the 3-dimensional analysis is mitigated substantially.     

An angular constraints solving approach for assembly modeling based on spherical geometry

In this paper, a novel approach for solving angular constraints based on spherical geometry is presented. This method can determine the orientation of a set of parts given the mating constraints between them with the decoupled property of the angular and distance constraints. The combination of angular constraints can be categorized into two cases: operable and un-operable. The former can be solved efficiently by introducing simple spherical surface reasoning. The latter is solved by employing spherical surface four-linkage mechanism. In this way, the rotation transformation matrix of the dependent rigid body is worked out. This new method has the advantages over numerical approach and symbolic approach of clear geometric solubility, geometric operability, and avoiding simultaneously solving all the constraint equations in the model. Moreover, it is an easy and efficient way to determine whether there exist redundant constraints. The presented algorithm has been successfully implemented in our assembly prototype system, InteVue.     

用广义逆矩阵进行平面四杆机构的近似函数综合

提出了平面四杆机构近似函数综合的一种新方法,其基本思路是：首先利用广义逆矩阵将四杆机构的近似函数综合方程组转化为一个二元二次方程组,然后采用消元法得到一个一元三次方程,由此可得机构近似运动综合方程组的所有解。为平面四杆机构近似函数综合提供了高效的实用方法。