Over-constraint and a Unified Mobility Method for General Spatial Mechanisms Part 1: Essential Principle

Compared with the parallel mechanisms, the mobility analysis of the general multi-loop spatial mechanisms(GMSMs) is more difficult to obtain correct results. The reason is that its multi-loop is formed through several times of closings and there also exists motion coupling even strong coupling, where the over-constraints are concealed. However, the mobility analysis for this kind of mechanisms has been paid few attentions. A new systemic methodology for analyzing mobility is proposed for GMSMs also based on the screw theory. The key issue for mobility analysis is to recognize the over-constraint. Firstly, three theorems are given and point out: the reason and site of over-constraint occurrence, calculating the number of over-constraints by the screw theory, and how to analyze the over-constraints for a single-loop mechanism as well. Then, three closing forms for GMSMs are proposed including rigid closure, movable closure and dynamic closure, and for the three different forms the different analysis methods are also given. Especially, for the most difficult issue of GMSMs with the multi-loop closure in many times and the inevitable motion coupling, two important methods are proposed: "recognizing over-constraints by analyzing relative movement" and "recognizing over-constraints by virtual loop". The two methods are well used to solve the issue. Above-mentioned principles are not only systematic and effective but also unified. They provide a theoretical basis for the general multi-loop spatial mechanisms.     

基于螺旋理论的单闭环多自由度过约束机构综合

以螺旋理论为基础,分析构成单闭环过约束机构的约束数目、运动副数目和自由度数目之间的关系,给出针对单闭环过约束机构的自由度计算公式。按照约束螺旋的性质将过约束螺旋分为具有不同阶数的力约束和力偶约束两类,总结所有可能形式的独立过约束性质和数目及其组合。在给出特定过约束组合的条件下,应用虚功原理,以反螺旋理论为计算手段,得到多自由度单闭环机构的综合条件。应用解析的方法,得到满足机构为非瞬时运动的条件,给出机构的运动副轴线布置、运动副数目、运动副排列和空间几何条件。全面系统地解决了单闭环多自由度过约束机构的构型综合问题,群举所有可能的单闭环过约束并联机构。给出机构综合步骤以及部分典型机构的设计范例。     

平行多回路机器人机构的瞬时螺旋运动

本文分析了6自由度平行多回路机器人机构的瞬时螺旋运动,建立起6个输入运动与机器人端执行器或机构中其他构件的瞬时运动关系的显表达式。所有导出的公式十分简明,便于应用,文章后部还将这种方法推广到一般空间非平行多回路机构。     

多环耦合机构末端件自由度计算的等效法

针对新型耦合机器人与常见并联机器人机构结构的迥异性,提出一种适应多环耦合机构末端件约束分析和自由度计算的新方法,此方法的主要思路是将多环耦合机构转化为并联机构。提出机构拆分原则,将连接输入和输出的部分拆分为多个独立单元体。应用螺旋理论逐一分析拆分出的单元体中各个耦合节点构件相对于机架的独立运动,将含耦合结构的独立单元体等效为一个串联分支,整个机构就等效为一个并联机构。分析等效并联机构各分支的运动螺旋系和约束螺旋系,采用二次反螺旋求得机构末端件的自由度。应用提出的等效替代法计算一个耦合机构的自由度,计算结果与原型一致,表明提出的新方法能够有效化简耦合机构的复杂性并正确求得自由度。     

Applicability and generality of the modified Grübler-Kutzbach criterion

A generally applicable criterion for all mechanism mobility has been an active domain in mechanism theory lasting more than 150 years. It is stated that the Modified Grübler-Kutzbach criterion for mobility has been successfully used to solve the mobility of many more kinds of mechanisms, but never before has anyone proven the applicability and generality of the Modified Grübler-Kutzbach criterion in theory. In order to fill the gap, the applicability and generality of the Modified Grübler-Kutzbach Criterion of mechanism mobility is systematically demonstrated. Firstly, the mobility research background and the Modified Grübler-Kutzbach criterion are introduced. Secondly, some new definitions, such as half local freedom, non-common constraint space of a mechanism and common motion space of a mechanism, etc, are given to demonstrate the correctness and broad applicability of the Modified Grübler-Kutzbach criterion. Thirdly, the general applicability of the Modified Grübler-Kutzbach criterion is demonstrated based on screw theory. The mobilities of the classical DELASSUS mechanisms and a modern planar parallel mechanism, are determined through the Modified Grübler-Kutzbach criterion, which are as examples to show the practical application of the Modified Grübler-Kutzbach criterion.     

空间单环RPSC机构的运动和奇异分析

单环机构又称单闭链机构,这类机构运动巧妙,在诸多领域有着广泛应用。另外,在工程实际中还常常在开链机构中加入局部闭链以改善动力学性能,增加结构刚度等。介绍一种能够实现垂直Darboux运动(Vertical Darboux motion,VDM)的空间单环RPSC机构,运用螺旋理论对其约束及运动性质进行分析。通过对锁住其驱动关节后的等价机构进行约束分析,确定了该机构的一类特殊驱动奇异,并借助相对直观的几何方法对RPSC机构中存在的这种奇异位形做进一步解释与说明。对机构中RPS分支的主要特点进行概括,并由特殊到一般地提出了一类具有相似特性的单环机构。     

Design of a novel side-mounted leg mechanism with high flexibility for a multi-mission quadruped earth rover BJTUBOT

Earth rover is a class of emerging wheeled-leg robots for nature exploration. At present, few methods for these robots’ leg design utilize a side-mounted spatial parallel mechanism. Thus, this paper presents a complete design process of a novel 5-degree-of-freedom (5-DOF) hybrid leg mechanism for our quadruped earth rover BJTUBOT. First, a general approach is proposed for constructing the novel leg mechanism. Subsequently, by evaluating the basic locomotion task (LT) of the rover based on screw theory, we determine the desired motion characteristic of the side-mounted leg and carry out its two feasible configurations. With regard to the synthesis method of the parallel mechanism, a family of concise hybrid leg mechanisms using the 6-DOF limbs and an L_1F1C limb (which can provide a constraint force and a couple) is designed. In verifying the motion characteristics of this kind of leg, we select a typical (3-UPRU&RRRR)&R mechanism and then analyze its kinematic model, singularities, velocity mapping, workspace, dexterity, statics, and kinetostatic performance. Furthermore, the virtual quadruped rover equipped with this innovative leg mechanism is built. Various basic and specific LTs of the rover are demonstrated by simulation, which indicates that the flexibility of the legs can help the rover achieve multitasking.     

多模式空间6R地面移动机构

提出一种新型空间单闭链F1C1（约束力F和约束力偶C）约束型6R（转动副）机构,并应用其研制一种地面移动机器人。基于单环运动链构型综合方法,构造出空间单闭链单自由度F1C1约束型6R机构,应用螺旋理论进行自由度和奇异位置分析,结合地面移动需求构造地面移动机器人,进行了杆件形状的设计,规划驱动电动机布局方案,完成运动学和移动机理分析,规划类蠕动、平面4R转向和内翻三种移动模式,分析越障性能,揭示其突出的折展特性。制作样机,验证了多模式空间6R地面移动机构方案和运动规划的可行性。     

采用过约束冗余驱动提高球面并联机构精度容错能力的研究

将误差源对球面并联机构运动精度的不利影响看作一种机械系统故障,提出了球面并联机构精度容错的概念和基本思想,定义了描述球面并联机构精度容错能力的指标———精度容错度。基于螺旋理论,利用球面3-RRR并联机构的过约束性设计了具有冗余驱动的球面m-RRR(m≥4)型改进机构。通过求解原机构和改进机构的精度容错度,比较了它们的精度容错能力,并结合实例进行了仿真研究,结果表明所提出的以精度容错度为依据的精度容错策略能有效提高球面并联机构的精度,克服误差源的不良影响。     

Kinematics and dynamics of deployable structures with scissor-like-elements based on screw theory

Because the deployable structures are complex multi-loop structures and methods of derivation which lead to simpler kinematic and dynamic equations of motion are the subject of research effort, the kinematics and dynamics of deployable structures with scissor-like-elements are presented based on screw theory and the principle of virtual work respectively. According to the geometric characteristic of the deployable structure examined, the basic structural unit is the common scissor-like-element（SLE）. First, a spatial deployable structure, comprised of three SLEs, is defined, and the constraint topology graph is obtained. The equations of motion are then derived based on screw theory and the geometric nature of scissor elements. Second, to develop the dynamics of the whole deployable structure, the local coordinates of the SLEs and the Jacobian matrices of the center of mass of the deployable structure are derived. Then, the equivalent forces are assembled and added in the equations of motion based on the principle of virtual work. Finally, dynamic behavior and unfolded process of the deployable structure are simulated. Its figures of velocity, acceleration and input torque are obtained based on the simulate results. Screw theory not only provides an efficient solution formulation and theory guidance for complex multi-closed loop deployable structures, but also extends the method to solve dynamics of deployable structures. As an efficient mathematical tool, the simper equations of motion are derived based on screw theory.     

旋量键合图在并联机构动力学建模中的应用

旋量键合图将旋量理论与键合图相结合,兼具了旋量理论描述空间并联机构简洁、直观及键合图多能域建模统一、规范的特点。对空间并联机构基本组成单元--构件和运动副,利用旋量键合图,构建动力学模型,并进行模块化处理。在此基础上,调用单元模块,就可建立与可视化的机构一一对应的并联机构旋量键合图模型,按照规则化推导方法,得到适用于现代控制理论的空间并联机构状态方程。以曲柄滑块机构及空间3-UPS/S并联机构为研究对象,验证旋量键合图模块化建模的可行性,给出空间并联机构具有通用性的规则化动力学建模过程,并且进一步分析空间3-UPS/S并联机构匀速及加速运动状态下驱动力、支链约束反力变化规律。这种建模方法的应用为后续构建机器人系统全局动力学模型及控制研究奠定基础。     

独立杆组参数矩阵的表达方法

并联机构中由于各杆组间的约束类型不同导致部分杆组参数向量中含有不独立的混合参数,使得对机构中输出构件自由度数目及性质、机构过约束判断的直观性变差。为构建仅含独立运动参数的杆组参数向量,分别就向量中非独立的"角运动参数"、"非衍生线运动参数"、"衍生线运动参数"展开讨论,基于螺旋理论,通过研究螺旋系的相关性,得到线性无关的基螺旋系,并等价到杆组参数矩阵中,建立独立杆组参数矩阵,最终提出参数垂直分量有效准则。结合该准则,基于GOM自由度新公式,对几种典型机构进行自由度分析,验证这些理论在独立杆组参数矩阵确定、机构自由度求解、输出构件自由度及运动性质分析、过约束判断等方面的应用。     

闭环双驱动混合输出六自由度并联机构运动分析

提出一种分支含闭环双驱动单元、可实现混合输出的六自由度并联机构。分析了动平台混合运动时驱动分支的等效形式,以及独立位姿运动和振动时驱动分支的等效形式;分析了混合运动关于位姿运动输入和振动输入的位置反解,对振动输入的位置反解设计了基于机构运动特点的逐次逼近法;运用螺旋理论求得动平台混合运动时关于全体12个独立广义坐标的一、二阶影响系数,得到从广义输入到动平台旋量速度、加速度的线性映射;通过数值算例分别对位姿运动输入和振动输入的理论分析结果进行了验证,算例仿真表明,提出的两种双驱动输入分配计算规则均能得到确定的混合运动输出。     

Mobility analysis of the deployable structure of SLE based on screw theory

Scissor-like element has a number of applications in deployable structures such as planar deployable structure (PDS) and ring deployable structure(RDS). However, the mobility analysis of the multi-loop deployable structures is made more difficulty by the traditional mobility formula, because the deployable structure is a very complex structure with multi-loop. Therefore, On the basis of screw theory, the calculation method of mobility of deployable structures of SLE is thoroughly discussed. In order to investigate the mobility, decomposing and composing structures(DCS) are developed, and the basic units are able to be obtained. On the basis of the deployable structures’ geometrical characteristics, there exists a closed-loop quadrilateral structure and some non-closed-loop quadrilateral structures in PDS. Also, a six legs parallel structure is present in RDS. The basic units’ mobility can be solved by both the methods of screw theory and topology constraint graphs. Then, composing the related basic units, the formula of planar deployable structures’ mobility can be built and solves the mobility of ring deployable structure. The analysis method solves the mobility analysis of the multi-loop deployable structures which is difficulty by the traditional method, and plays an important role in further research about the mobility of other complex deployable structures.     

Type Synthesis of Lower Mobility Parallel Mechanisms: A Review

Type synthesis of mechanisms aims to systematically determine all possible structures for a specific mobility requirement. Numerous methods based on di erent theories were proposed for type synthesis of lower mobility parallel mechanisms in past decades. However, there does not exist a comprehensive review on these approaches. Therefore, the goal of this paper is to give such a review, classifying the approaches proposed in the literature into three groups, namely, motion-based methods, constraint-based methods, and other methods. The motion-based methods include the Lie group based method, the GF set method, the linear transformation method, the POC set method,and the finite screw method. The constraint-based methods involve the screw theory-based method, the virtual chain method, the method based on Grassmann line geometry and line graphs, and the motion constraint generator method. Other methods contain the enumeration approach based on the general CGK mobility formula and the graph theory method. Upon thoroughly analyzing the characteristics and/or limitations of each method, this review provides a well reference to help researchers find an e ective synthesis method for innovative design and further scientific investigations for mechanisms.     

基于螺旋理论的空间机构自由度分析方法

将螺旋理论应用于空间机构的自由度分析中,采用螺旋理论中的运动螺旋和力螺旋分别来表示空间机构的自由度和约束,并利用螺旋理论中的互逆原理,对空间机构进行约束和自由度分析,总结出求解空间机构的自由度和过约束的方法,举出算例.研究从自由度和约束的基本概念入手,从而保证了方法的准确性和通用性.     

Synthesis of cam-link mechanisms for exact path generationSynthese de mecanismes came-coulisse pour la generation exacte de trajectoires

In this paper, it is shown that there are a significantly large number of cam-link mechanisms that may be used for generating an exact path or for guiding a body through exactly specified infinite positions. Using Gruebler's mobility criterion, structural synthesis is performed to obtain several cam-link mechanisms for path and motion generation. A synthesis technique is also presented to design track-follower mechanisms. The technique utilizes the complex loop closure method and the envelope theory to find the centerline and the contact points of the track. The approach is general and may be applied to any cam-link mechanism used to generate exact paths or to guide a body through infinitely many positions. A method for finding the curvature of the track at the contact points is also given.     

3-P⊥R//4r//R型三维平移解耦并联机构及其位置分析

基于以单开链为单元的三维平移并联机构 ,设计构造了一种 3 P⊥R/ / 4r/ /R型三维纯移动的并联机器人机构 ,进行了机构运动确定性分析及运动输出特性分析 ;给出了其位置分析的正、逆解析解 ,讨论了其运动参数的取值范围及实例计算 ,并分析了该机构的输入 输出运动解耦性。该机构仅由转动副组成 ,便于制造安装 ,动力综合性能好 ,为虚轴机床、机器人、虚轴坐标测量机提供了新型实用机型。     

基于非瞬时支链位形设计的并联机构内部奇异消除方法

引入新支链的冗余驱动方法是目前减少或消除并联机构奇异的有效方法,如何确定所引入支链的结构形式、布置方式和最少支链个数是该冗余驱动方法的核心问题,然而关于这些问题至今尚没有系统的理论和方法。依据螺旋理论系统分析并联机构的约束奇异、驱动奇异和支链奇异三种奇异位形,强调位于工作空间内部的约束奇异和驱动奇异位形是对机构性能影响最为严重的位形,提出一种基于非瞬时支链位形设计的并联机构内部奇异消除方法,以3-RPR型、3-RRR型、4-RPTR型、3-RRRT型和3-RPS型等五种典型的并联机构为例,系统阐述该方法的设计过程。结果表明除了动平台和基平面重合的位形以外,该方法能够消除并联机构的其所有内部奇异位形。该成果为解决冗余驱动方法的关键理论问题提供了参考。     

一种3-TPT并联机构的位置分析与运动仿真

介绍了一种3-TPT并联机器人机构的结构特点,利用螺纹理论分析了该机构的自由度,并对该机构的运动学位姿进行了分析,给出了运动学位姿反解和运动学位姿正解的显式表达式.最后用ADAMS软件对其进行运动学仿真,对动平台自由度及其位姿的理论分析进行了验证.