可重构并联机构研究综述——设计、分析与挑战

王林 ,  James W. Zhang ,  Dan Zhang

Engineering ›› 2025, Vol. 47 ›› Issue (4) : 108 -124.

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Engineering ›› 2025, Vol. 47 ›› Issue (4) : 108 -124. DOI: 10.1016/j.eng.2024.09.022
研究论文

可重构并联机构研究综述——设计、分析与挑战

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A Review on Reconfigurable Parallel Mechanisms: Design, Analysis and Challenge

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摘要

可重构并联机构的兴起源于各应用领域对柔性化与自适应系统日益增长的需求。不同于为特定任务设计且拓扑构型和运动特性固定的传统机构，可重构并联机构能够通过改变自身结构、运动方式及功能特征，动态适应不同任务需求。这种适应性使单一机构能够完成多样化任务，从而减少对多套专用系统的需求。本文系统综述了可重构并联机构的研究进展，阐述了其设计特征、性能分析方法及面临的关键挑战。文中首先介绍可重构并联机构及其类型分类，进而探讨了机构构型综合方法，建立了涵盖可重构度、工作空间、奇异性、刚度及动力学等相关的性能评价指标体系。研究还揭示了在系统化设计理论、统一性能分析、评价指标体系，以及在工程实现中高效控制策略开发与多技术融合等方面所面临的挑战。最后，本文对可重构并联机构的未来研究方向进行了展望。

Abstract

Reconfigurable parallel mechanisms were first discovered in response to the growing demand for flexible and adaptive systems in various fields. Unlike traditional mechanisms, which are designed for specific tasks and have fixed topology and mobility characteristics, a reconfigurable parallel mechanism can be adapted to different situations by changing its structure, motion, and function. This adaptability enables a single mechanism to perform a wide range of tasks, reducing the need for multiple dedicated systems. This paper presents a comprehensive review of reconfigurable parallel mechanisms. The characteristics of their designs, analyses of their properties, and challenges they face are reported. The beginning of this paper features an introduction of reconfigurable parallel mechanisms and their classification into different types. Methods for synthesizing reconfigurable parallel mechanisms are discussed. A performance evaluation index related to reconfigurability, workspace, singularity, stiffness, and dynamics, among other indices, is presented. This review covers the challenges faced in the creation of systematic design theories, unified performance analyses, evaluation index systems, and in the implementation of reconfigurable parallel mechanisms, such as the development of efficient control strategies and integration with other technologies. The paper concludes with a discussion of future research directions for reconfigurable parallel mechanisms.

关键词

可重构并联机构 / 设计综合 / 性能指标

Key words

Reconfigurable parallel mechanism / Design synthesis / Performance index

引用本文

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王林,James W. Zhang,Dan Zhang. 可重构并联机构研究综述——设计、分析与挑战[J]. 工程（英文）, 2025, 47(4): 108-124 DOI:10.1016/j.eng.2024.09.022

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1 引言

随着科学技术的快速进步以及服务业、制造业、航空航天和自动化生产线等不同应用领域的需求日益增长，市场对机器人装备的需求也显著增长。目前已经研制出包括串联机器人、并联机器人和混联机器人在内的多种机器人类型，其中部分机型在各类应用场景中展现出显著优势并成功实现商业化[1‒4]。然而，不断变化的环境与操作条件使得任务日益复杂多样。因此，这些任务需要具备更强灵活性与适应性的机器人装备。传统机器人专为特定任务设计，具有固定的拓扑结构与运动特性，很难满足现代工业应用需求。为此，具有可重构拓扑结构与可变运动特性的可重构并联机构应运而生，以满足复杂多样的应用需求[5‒6]，如医疗护理[7‒8]、航空航天[9‒10]、足式机器人设计[11‒14]、灵巧机械手设计[15‒17]、智能制造[18‒19]、低压断路器机构设计[20]、抓取装置设计[21‒24]以及建筑可重构连杆结构设计[25‒27]。面对这些不断变化的需求，机器人结构的创新设计显得尤为重要。

可重构并联机构是指构型与自由度可动态调整的机械系统或装置。这类系统能够适应多种作业条件并执行不同任务，无需进行部件更换或结构性改造。可重构并联机构主要分为五类：运动转向机构、变胞机构、折纸启发机构、张拉整体机构及其他多模态机构。Wohlhart [28]首次提出了运动转向机构的概念，他发现该类机构在通过特定奇异位形后，其运动度会发生变化，而拓扑结构保持不变。Dai和Rees Jones [29]在研究装饰性纸盒折叠时提出了变胞机构。基于演变机理，机构可以改变拓扑结构和运动特性。这两类机构的提出推动了可重构并联机构的研究。Mruthyunjaya [30]指出，变胞机构的出现极大地推动了机构学创新设计的发展。变胞机构是一类源于折纸等效机构[29]的可折叠、可展开的机构，也可称为折纸变胞机构。因此，这类机构通过折纸原理实现多样的形态变化[31]。这类机构包括变胞经典机构[32‒34]、变胞拓扑机构[5,35‒36]、变胞折纸机构[29,31,37]、变胞变换机构[38]以及变胞并联机构[39‒43]。折纸启发机构源自装饰性纸盒折叠技术[29]。通过将折痕作为旋转轴、面板作为连杆，基于折叠原理构建出新型可展机构。这类机构是实现建筑应用适应性与变形性的关键赋能技术，能够提供所需的结构与功能多样性，从而创建响应变化需求、优化空间利用、提高能源效率的建筑，同时实现创新且美观的设计[44]。折纸启发机构的典型代表包括Sarrus折纸机构[45]和球面变胞机构[46]。该类机构具备可展开使用、可折叠储运的显著优势特性[47]。在当代机器人技术发展背景下，人机共融已成为下一代机器人系统的显著特征。为满足建筑与结构工程领域的需求，大量研究致力于探索融合刚柔特性的张拉整体机构[48‒50]。此外，多模态机构（又称无拆解重构并联机构）因其卓越的环境适应性，近年来也受到广泛关注[51‒54]。

对可重构并联机构设计方法的研究已相当广泛。这类综合方法大致可分为五类：①经典机构的组合；②增加运动副；③经由可控的奇异位形[28,55‒61]；④特殊轨迹规划[62]；以及⑤可变驱动方式[63‒64]。经典机构的组合方法又可进一步分为两类：基于Bennett机构的组合[32,53‒54,65‒70]，以及源自Bricard机构的组合[21,71‒75]。通过将这些机构进行装配，去除公共构件并固化公共关节后，可以获得全新的可重构并联机构。另一类思路是通过增加关节来实现可重构，如引入若干低副关节[11,32,76‒79]、可重构关节[39‒42,80‒83]，以及可锁定关节[35,84‒87]。其中，可重构关节能够通过施加几何约束来改变关节属性；而可锁定关节在锁定后，则能够改变机构中的构件数目和关节数。

可重构可实现多种目的，包括提升效率、降低成本、提高生产率以及改善性能。从性能分析的角度来看，可重构具有诸多优势，如扩大工作空间[88‒90]、改善动力学性能[91‒93]、改变自由度[23‒24,32,86]，以及避免奇异位形[94]。事实证明，可重构是提升并联机构整体性能的一种行之有效的方法，能够带来多方面的收益。

大量研究集中在可重构并联机器人设计方法、性能评价、控制策略以及优化方面。然而，针对可重构并联机构的综述性工作仍然十分有限。早在2009年，Zhang和Dai [5]就对变胞机构的发展进行了综述。Brunet等[95]提出了关于模块化可重构机器人发展趋势的综述。Aimedee等[96]于2016年系统回顾了所有可重构机构。近期，文献[6]阐述了关于变胞机构的新设计理念及其创新应用。然而，针对可重构并联机构在分类、设计、性能分析及其面临挑战等方面，仍缺乏系统性的总结。本文正是围绕这三个方面展开研究，以期为可重构并联机构领域的研究人员提供参考。此外，我们还对现有研究中的问题与挑战进行了分析，以推动该方向的进一步研究。

2 可重构并联机构的分类

在过去的数十年中，研究者针对多种类型的可重构并联机构开展了广泛研究，其中包括运动转向机构、折纸启发机构、张拉整体机构以及其他多模态机构。可重构并联机构的快速发展主要得益于其关键优势：仅需较少驱动器即可实现多种运动模式，以及可在无需拆解的情况下通过重构节省时间。

近年来，研究人员设计并分析了大量新的可重构并联机构，并提出了多种切实可行的实现途径。这些进展极大地推动了机构学的发展，使可重构并联机构在诸多应用中能够显著提升效率、降低成本并改善性能。表1对不同类型的可重构并联机构在优势、局限性以及重构策略等方面进行了对比。

2.1 运动转向机构

根据Wohlhart [28]的定义，运动转向机构在经过奇异位形时会改变其整体运动自由度。Wunderlich机构就是一种典型的运动转向机构，如图1所示。运动转向机构主要可以分为两大类：单环机构与多环机构。单环机构由于结构更为简洁、关节数量少，逐渐引起越来越多的关注。

López-Custodio等[97]通过研究两个同心奇异环面相交所形成的运动，探索了可重构的Bricard平面对称机构，并在此基础上组合形成新的可重构机构。采用同样的方法，文献[98]又提出了若干具有不同重构分支的Bricard机构。Feng等[73]证明5R/4R（其中，R表示转动副）机构可由平面对称的Bricard机构演变而来，并能够分岔生成Bennett机构。Guo等[68]通过装配Bennett机构，设计了一系列空间单环过约束机构，可用于综合可折展机构。Zhang和Dai [99]研究了双球面6R过约束机构的二分岔和三分岔运动，并证明该机构通过可控奇异位形可实现重构，从球面4R机构转变为串联运动链。Liu等[53]提出了一种基于代数的系统的方法，设计了具有多种运动模式的单环6R、7R和8R Bennett类机构。Pfurner [100]通过组合两个单环过约束6R机构综合出一种新的单环8R机构，并进行了运动分析。Chai等[68]设计了一种单环8R运动型机构，并识别出了其可控奇异位形。文献[101]又提出了两类由球面和平面4R机构构成的8R机构。Hsu和Ting [102]提出了一种基于RPRP链（其中，P表示移动副）作为单元的系统化设计方法，用以设计过约束机构。Kong [52]基于双四元数的环路方程求解，揭示了一种新型7R空间机构的运动模式。

研究者还提出并探索了多环运动转向机构。Qin等[55]设计了一种基于“Queer Square折纸”的机构，并研究了约束奇异对多分岔现象的影响。Song等[65]通过四个Bennett机构构建了一个网状机构，并进一步优化装配，形成了五种新的过约束机构。López-Custodio和Dai [103]提出了一种利用二自由度运动链来设计运动转向机构的方法，该方法能够生成“Bohemian dome机构”，并给出了一个具体实例。在另一项研究中，López-Custodio和Müller [104]提出了一种综合运动转向并联机构的方法，其核心思路是通过增加附加支链并施加约束来改变运动自由度。Ye等[105]将可重构支链与菱形运动转向支链结合起来，设计了一类新型可重构并联机构，如图2所示。

2.2 变胞并联机构

变胞机构的设计原理是在连续运动过程中通过施加几何约束实现拓扑结构的重构和运动自由度的改变。这种适应性使机构能够在不同的工作环境中工作，并满足多样化的任务需求。变胞机构与运动转向机构的区别在于重构的方式。前者可以通过可控的奇异位形或可重构关节来改变拓扑结构和自由度，而后者必须经过奇异位形才能改变自由度，并且其拓扑结构保持不变[6]。

Ma等[32]提出了具有球面和平面运动的6R变胞连杆机构以及具有Bennett和球面运动的 6R变胞连杆机构，并给出了其构型转变条件。Zhang和Dai [67]设计了一种新型可切换Bennett、平面和球面运动的混联支链，并用于构建新型变胞并联机构。文献[70]在Bennett机构中增加两个转动副后，形成了一种新型6R变胞并联机构，并进一步研究了其运动曲线、分岔点和运动分支。Kang等[76‒77]提出一种新方法，通过在Schatz连杆中增加一个转动副，构造了两类新型7R变胞并联机构，并通过求解约束方程分析了其不同的运动分支与分岔点。Tang和Dai [38]研制了一种仿生四足机器人，其躯干部分采用八杆单环变胞机构，并提出了相应的控制策略。Chai等[33]将Bennett机构串联连接，构建了六类新型变胞并联机构，并揭示了其分岔特性与群结构之间的关系。

此外，采用可重构关节同样是一种极具潜力的变胞并联机构设计思路。Wei和Dai [106]首次提出了可重构转动副（vR），并据此构建了一类可重构且可折展的柏拉图机构。Zhang等[80]探索了多种不同形式的变胞机构，这些机构引入了基于折纸启发的变胞运动副，可在3R模式与Hooke副模式之间切换。此外，研究者还进一步研究了轴线可变运动副（vA）以及SvPSv变胞支链（Sv：vA副的源相位；P：移动副）[81]，并研究了具有Bennett、平面和球面运动机构及其具有不同运动模式的混合支链[107]。Gan等[39-42,82]设计并分析了一种新型可重构Hook副（rT），并开发了3-(rT)C(rT)、3-(rT)PS、3-R(rT)S和3SPS-1C(rT)等机构（C：柱面副；S：球面副）。与此同时，他们还提出了可重构转动副（rR）与3(rR)PS机构，并对其拓扑进行了优化，以提升运动性能[83]。文献[108]又提出了一类具有3~6自由度的新型变胞机构，其支链采用混合可重构形式。Wang等[109]基于螺旋的线性相关及其几何特性，设计了一种可重构球面副并构建了变胞机构。Zhao等[110]针对空间应用，设计了一种大型多指手结构，其指关节单元采用变胞机构，并在其中集成了可锁止球面副。此外，Wei和Dai [43]生成了一类包含变胞关节的新型变胞机构，该关节在1R2T到2R1T模式的重构转变中发挥着关键作用。图3展示了该变胞机构的两种典型运动形式。

2.3 折纸启发的变胞机构

折纸艺术与工程的交汇催生了许多新成果，折纸启发的变胞机构在机构学的创新发展中取得了重要进展。另一类与之相关但有所区别的机构来源于剪纸。这两种方法同为纸艺与工程技术的结合，但各有特征。剪纸通过折叠与切割纸张形成三维结构，而折纸仅通过折叠即可实现类似效果。折纸启发的变胞机构利用折叠图样设计结构，其形态或构型可通过折叠与展开实现变化。折纸启发机构的典型代表是Sarrus机构[111]，其设计灵感正是来源于折纸折叠。Nelson等[112]设计了一种受折纸启发的顺应性滚动接触元件，该元件能够在舒展状态与收缩状态之间切换，并可应用于具有大角度位移的顺应性多稳态转动副。Wang等[36]提出了一种源自折纸的设计方法，并构造了8R机构。其设计流程如图4所示。所设计的折纸启发的8R机构的运动模式的切换过程如图5所示。Wei和Dai [37]提出了两种单自由度具有平面-球面运动的过约束机构，并揭示了其装配条件和几何约束关系。

部分运动转向机构也可由折纸演化而来。Qin和Dai [55]分析了一种基于Queer Square折纸机构[28]的新型机构的多分岔现象与约束奇异性。Kang等[56]运用螺旋代数方法识别出Queer Square折纸机构的六种运动分支，结果表明该方法能够有效且简明地求解复杂多环机构的约束系统。

此外，已经有大量研究围绕折纸启发的变胞机构展开。Salerno等[113]开发了一种新型4自由度抓取装置，适用于微创手术，该装置由折纸启发的并联机构和扭转部件以及柔顺抓取装置组成。Zhang和Dai [114]描述了基于剪纸折叠的8R变胞机构，并给出了由该8R机构演化得到的两类6R变胞机构的构型过程。Xiu等[115]提出了一种类Fulleroid的可折展阿基米德机构的设计方法，并完成了自由度与运动学分析。Wei和Dai [116]研究了2自由度双平面对称空间八杆机构，该机构能够实现精确的直线运动，并进一步利用该八杆机构构建了一类具有径向往复运动的可折展柏拉图机构。Barreto等[117]提出了一种基于图论与群论的方法，用于设计具有更高复杂度和更强运动能力的折纸启发机构，可作为构建多环折纸启发球面机构的基本单元。Tang和Dai [118]通过八环八面翻转体的运动等效关系获得了一种八杆机构，并研究了其运动分支特性。文献[119]提出了一种受折纸启发的双球面机构，并发现其存在两种运动模式（曲柄-摇杆模式与双曲柄模式）。Qiu等[120]提出了一种适用于折纸启发机构的反作用力分析建模方法。

2.4 张拉整体机构

张拉整体机构是一类具有独特特性的可重构结构，近年来在诸多领域受到了广泛关注。据文献[121‒124]报道，张拉整体结构由承压构件（压杆）和承拉构件（绳索与弹簧）共同组成，并通过整体平衡保持稳定。张拉整体机构具有一些显著的内在优势，如惯量小、自然柔顺性以及可折展性。

在机器人领域，Venkateswaran等[125]设计出一种仿生毛毛虫式管道检测机器人。该装置结合了张拉整体机构与四杆轮系机构，有效解决了机器人在管道弯头及分支处灵活运动的难题。Cimmino等[126]进一步提出了利用张拉整体结构构建可再生能源供应系统的概念。他们设计了一种风力发电机，能够将受风激励单元中绳索储存的应变能转化为电能，从而为可持续能源提供了一种新的途径。在空间探测方面，Khaled等[127]提出了基于张拉整体原理的创新型微型钻机，该钻机可同时应用于地球与空间的钻探任务，能够提升机动性、降低钻探成本，并通过减少碳排放来减轻地面钻探对环境的不良影响。

与传统机构相比，张拉整体机构的分析更具挑战性，这是由于满足静力平衡条件所需的方程具有高度复杂性。借鉴Wenger和Chablat [128]的研究成果，提出了一种适用于特定类别平面张拉整体机构的解分类方法。该方法不仅有助于深入理解机构的运动学特性，还为精确设计与控制策略提供了新思路。针对弹性变形、几何非线性、摩擦和冗余驱动等复杂因素带来的挑战，Peng等[129]提出了系统化的张拉整体机器人建模与控制方法，其框架如图6所示，为方法应用提供了形象参考。在控制层面，文献[48]探讨了主动张拉整体结构的路径跟随问题，旨在通过先进控制算法实现所需的张拉整体构型或末端执行器位置。进一步地，Furet和Wenger [49]针对一个由两级X型机构串联构成的2自由度张拉整体操作臂，研究了其复杂运动学问题，尤其是X型机构围绕可变瞬时中心旋转所引发的独特挑战。为提升扭绞线圈驱动器的输出力，Zhou等[50]提出了多股扭绞线圈驱动器的制造与力学增强原理。与传统单股扭绞线圈驱动器相比，该方法在使用相同纤维材料的情况下实现了超过三倍的输出力提升。

2.5 其他多模式机构

多模式机构是一类广泛的可重构并联机构，能够呈现多种操作模式或构型。这些机构可通过不同模式间的切换来执行多样化功能或适应不同需求。模式转换可通过机械驱动、形状记忆材料或其他方法实现。Kong [130]开发了一种具有两种操作模式的三自由度多模式机构DIRECTOR。为克服模式切换时的约束奇异问题，该机构采用了制动器与同步带。Li和Hervé [131]通过群论方法确定了通过分岔运动实现两种工作模式的几何条件。Gogu [57]提出新方法并构建了一类具有分岔空间运动的T2R1型并联机构。Nurahni等[132]设计了一种新型踝关节康复装置，通过训练模式切换实现不同的康复运动。然而，这些无锁止关节的多模式机构必须经过约束奇异位形才能完成运动模式切换。

带锁止关节的多模式机构已得到广泛研究。在Kong [130]研究的基础上，文献[133]进一步提出了一种带锁止关节的三自由度可重构多模式机构，可在不需要通过约束奇异位形或支链中子链自身运动的情况下实现模式切换。Carbonari等[84]提出了一类采用锁止系统的可重构模块化并联机器人，可实现构型与自由度的变换。Li等[85]提出基于块邻接矩阵的新方法研究带锁止关节多模式机构的构型变换。文献[35]实现了通过双轴变胞关节构建具有1R2T与2R1T模式的可重构机构综合方案。Flores-Mendez等[86]阐述了将带锁止旋转关节的可重构平台与3T并联机构集成的3T1R可重构机构综合方法。Riabtsev等[87]提出新型二自由度锁止关节，并分析了相关运动学指标。

此外，采用可重构平台可使机构无需经过约束奇异即实现操作模式转换。可重构平台通常由低副与二元连杆构成单环路结构。Kong和Jin [134]设计了通过Bricard连杆可重构动平台实现的多模式平移/球面机构，如图7所示。通过锁止Bricard连杆可重构动平台的不同转动关节，该平台可实现5种运动模式。Wang等[22]提出具有可重构动平台的广义并联机构，可用于抓取重型大尺寸物体。Tian和Zhang [21,135]及Tian等[136]采用新型闭链可重构平台系统性地提出了多模式可重构机构的综合方法，显著提升了运动性能与功能性。Hoevenaars等[137]设计了两类带可重构平台的三自由度机构，并系统分析了雅可比矩阵[24]。Wu和Dong [138]介绍了能输出Schönflies运动的Hexa并联机构。Haousa等[23]开发了可通过折叠顶部平台实现微创手术抓取的球面并联腕部机构。

3 可重构并联机构分析

近年来，可重构并联机构因其能够重新配置构型并改变输出运动而得到广泛研究。这类机构在适应复杂多样化任务需求方面展现出巨大潜力。与传统并联机构相比，可重构并联机构具有多重优势，且应用前景广阔。其性能分析对此类机构的设计、性能评估与优化具有重要作用，其分析维度涵盖重构特性（确定所有运动分支）、工作空间、奇异性、动力学及刚度等多重指标。

3.1 重构特性

具有可变操作模式的可重构机构的复杂结构及运动学特性为重构特性分析带来了重大挑战。然而，为实现进一步控制、优化与应用，亟须确定可重构机构的所有运动模式。学术界已开展广泛研究以识别可重构机构在可变运动模式方面的特性，并由此提出多种分析方法。

值得注意的是，通过分析可重构机构的全局运动学，可描述其整体运动行为（包括可变操作模式）。代数几何法是广泛应用的有效方法[139‒144]。Pfurner和Kong [69]对具有可变自由度的7R机构进行代数分析，为运动模式与过渡构型的识别提供了理论依据。Liu等[53]提出采用代数几何工具高效论证基于Bennett机构的多模式特性。

在具体分析过程中，常将旋量理论与代数方法结合运用。文献[32]利用旋量理论分析了6R机构的球面运动展开与重构过程，结果表明，闭环方程的解与可变运动模式之间存在关联性。Tian等[136,145]运用旋量理论推导单环可重构连杆机构中的约束力和力偶，从而改变构型与自由度特性。Kang等[146]采用旋量理论分析了双环6R1P变胞机构的多分岔重构特性，获得6个分岔点及对应运动分支的特征，最终机构重构变换过程如图8所示。

为克服代数几何法中半角正切替换在重构分析中的局限性，研究者采用基于对偶四元数的方法[53,147‒148]分析多模式机构。Liu等[54,149]提出基于对偶四元数与质分解的统一运动学映射方法，该方法被证明能有效分析多环和单环机构的操作模式与运动特性。研究[52,150‒152]采用对偶四元数与自然指数函数替换的高效方法，论证了7R机构具有五种运动模式并揭示其过渡条件。作者后续运用对偶四元数及代数几何工具在构型空间中进行重构分析，发现可变自由度空间4G机构具有一种二自由度运动模式及一至两种单自由度运动模式[150]。

此外，Study运动学映射还可用于推导代数约束方程。文献[153]通过基于Study运动学映射计算约束方程，表征了4-RUU（4-R：4个旋转关节；U：万向节）机构的操作模式。文献[154]讨论了3-RPS并联机构的全局运动学行为特性，并通过约束方程对应理想条件的质分解检测其操作模式。Kong运用运动学映射与代数几何对三自由度并联机构[155]及可变自由度单环机构进行可重构分析，成功识别不同模式间的切换点[156]。随后Nayak等[157‒158]利用Study运动学映射获得两种典型三自由度并联机构的操作模式。文献[159]通过运动学映射与代数方法导出的运动曲线，展示了不同运动模式及过渡构型。

其他方法也在不同研究中得到应用。He等[79]采用数值方法处理单环7R机构的运动学分析，给出三种操作模式，并通过代数方法验证分析结果。文献[34]使用数值方法探索源自Waldron连杆和Bricard连杆的三种连杆机构的多个运动分支。Schadlbauer等[160]采用瞬轴面法表征低自由度并联机械手的操作模式。文献[73]运用Denavit-Hartenberg（DH）矩阵法对平面对称Bricard连杆进行全面运动学分析，揭示了显著的分岔行为特征。Ma等[161]采用DH矩阵法进行运动学分析，将闭环方程的运动曲线映射至构型环面，发现运动周期与双点是连杆分岔的判定基础。

3.2 工作空间

机构工作空间的评估是确定操作空间和规划运动轨迹的重要依据。传统并联机构的工作空间有限，因此需要研究其扩展方法。工作空间的尺寸和形状受多种因素影响，包括杆件长度、关节旋转角度以及部件间的干涉等。

Nurahmi等[162‒165]采用代数几何方法和欧拉参数化计算了3-rRPS变胞并联机构的工作空间，发现工作空间形状随关节参数值变化而改变。Zhao等[166]研究了一种新型空间站远程机器人系统（SSRMS）式可重构机构的工作空间，该机构配备可锁止被动伸缩杆，并对比了四种构型的可达球面区域映射，图9中的结果显示两个可锁止被动伸缩杆对该机器人运动能力的影响。Wang等[167]报道了由三个柔性手指构成的可重构机械手，并获取其抓取工作空间。采用三维搜索法[168]求解3-RPRP机构工作空间，无需复杂运动学建模，使过程比以往更直观可控。Nayak等[169]通过对约束方程关于驱动关节变量求导，研究了4-rRUU机构的工作空间。

工作空间的扩展主要分为设计阶段和优化阶段。目前已探索多种并联机构工作空间扩展策略：Viegas等[88]采用三种技术（扩展驱动范围、增大基座平移量和动态关节重构）并验证其有效性；类似地，文献[89]采用移动基座扩大机器人工作空间；文献[90]提出基于Delta机构的冗余可重构机构，分析表明该重构设计相比Delta机器人提升了操作工作空间性能。此外，Gao等[170]通过将变胞手部工作空间分解为手掌和手指两部分进行研究，仿真结果表明重构设计有助于工作空间拓展。为避免绳索与周边环境干涉，Zhang等[171]设计了一种具有大工作空间的新型可重构绳驱动并联机器人。

在完成机构结构设计后，另一种有效的工作空间扩展方法是参数优化。Nayak等[172]通过可视化4rRUU机构的平移工作空间，优化其设计参数，在减小机构尺寸的同时增大了无奇异且无干涉的工作空间，从而提升性能。Huang等[173]对新型可重构机构进行工作空间分析，并将分析结果作为优化指标以改进机构性能。Essomba等[174]揭示了机构参数对工作空间的影响机制，并通过参数优化实现了性能提升。

3.3 奇异性

奇异性分析是可重构并联机构设计与控制的关键环节，因为奇异位形会显著影响系统的性能与稳定性。作为一种具有多构型特征的机器人系统，可重构并联机构可能在特定构型或构型转换过程中出现奇异位形。奇异位形是指运动学方程未定义的构型，会导致机构失去控制和稳定性。本文将探讨可重构机构奇异性分析的研究现状。奇异性分析方法主要包括解析法、仿真法和实验法。奇异规避与检测作为奇异性分析的重要方面，能够有效提升机构性能与稳定性。该分析技术在新机构设计方法开发、控制策略改进以及可重构机构性能与稳定性评估等领域具有广泛应用。

Karimi等[175]提出一种具有自重构能力的新型3-RPR机构，可通过几何形变规避奇异位形，从而扩大工作空间。Nurahmi等[176]通过雅可比矩阵研究驱动奇异并绘制奇异曲面。Bouzgarrou等[177]采用新的几何方法分析3-CRS机构的奇异性，该方法通过考虑支链远端连杆形成的三个平面的相对几何构型来简化分析过程。为减少计算时间并克服奇异性限制，Camacho-Arreguin等[178]引入基于傅里叶分析的新方法，通过分解雅可比矩阵识别奇异，并对其进行规避优化以改变可重构机构运动。Han等[179]基于旋量雅可比矩阵研究三种操作模式下正逆奇异与构型的关联性，并通过格拉斯曼几何法验证分析结果。Marchi等[180]在双边法分析3-RRR机器人的基础上，推广了n-RRR（n：链数量）平面可配置机构正、逆及复合奇异性分析方法。Wei等[181]研究发现可折展多面体机构的奇异性与多重分岔密切相关，两者共同影响机构运动。Wang等[182]揭示具有远程运动中心（RCM）的机构存在三个运动分支和两个分岔点，并证明工作空间内除分岔点外不存在驱动或约束奇异。Wu和Bai [183]对重新设计的可重构3-RRR球面机构进行两类奇异性分析，如图10所示。图10（a）表示奇异轨迹位于规则工作空间边界；图10（b）展示约束奇异出现在内部规则工作空间；图10（c）表明驱动奇异轨迹分布于可达工作空间的内部与外部。通过消除所有奇异轨迹可扩大灵巧工作空间范围。Valero等[184]研究4自由度3UPS/RPU机构的重构策略以规避工作空间内II型奇异位形。文献[90]分析了冗余可重构Delta型并联机器人的奇异条件与重构策略的关联性。Li等[185]采用格拉斯曼线几何法阐明参数可重构并联机构的所有奇异状况，为执行器精确控制提供必要依据。

3.4 动力学特性

可重构机构的动力学特性指其运动行为特征，包括速度、加速度、稳定性及对外力的响应等方面。这些特性对可重构机构的设计与控制至关重要，直接影响系统的整体性能与功能。动力学特性研究有助于改进控制策略并开发新型机构设计。并联机构动力学建模常用方法包括拉格朗日能量法、牛顿-欧拉方程和虚功原理。然而，由于可重构机构能够改变拓扑结构与操作模式，研究不同运动阶段对应的运动学与动力学特性成为可重构并联机构的重要方向。

Chang和Jin [186]基于牛顿-欧拉公式构建动力学方程。Song等[187]开发了基于牛顿-欧拉法的分析方法，用于研究力约束与几何约束对受约束变胞机构的影响，最终建立了统一动力学模型及系统化的数值迭代算法求解动力学方程。文献[188]采用基于全局矩阵描述的递归牛顿-欧拉法生成自重构机器人的动力学方程。Gan等[189]对具有纯转动和纯移动的变胞并联机构进行了动力学模型构建的解析研究。Tang等[190]利用拉格朗日公式推导了虚拟等效并联机构的动力学模型。Gan和Dias [191]运用旋量理论对变胞并联机构进行统一动力学分析，重点基于虚功原理确定控制输入力。Rong等[192]依据虚功原理推导了统一逆动力学模型，并采用Adams软件（美国MSC软件公司）获得3-PXPS（X代表U或R运动副）机构的动力学分析结果，如图11所示。此外，瞬时螺旋轴（ISA）法可在无需构建雅可比矩阵的情况下推导并联机构的速度与加速度，因此该法能通过代数几何方法方便地实现操作模式的参数化。Nurahmi和Gan [193]运用此方法研究了3-rRPS机构在两种运动模式下的动力学行为。

构型转换的动态可靠性是确保具有多构型变胞机构在工程应用中正常运行的关键因素。Chen等[194]结合所提方法与基于神经网络的蒙特卡洛法，构建了针对不同转换过程的动态可靠性模型。Wang [195]通过计算最大李雅普诺夫指数评估可控变胞码垛机器人的动态稳定性。文献[196]开发了综合考虑多重失效模式及随机/区间变量的评估方法。Song等[197]研究了重构转换过程中产生的运动对平面约束变胞机构动力学特性的影响。

动力学研究的目的常与控制策略的开发和理解密切相关。可重构并联机构的实时控制始终是项挑战。机构需具备实时构型切换能力，这要求高速高精度的控制技术，对于大型复杂机构尤为困难。该过程需采用先进控制算法及高性能传感器与执行器。多位学者致力于解决该问题。Nouri等[198]应用神经网络方法进行可重构机器人的运动规划，采用基于多层感知器的神经网络进行数据训练。Huang等[199]根据动力学模型采用模糊比例-积分-微分（PID）控制器管理可重构机构。Liu等[200]研究基于电机分时控制的运动策略，并通过样机实验验证其有效性。其他关于可重构机构控制的研究可参考文献[201‒205]。

3.5 刚度分析

可重构机构的刚度分析涉及评估机构在载荷或力作用下的刚性及抗变形能力。深入理解可重构机构的刚度特性有助于工程师做出科学的设计决策、优化性能，并确保机构在实际工况下按预期运行。此外，刚度分析有助于识别潜在失效点，并为制定控制策略提供依据以提升机构整体可靠性。

Zhao等[206]推导了连续刚度矩阵以及任意方向的移动与转动刚度。Moosavian和Xi [207]提出通过锁止被动关节静态提升机器人刚度的新方法。Qiu等[208]将折痕视为转动关节、面板视为连杆，研究了折纸式纸盒的刚度特性。Zhang等[209]对模块化可重构并联机器人进行静刚度分析，探究影响刚度的因素并提升整体刚度。Zhao等[210]比较可折展铰接桅杆与其结构等效体的刚度模型（包含剪切刚度和扭转刚度），发现刚度显著提升。为评估类Exechon并联运动机构的刚度，Tang和Zhang [211]构建包含所有关节和支链柔度的扩展运动静力学模型，数值结果验证了扩展刚度模型的准确性。图12的对比刚度分析表明，所提出的Exechon变体机构具有与Exechon机构相当的刚性性能。文献[212]提出考虑驱动与约束引起主要部件变形以及期望轨迹周边子工作空间内刚度分布的刚度模型。Zhao等[213]采用虚拟关节法与矩阵结构分析对n(3RRlS)可重构串并联机器人进行理论刚度分析。You等[214]通过集成可重构性设计新型Stewart机构并推导量纲统一的整体旋转刚度矩阵，建立刚度优化函数。Huang等[215]分析新型四自由度可重构机构的刚度特性。

3.6 其他性能指标

除上述指标外，学者们还研究了其他性能指标。Gan等[216]提出基于旋量理论的运动/力传递分析方法，据此可优化机构参数。Ge等[217]随后开发了运动学与误差分析技术，用于确定多级变胞机构的运动轨迹与运动精度。Li等[218]通过将增广阿苏尔杆组转换为阿苏尔杆组，探索了一种分析变胞关节约束力的简单方法。Kumar和Rani [219]采用李雅普诺夫理论和Barbalat引理对闭环系统进行稳定性分析。

4 挑战与展望

设计和实现可重构并联机构所面临的挑战在于如何平衡可重构性优势与设计、控制和实施过程中的实际限制。相比传统机构，可重构并联机构具有灵活性、适应性和多功能性等优势，但这些优势是以增加设计与控制复杂性、维持稳定性与可靠性以及对任务变化的高适应性为代价的，平衡这些因素均具有挑战性。

可重构并联机构的关键挑战在于机构本身的复杂性。机构需以安全、高效、可靠的方式实现构型变换，这要求使用多个驱动关节，从而增加设计与控制的复杂度。此外，机构必须承受重复重构、重载荷及恶劣环境的需求，需要采用兼顾耐久性与可靠性的稳健设计。可重构并联机构还需与传感器、执行器和控制系统等其他系统集成，该过程需要精心设计与协调，由于涉及多种不同要求和规格系统的整合，实施难度较大。尽管目前已开发多种方法应对这一挑战，但仍缺乏系统性和通用性设计理论的研究。需要深入探索综合考虑环境变化功能需求、构型转换以及可变自由度的可重构并联机构综合设计方法。

另一挑战在于缺乏统一的性能分析与评价指标体系。现有研究大多沿用传统并联机构的分析方法，并针对可重构特性进行适当调整。特别是需要重点解决可重构性理论体系构建、可控奇异位形的影响机制以及不同模式性能评价指标的对比等关键问题。因此，有必要建立通用性能指标体系与综合分析框架。

最后，可重构并联机构的成本是制约其应用的重要障碍。这些机构的研发与生产成本高昂，难以在某些应用中体现成本效益。

总体而言，可重构并联机构的挑战在于平衡可重构性优势与设计、控制和实施的实际限制。这需要全面理解机构的设计、性能与操作要求，并重点关注先进控制算法及高性能传感器和执行器的开发。

可重构并联机构的发展前景与趋势高度依赖于机器人学、控制工程、机电一体化和材料科学等领域的进步。其主要发展趋势与前景如下。

（1）创新应用领域拓展。可重构并联机构正被日益广泛地应用于空间探索、水下作业、机械操作、制造、印刷、地面行走、农业、电力检测、微操作、微装配及医疗健康等领域。随着新结构的提出，其应用领域将进一步扩大。

（2）加强设计、演变与分岔理论研究。需要形成通用性能评价指标体系，并推进控制算法发展以提升机构精度、效率与可靠性。

（3）多技术融合创新。通过与人工智能、物联网等技术融合，提升实时适应性、预测性维护、能效优化、精度提升与可及性增强等能力，拓展在农业、制造、航空及手术机器人等领域的应用。

（4）注重可持续性发展。通过设计提高能源效率与环境友好性，顺应可持续发展趋势。

总体而言，可重构并联机构前景广阔，相较传统机构，其优势明显，应用领域持续扩展。技术进步与对柔性自适应系统需求的增长将共同推动其未来发展。

5 结论

综上所述，近年来可重构并联机构取得显著进展。日益增长的复杂多功能系统需求推动该领域研究迅速发展。本文综述了已提出的各类可重构并联机构及其设计方法，探讨了不同机构的可重构特性，论述了常用性能指标与分析方法，最后指出了面临的挑战与发展趋势。

可重构并联机构未来发展前景广阔，持续研发将推动机构学的进一步创新突破，包括集成先进控制算法，开发较现有材料更轻质、更强韧、更柔性的新材料，从而打造更具适应性的可重构并联机构。此外，新型智能化系统的开发将使可重构并联机构能够在真实环境中实现自主运行。

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