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对于多个运动任务的平面连杆机构的拓扑与尺寸综合

摘要：本文介绍了结合使用 of planar linkage mechanisms satisfying multiple kinematic tasks. First, a Graph满足多个运动任务的平面连杆机构用于合成两系统的方法。首先Theory-based method is used to exhaustively enumerate the topological alternatives for a基于理论的方法进行详尽列举一个拓扑方案 given problem. Then each feasible alternative is automatically dimensioned using the Precision给定的问题。然后每一个可行的替代方案是使用自动尺寸精度 Position Method; this computation includes space and design constraints. The existing位置方法；该计算包括空间和设计约束。用现有的methods to synthesize multiple tasks solve, in sequence, a decomposition of the problem方法来合成多个任务的解决方案，在序列中，分解单运动任务的问题 into single kinematic tasks. The task decomposition and the topology selection for each task。任务分解和每个任务的拓扑选择are usually performed by hand. This process leads to topologies with a repeated pattern and通常用手执行。这个过程会导致拓扑结构进入一个重复的模式和could lead to ignoring potentially desirable topologies. This paper analyzes a design strategy可能导致忽略潜在的可取的拓扑结构。本文分析了一种同时解决多运动人物的设计策略

for the simultaneous solution of multiple kinematic tasks. This strategy has two advantages:

。这一战略有2个优势：

1. 它消除了任务分解的需要，（二）它可以彻底的探索 of all non-isomorphic topologies up to a defined number of links. An example of simultaneous所有非同构的最多一个定义数量链接的拓扑结构。同时列举了一种应用于皮瓣标签机构的双刚体导引任务合成的例子来说明。

关键词：平面连杆机构，图形理论，数字合成，模块化 dimensional synthesis · Multiple kinematic tasks · Synthesis strategies尺寸综合，多个运动任务，合成策略

1引言

机制的合成包括对给定的结构and functional requirements, including the design constraints (e.g., allowable space and minimum和功能要求寻找一个合适的机制，还包括设计约束（例如，允许的空间和最小 length of dimensions) and the motion of points or bodies to guide, defined as single尺寸的长度）和点或机构的运动来引导，定义为单个or multiple kinematic tasks [10].或多个运动任务[ 10 ]。单一的运动任务可以分为三大类[10, 13]: 函数发生器（FG），路径跟踪（PF），和刚体导引 (RBG). The prescription of multiple kinematic tasks and the allowable space constraint are（RBG）。多运动任务的处方和允许的空间约束是two design requirements that frequently appear in industrial problems; however, techniques工业问题中经常出现的2种设计要求，但是，用技术 to solve them in a combined way have received little attention in the literature.解决这些问题的方法，在文献中很少受到关注。

合成型和尺寸型都可以通过同步的方法彻底解决 。三种启发式方法在同步方法中被提及。In 1994, Fang [11] pioneered the use of Genetic Algorithms [18] to solve synthesis在1994，方[ 11 ]开创了利用遗传算法[ 18 ]解决合成 成 problems, including both the choice of the topology and its sizing. In 2007, Liu and McPhee问题的方法，包括选择的拓扑结构和它的大小。2007、刘、麦克菲 [15] gave a genetic representation to the topologies and swept the topological space randomly;[ 15 ]给出了一个遗传表示的拓扑结构和扫频的拓扑空间； however, this approach ensures the complete exploration of the feasible topologies然而，这种方法只有当功能评估的数量是足够高的时候才能探索完整的可行的拓扑结构 only if the number of function evaluations is high enough. Recently, Oliva and Goodman。最近，奥利瓦和古德曼 [20] achieved the selection of the best type for a given task by means of evolutionary algorithms[ 20 ]通过进化算法实现了给定任务的最佳类型的选择 and convertible agents; because they used a topological space defined by a four-bar；他们用一个拓扑空间的四杆定义and all six-bar, single degree-of-freedom (DOF) topologies, the randomness in the exploration，把单一程度的自由（自由度）的拓扑结构，在探索中的随机性淘汰。这些技术应用于单一 tasks and without space constraints.任务和空间约束。 methods. Three heuristic approaches can be mentioned among the simultaneous methods.synthesis for a double rigid-body guidance task with application to a flap-tab mechanism

在详尽的相反的启发式的方法中，对一个由一个拓扑的替代品进行了分析，避免了丢失任何潜在的useful alternative, as the topological alternatives are analyzed one-by-one in order. Most of有用的替代，大多数the exhaustive methodologies first solve the type and number syntheses using Graph Theory的方法首先详尽的解决了使用图论的类型和数量的合成concepts [35]. Then, for each topological option, several methods can be employed for the概念[ 35 ]。然后，对于每一个拓扑的选择，有几种方法可以用于dimensional synthesis; for instance, Vucina and Freudenstein [36] used nonlinear programming,三维合成；例如，vucina Freudenstein和[ 36 ]用非线性规划， Raghavan [28] used iterative kinematic analyses, Sandor and Erdman [30] and SardainRaghavan [ 28 ]用迭代的运动学分析，Sandor和厄尔德曼[ 30 ]和sardain [31] exploited Precision Position Methods, and more recently, Luo and Dai [16] used[ 31 ]利用精密定位方法，最近，罗和戴[ 16 ]使用the Patterned Bootstrap method, which combines Precision Position and Homotopy methods.组合精度定位和同伦方法的图形引导方法。

用典型的策略来解决多个运动任务的问题是解决每个单task in sequence. Another possible strategy, explored and developed in this paper, is to generate序列任务的策略。另一个可能探索和发展的策略，在本文中，是产生满足所有的要求and size the topologies that satisfy all the requirements at once; this process is called a

和大小的拓扑结构，这个过程被称为simultaneous synthesis.同时合成。In this context, Pucheta and Cardona have proposed an algorithmic implementation在这样的背景下，pucheta和卡多纳已经提出了一个算法的实现called Exhaustive Search Synthesis [26], which consists of (i) an exhaustive enumeration所谓的详尽搜索综合[ 26 ]，其中包括（我）一个详尽的枚举of topological alternatives up to certain complexity and satisfying topological constraints拓扑的选择，以一定的复杂性和令人满意的拓扑约束[24], followed by (ii) a sizing of each feasible alternative using Precision Position Methods[ 24 ]，其次是（二）每一个可行的替代使用精密定位方法的大小subject to space and other design constraints [23].受空间和其他设计限制[ 23 ]。

在本文中，详尽的搜索综合应用于解决多个运动任务的方法， and it is illustrated by applying it to the design of a flap-tab mechanism passing through并将其应用于一个皮瓣的设计，通过three positions of a complex motion; see Fig. 1(a). For the sake of conciseness, the study is复杂运动的三个位置，见图1（1）。为了简明起见，研究 limited to the design of planar linkage mechanisms with simple joints. It is worth mentioning平面连杆机构的设计与简单的关节。值得一提的是that the method can also be used to solve synthesis problems with multiple inputs.该方法也可用于解决多个输入的综合问题。A brief classification of the multiple kinematic tasks and a short description of the flaptab一个简单分类的多个运动任务和flaptab的简短描述problem are given in Sect. 2. The number and dimensional synthesis methods are reviewed问题是教派.2。中的数量和尺寸的合成方法的检讨 。in Sects. 3 and 4, respectively. Two synthesis strategies for multiple tasks are defined在教派.3和4，中分别定义多任务的合成策略and illustrated in Sect. 5, and the results for a simultaneous synthesis case are presented and和插图。教派.5，是同时合成的情况下的结果。discussed in Sect. 6. The main conclusions are drawn i

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