基于螺旋理论的单闭环多自由度过约束机构综合

第45卷第11期 2009年11月

机 械 工 程 学 报

JOURNAL OF MECHANICAL ENGINEERING

Vol.45 No.11 Nov. 2009

DOI：10.3901/JME.2009.11.038

基于螺旋理论的单闭环多自由度过约束机构综合*

郭 盛 方跃法 岳 聪

(北京交通大学机电学院 北京 100044)

摘要：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。 关键词：过约束 单闭环机构 螺旋理论 自由度 综合 中图分类号：TH112

Structure Synthesis of Single Closed-loop Multi-degree of Freedom of

Over-constrained Mechanism Based on Screw Theory

GUO Sheng FANG Yuefa YUE Cong

(College of Mechanical Engineering, Beijing Jiaotong University, Beijing 100044)

Abstract：Based on screw theory, the relationship among the numbers of constraints, joints and degrees of freedom that constitute single closed-loop over-constraint mechanism are analyzed. Also the calculation formula of the degree of freedom for single closed-loop over-constrained mechanism is presented. Moreover, over-constraints are classified into two types of forces and couples which have different orders, in terms of reciprocal screws. All possible forms of characters of independent over-constraints and numbers as well as their combinations are summarized. Under the condition of having a given special combination over-constraints, by using the principle of virtual work and taking reciprocal screw theory as calculation means, the structural synthesis method for the multi-degree of freedom single closed-loop mechanism is obtained. The non-instantaneous conditions of mechanism are obtained by using analytical method, and axis layout, number, arrangement and spacegeometric conditions of joints are presented. The problem for synthesis of multi-DOF single loop over-constraint mechanisms is solved systematically and wholly and all the possible single closed-loop over-constrained parallel mechanisms are enumerated. The structure synthesis procedure, and design examples of some typical mechanisms are given.

Key words：Over-constraint Single closed-loop mechanisms Screw theory Degree of freedom Synthesis

0 前言

机构学中，闭环机构保持确定运动所需独立驱动个数称为机构自由度。通常，机构自由度数目和机构运动副数之间存在确定的关系，按照这一确定关系，即可得到不同自由度的闭环机构。但过约束机构由于多余约束的存在，导致其自由度计算不能* 国家自然科学基金资助项目(50675016)。20081209收到初稿，20090712收到修改稿

满足传统自由度计算公式。长期以来，这类机构的全面系统综合属于机构学领域的难题。而早期的过约束机构综合主要是依赖研究者的经验和直觉。

对于1自由度单闭环过约束机构，其综合工作的研究逐渐趋于系统和全面。WALDRON[1-2]得到了具有4条连杆而由低副联接的该类过约束机构。GOLDBERG[3]以bennett连杆为灵感设计出一种5-R单闭环过约束机构。WOHLHART[4-5]和 BAKER[6]应用同样的方法得到了一种6-R单闭环过约束机构。除此之外，PAMIDI等[7]推导出一种构成

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