基于约束图谱旋量分析方法的调平机构约束设计

Constraint Design of a Leveling Mechanism via a Screw Theory Approach for Constraint Pattern Analysis

约束图谱分析方法从自由度和约束的视角处理机械设计问题,由于自由度和约束概念的一般性,因而该方法对机械设计问题具有广泛的指导意义。从刚性机构及机械接口通用设计方法角度,将旋量理论应用于约束图谱分析方法研究,采用纯力旋量表示点接触约束,采用运动旋量表示自由度,给出约束图谱分析几何概念的旋量描述;基于互易旋量,提出自由度超平面的概念,用以描述点接触约束的单向性,给出并联机构自由度分析及串联机构约束分析方法;在此基础上,提出自由度线等价原则及自由度约束互补原则的代数基础,由此形成集成几何概念的约束图谱旋量分析方法。以光刻机调平机构为例开展应用研究,指出常用2-SPS&1-SP调平机构欠约束和欠确定运动问题,进而提出1-PSV&1-PSE&1-S调平机构,介绍约束图谱旋量分析方法在机构约束设计问题中的应用。

Constraint pattern analysis handles the mechanical design problem from a viewpoint of freedom and constraint,because of the generality for the concept of freedom and constraint,the method is a wide guide for machine design.From a viewpoint of a general design method for rigid mechanisms and mechanical interfaces,screw theory is applied in constraint pattern analysis.Point contact constraint and degree of freedom are denoted as a pure wrench and a twist,respectively.The geometrical concept for constraint pattern analysis is provided.The freedom hyper-plane is presented via reciprocal screw,and the analytical approach for freedom of parallel connections and constraint of serial connections are provided.The screw algebra basis for the equivalence rule for a freedom line and the rule of complementary pattern are proposed,a screw theory approach for constraint pattern analysis is formed.The application for the approach is carried out by a leveling mechanism for an optical projection exposure machine.The under-constraint and uncertain motion in the common 2-SPS1-SP leveling mechanism is pointed out,and a 1-PSV1-PSE1-S leveling mechanism is proposed in order to introduce the application of the approach in the constraint design of mechanisms.