六点定位原理详解：坐标系的基础理论

六点定位原理详解：坐标系的基础理论

六点定位原理是机械制造和测量领域的重要基础知识，它通过合理分布的支承点限制工件的六个自由度，使工件在夹具中占据正确的位置。本文将详细介绍六点定位原理的概念、具体应用以及在RationalDMIS测量软件中的操作步骤。

六点定位原理概念

一个自由的物体，它对三个相互垂直的坐标系来说，有六个活动可能性，其中三种是移动，三种是转动。习惯上把这种活动的可能性称为自由度，因此空间任一自由物体共有六个自由度。

在空间直角坐标系中，刚体具有六个自由度，即沿X、Y、Z轴移动的三个自由度和绕此三轴旋转的三个自由度。采用六个按一定规则布置的支承点，限制工件的六个自由度，使工件在机床或夹具中占有正确的位置，称为六点定位法则。

未受约束的刚体，在空间的位置是不确定的，它具有六个自由度：绕X轴、Y轴、Z轴方向的3个转动自由度和沿X轴、Y轴、Z轴的三个平动自由度。为使刚体在空间具有确定的位置，就必须限制其六个自由度。

定位就是用各种形状不同的定位元件，来限制工件的自由度。

关于“六点定位”的几个问题

1. 定位限制自由度，几“点”定位不能机械地理解成几个接触点；
2. 限制自由度应理解为：定位支承点与工件定位基准面始终保持紧贴接触；
3. 定位支承点数目原则上不应超过工件自由度数目；
4. 自由度被限制，是指工件在此方向上有确定的位置：不考虑外力的影响（注：定位和夹紧的区别）；
5. 定位支承点是抽象的，通过具体定位元件来体现；
6. 工件应限制几个自由度，由工件加工技术条件来确定。

六点定位原理举例

1. 在XOY平面内布置了3个支承点，工件被限制的自由度为三个：约束了两个旋转自由度（绕X，Y轴旋转）和一个平动自由度（沿Z轴移动）。
2. 在XOZ平面内布置了2个支承点，工件被限制的自由度为二个：Z轴旋转和Y轴平移。
3. 在YOZ平面内布置了1个支承点，工件被限制的自由度为一个：X轴平移。

此时，六个自由度完全锁定。

基准的相关概念

• 基准：零件上用以确定其它点、线、面位置所依据的那些点、线、面。
• 设计基准：零件图上用以确定点、线、面位置的基准。
• 定位基准：零件加工、测量和装配过程中使用的基准。分为工序基准、定位基准、度量基准和装配基准。

几点注意

1. 作为基准的点、线、面在工件上不一定存在，而常常由基准面来体现；
2. 基准可以是没有面积的点或线，但基准面一定是有面积的；
3. 基准包含尺寸之间的联系和位置之间的关系（如平行度、垂直度等）。

RationalDMIS测量软件六点定位详解

DMISMN/'Created by [深圳力合精密装备科技有限公司-090118] on 星期二, 七月 10, 2018', 4.0  
UNITS/MM, ANGDEC, MMPS  
WKPLAN/XYPLAN  
PRCOMP/ON  
TECOMP/ON  
FLY/1.000000  
MODE/PROG, MAN  
SNSET/APPRCH, 2.000000  
SNSET/RETRCT, 2.000000  
SNSET/DEPTH, 0.000000  
SNSET/SEARCH, 10.000000  
SNSET/CLRSRF, 50.000000  
RECALL/D(MCS)  
SNSLCT/S(ROOTSN1)  
GEOALG/BF, LSTSQR  
GEOALG/ANGLB, DEFALT  
GEOALG/CIRCLE, LSTSQR  
GEOALG/ARC, LSTSQR  
GEOALG/PLANE, LSTSQR  
$$  
$$  
MODE/MAN  
F(PT1)=FEAT/POINT,CART,8.326538,75.352898,35.000000,0.000000,0.000000,1.000000  
$$ Empty Meas Block  
MEAS/POINT, F(PT1), 1  
ENDMES  
F(PT2)=FEAT/POINT,CART,7.381094,27.180397,35.000000,0.000000,0.000000,1.000000  
$$ Empty Meas Block  
MEAS/POINT, F(PT2), 1  
ENDMES  
F(PT3)=FEAT/POINT,CART,89.036491,28.313187,35.000000,0.000000,0.000000,1.000000  
$$ Empty Meas Block  
MEAS/POINT, F(PT3), 1  
ENDMES  
F(PT4)=FEAT/POINT,CART,8.672945,0.000000,14.855032,-0.000000,-1.000000,-0.000000  
$$ Empty Meas Block  
MEAS/POINT, F(PT4), 1  
ENDMES  
F(PT5)=FEAT/POINT,CART,63.419529,0.000000,14.033564,-0.000000,-1.000000,-0.000000  
$$ Empty Meas Block  
MEAS/POINT, F(PT5), 1  
ENDMES  
F(PT6)=FEAT/POINT,CART,0.000000,25.224169,29.234194,-1.000000,0.000000,0.000000  
$$ Empty Meas Block  
MEAS/POINT, F(PT6), 1  
ENDMES  
F(PT1)=FEAT/POINT,CART,8.326538,75.352898,35.000000,0.000000,0.000000,1.000000  
F(PT2)=FEAT/POINT,CART,7.381094,27.180397,35.000000,0.000000,0.000000,1.000000  
F(PT3)=FEAT/POINT,CART,89.036491,28.313187,35.000000,0.000000,0.000000,1.000000  
F(PT4)=FEAT/POINT,CART,8.672945,0.000000,14.855032,-0.000000,-1.000000,-0.000000  
F(PT5)=FEAT/POINT,CART,63.419529,0.000000,14.033564,-0.000000,-1.000000,-0.000000  
F(PT6)=FEAT/POINT,CART,0.000000,25.224169,29.234194,-1.000000,0.000000,0.000000  
D(CRD1) = LOCATE/FA(PT1), FA(PT2), FA(PT3), FA(PT4), FA(PT5), FA(PT6)  
$$ coordinate system Iteration  
$$  
$$  
(ITR_START)  
MEAS/POINT, F(PT1), 1  
PTMEAS/CART, 8.326538,75.352898,35.000000,0.000000,0.000000,1.000000  
ENDMES  
MEAS/POINT, F(PT2), 1  
PTMEAS/CART, 7.381094,27.180397,35.000000,0.000000,0.000000,1.000000  
ENDMES  
MEAS/POINT, F(PT3), 1  
PTMEAS/CART, 89.036491,28.313187,35.000000,0.000000,0.000000,1.000000  
ENDMES  
MEAS/POINT, F(PT4), 1  
PTMEAS/CART, 8.672945,0.000000,14.855032,-0.000000,-1.000000,-0.000000  
ENDMES  
MEAS/POINT, F(PT5), 1  
PTMEAS/CART, 63.419529,0.000000,14.033564,-0.000000,-1.000000,-0.000000  
ENDMES  
MEAS/POINT, F(PT6), 1  
PTMEAS/CART, 0.000000,25.224169,29.234194,-1.000000,0.000000,0.000000  
ENDMES  
F(PT1)=FEAT/POINT,CART,8.326538,75.352898,35.000000,0.000000,0.000000,1.000000  
F(PT2)=FEAT/POINT,CART,7.381094,27.180397,35.000000,0.000000,0.000000,1.000000  
F(PT3)=FEAT/POINT,CART,89.036491,28.313187,35.000000,0.000000,0.000000,1.000000  
F(PT4)=FEAT/POINT,CART,8.672945,0.000000,14.855032,-0.000000,-1.000000,-0.000000  
F(PT5)=FEAT/POINT,CART,63.419529,0.000000,14.033564,-0.000000,-1.000000,-0.000000  
F(PT6)=FEAT/POINT,CART,0.000000,25.224169,29.234194,-1.000000,0.000000,0.000000  
D(CRD1) = LOCATE/FA(PT1), FA(PT2), FA(PT3), FA(PT4), FA(PT5), FA(PT6)  
KNPTR1 = ITERAT/(ITR_START), (ITR_FAIL), 0.010000, ABSL, 10,$  
FA(PT1), ZAXIS,$  
FA(PT2), ZAXIS,$  
FA(PT3), ZAXIS,$  
FA(PT4), YAXIS,$  
FA(PT5), YAXIS,$  
FA(PT6), XAXIS  
(ITR_FAIL)  

来源：山涧果子