六点定位--坐标系的基础理论

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。拥六个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，称为六点定位法则。

  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。 

         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

3.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。

1.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。

RE:

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)