六点定位--坐标系的基础理论

山涧果子

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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)

来源：山涧果子

RationalDMIS间距面功能全面超越PCDMIS

提示：Mode/Pro,Man模式下应用间距面。注意：（1）DMIS中安全平面（间距面）只在"AUTO"模式下起作用。需要在“程序设置”--勾选“MODE/PROG，MAN下应用间距面”，这项兼容性改变使得“安全平面”，在PROG模式下也可以起作用。（2）测量操作区，测量设置窗口“清除平面设置”可以设置自动测量元素测量前后的安全位置（PC-DMIS“两者”，“前”，“后”）。 Mode/Pro，Man模式下应用间距面：勾选后在程序模式下会自动调用间距面，间距面的位置根据理论位置来计算； Crete PTMEAS with Apprch/Retrct：设置为是，记录的DMIS程序中PTMEAS语句中会有接近回退参数；Creat MEAS with Clear Surface setting：设置为是，记录的DMIS程序中MEAS语句中会有安全平面设置参数；PC DMIS 和RationalDMIS间距面功能对比在文章下方：清除平面设置解读：用来设置测量前和测量后使用不同的安全平面来抬高；有3个设置选项：无、关闭、间距面，窗口内可以拖放平面：控制如下功能：A、 MEAS语句的清除平面设置MEAS/POINT, F(PT13), 1, CLRSRF, F(PLN2), 2.00, CLRSRF, F(PLN2), 20.00B、从Cad上选取并测量调用此设置；C、从元素数据区自动测量调用此设置；D、RMEAS/VECBLD支持‘创建MEAS时增加清除平面设置’设置；例如点: RMEAS/POINT, F(PT1), 1, VECBLD, 4.000, 3, CLRSRF, 15.0, CLRSRF, 26.0DMISMN/'Created by [深圳力合精密装备科技有限公司-090118] on 星期三, 七月 18, 2018', 4.0UNITS/MM, ANGDEC, MMPSWKPLAN/XYPLANPRCOMP/ONTECOMP/ONFLY/1.000000MODE/PROG, MANSNSET/APPRCH, 2.000000SNSET/RETRCT, 2.000000SNSET/DEPTH, 0.000000SNSET/SEARCH, 10.000000SNSET/CLRSRF, 10.000000RECALL/D(MCS)SNSLCT/S(ROOTSN1)GEOALG/BF, LSTSQRGEOALG/ANGLB, DEFALTGEOALG/CIRCLE, LSTSQRGEOALG/ARC, LSTSQRGEOALG/PLANE, LSTSQR$$$$MODE/PROG,MANF(PT1)=FEAT/POINT,CART,9.292552,80.861908,35.000000,0.000000,0.000000,1.000000MEAS/POINT, F(PT1), 1, CLRSRF, 20.000000, CLRSRF, 20.000000 PTMEAS/CART, 9.292552,80.861908,35.000000,0.000000,0.000000,1.000000, APPRCH, 2.000000, RETRCT, 2.000000ENDMESF(PT2)=FEAT/POINT,CART,8.651951,28.114450,35.000000,0.000000,0.000000,1.000000MEAS/POINT, F(PT2), 1, CLRSRF, 20.000000, CLRSRF, 20.000000 PTMEAS/CART, 8.651951,28.114450,35.000000,0.000000,0.000000,1.000000, APPRCH, 2.000000, RETRCT, 2.000000ENDMESF(PT3)=FEAT/POINT,CART,70.848228,23.717142,35.000000,0.000000,0.000000,1.000000MEAS/POINT, F(PT3), 1, CLRSRF, 20.000000, CLRSRF, 10.000000 PTMEAS/CART, 70.848228,23.717142,35.000000,0.000000,0.000000,1.000000, APPRCH, 2.000000, RETRCT, 2.000000ENDMESF(PT4)=FEAT/POINT,CART,85.526016,56.336372,35.000000,0.000000,0.000000,1.000000MEAS/POINT, F(PT4), 1, CLRSRF, 10.000000, CLRSRF, 20.000000 PTMEAS/CART, 85.526016,56.336372,35.000000,0.000000,0.000000,1.000000, APPRCH, 2.000000, RETRCT, 2.000000ENDMESF(CIR1)=FEAT/CIRCLE,INNER,CART,40.000000,55.000000,32.000000,0.000000,0.000000,1.000000, 45.000000$$ Measurement points are created through nominal pointsMEAS/CIRCLE, F(CIR1), 4, CLRSRF, 15.000000, CLRSRF, 30.000000 GOTO/CART, 40.000000, 74.500000, 43.000000 GOTO/CART, 59.500000, 55.000000, 43.000000 GOTO/CART, 59.500000, 55.000000, 42.000000 PTMEAS/CART, 62.500000, 55.000000, 32.000000, -1.000000, 0.000000, 0.000000, APPRCH, 2.000000, RETRCT, 2.000000 GOTO/CART, 58.015651, 47.537673, 32.000000 GOTO/CART, 53.788582, 41.211418, 32.000000 GOTO/CART, 47.462327, 36.984349, 32.000000 PTMEAS/CART, 40.000000, 32.500000, 32.000000, 0.000000, 1.000000, 0.000000, APPRCH, 2.000000, RETRCT, 2.000000 GOTO/CART, 32.537673, 36.984349, 32.000000 GOTO/CART, 26.211418, 41.211418, 32.000000 GOTO/CART, 21.984349, 47.537673, 32.000000 PTMEAS/CART, 17.500000, 55.000000, 32.000000, 1.000000, 0.000000, 0.000000, APPRCH, 2.000000, RETRCT, 2.000000 GOTO/CART, 21.984349, 62.462327, 32.000000 GOTO/CART, 26.211418, 68.788582, 32.000000 GOTO/CART, 32.537673, 73.015651, 32.000000 PTMEAS/CART, 40.000000, 77.500000, 32.000000, 0.000000, -1.000000, 0.000000, APPRCH, 2.000000, RETRCT, 2.000000 GOTO/CART, 40.000000, 74.500000, 42.000000ENDMESF(CIR2)=FEAT/CIRCLE,INNER,CART,56.000000,27.287187,32.000000,-0.000000,-0.000000,1.000000, 10.000000$$ Measurement points are created through nominal pointsMEAS/CIRCLE, F(CIR2), 4, CLRSRF, 10.000000, CLRSRF, 40.000000 GOTO/CART, 56.000000, 29.287187, 43.000000 GOTO/CART, 58.000000, 27.287187, 43.000000 GOTO/CART, 58.000000, 27.287187, 42.000000 PTMEAS/CART, 61.000000, 27.287187, 32.000000, -1.000000, -0.000000, -0.000000, APPRCH, 2.000000, RETRCT, 2.000000 PTMEAS/CART, 56.000000, 22.287187, 32.000000, 0.000000, 1.000000, 0.000000, APPRCH, 2.000000, RETRCT, 2.000000 PTMEAS/CART, 51.000000, 27.287187, 32.000000, 1.000000, 0.000000, 0.000000, APPRCH, 2.000000, RETRCT, 2.000000 PTMEAS/CART, 56.000000, 32.287187, 32.000000, 0.000000, -1.000000, 0.000000, APPRCH, 2.000000, RETRCT, 2.000000 GOTO/CART, 56.000000, 29.287187, 42.000000ENDMESPC-DMIS间距面功能三种如下：RationalDMIS间距面功能四种，对PC DMIS间距面功能全覆盖:来源：山涧果子