机械制图习题集答案 (1)
《机械制图》（第六版）
习题集答案
第3页图线、比例、制图工具的用法、尺寸注法、斜度和锥度●要掌握和理解比例、斜度、锥度的定义；各种图线的画法要规范。
第4页椭圆画法、曲线板用法、平面图形的尺寸注法、圆弧连接
1、已知正六边形和正五边形的外接圆，试用几何作图方法作出正六边形，用试分法作出正五边形，它们的底边都是水平线。
●注意多边形的底边都是水平线；要规范画对称轴线。
●正五边形的画法：
①求作水平半径ON的中点M；
②以M为圆心，MA为半径作弧，交水平中心线于H。
③AH为五边形的边长，等分圆周得顶点B、C、D、E
④连接五个顶点即为所求正五边形。
2、用四心圆法画椭圆（已知椭圆长、短轴分别为70mm、45mm）。
●参教P23四心圆法画椭圆的方法做题。注意椭圆的对称轴线要规范画。
3~4、在平面图形上按1：1度量后，标注尺寸（取整数）。
5、参照左下方所示图形的尺寸，按1：1在指定位置处画全图形。
第6页点的投影
1、按立体图作诸点的两面投影。
●根据点的两面投影的投影规律做题。
2、已知点A在V面之前36，点B在H面之上，
点D在H面上，点E在投影轴上，补全诸的两面
投影。
●根据点的两面投影的投影规律、空间点的直角
坐标与其三个投影的关系及两点的相对位置做
题。
3、按立体图作诸点的两面投影。
●根据点的三面投影的投影规律做题。
4、作出诸点的三面投影：点A（25，15，20）；点B距离投影面W、V、H分别为20、10、15；点C在A之左，A之前15，A之上12；点D在A之下8，与投影面V、H等距离，与投影面W的距离是与H面距离的倍。
●根据点的投影规律、空间点的直角坐标与其三个投影的关系及两点的相对位置做题。各点坐标为：
A（25，15，20）
B（20，10，15）
C（35，30，32）
D（42，12，12）
5、按照立体图作诸点的三面投影，并表明可见性。
●根据点的三面投影的投影规律做题，利用坐标差进行可见性的判断。（由不为0的坐标差决定，坐标值大者为可见；小者为不可见。）
6、已知点A距离W面20；点B距离点A为25；点C与点A是对正面投影的重影点，y 坐标为30；点D在A的正下方20。补全诸点的三面投影，并表明可见性。
●根据点的三面投影的投影规律、空间点的
直角坐标与其三个投影的关系、两点的相对
位置及重影点判断做题。
各点坐标为：
A（20,15,15）
B（45,15，30）
C（20,30,30）
D（20,15,10）
第7页直线的投影（一）
1、判断下列直线对投影面的相对位置，并填写名称。
●该题主要应用各种位置直线的投影特性进行判断。（具体参见教P73～77）
AB是一般位置直线； EF是侧垂线；
CD是侧平线； KL是铅垂线。
2、作下列直线的三面投影：
（1）水平线AB，从点A向左、向前，β＝30°，长18。
（2）正垂线CD，从点C向后，长15。
●该题主要应用各种位置直线的投影特性进行做题。（具体参见教P73～77）
3、判断并填写两直线的相对位置。
●该题主要利用两直线的相对位置的投影特性进行判断。（具体参见教P77）
AB、CD是相交线； PQ、MN是相交线；
AB、EF是平行线； PQ、ST是平行线；
CD、EF是交叉线； MN、ST是交叉线；
4、在AB、CD上作对正面投影的重影点E、F和对侧面投影的重影点M、N的三面投影，并表明可见性。
●交叉直线的重影点的判断，可利用重影点的概念、重影点的可见性判断进行做题。
5、分别在图（a）、（b）、（c）中，由点A作直线AB与CD相交，交点B距离H面20。
●图(c)利用平行投影的定比性作图。
6、作直线的两面投影：
（1）AB与PQ平行，且与PQ同向，等长。
（2）AB与PQ平行，且分别与EF、GH交与点A、B。
●利用平行两直线的投影特性做题。
第8页直线的投影（二）
1、用换面法求直线AB的真长及其对H面、V面的倾角α、β。
●利用投影面平行线的投影特性及一次换面可将一般位置直线变换成投影面平行线做题。（具体参见教P74、P80）
2、已知直线DE的端点E比D高，DE＝50，用换面法作d’e’。
●利用投影面平行线反映实长的
投影特性及一次换面可将一般位置
直线变换成投影面平行线做题。
3、由点A作直线CD的垂线AB，并用换面法求出点A与直线CD间的真实距离。
●利用直角投影定理及一次换面可将一般位置直线变换成投影面平行线做题。（见教
P83、P80）
4、作两交叉直线AB、CD的公垂线EF，分别与AB、CD交于E、F,并表明AB、CD间的真实距离。
●利用直角投影定理做题。
5、用换面法求两交叉直线AB、CD的最短连接管的真长和两面投影。
●利用两次换面可将一般位置直线转变为投影面垂直线及直角投影定理做题。
步骤：先将两交叉直线AB、CD中的一条直线转换为投影面的垂直线，求出AB、CD 的间的真实距离，再逆向返回旧投影面V/H，从而求出最短距离的两面投影。
6、用直角三角形法求直线AB的真长及其对H面、V面的倾角α、β。
●用直角三角形求一般位置直线的实长及其对投影面的倾角。
第9页平面的投影（一）
1、按各平面对投影面的相对位置，填写它们的名称和倾角（0°、30°、45°、60°、90°）。
●解题要点：利用各种位置平面的投影特性及有积聚性的迹线表示特殊位置平面的投影特性做题。
2、用有积聚性的迹线表示平面：过直线AB的正垂面P；过点C的正平面Q;过直线DE 的水平面R。
●利用有积聚性的迹线表示特殊位置平面的投影特性做题。
3、已知处于正垂位置的正方形ABCD的左下边AB，α＝60°，补全正方形的两面投影。已知处于正平面位置的等边三角形的上方的顶点E，下方的边FG为侧垂线，边长为18mm，补全这个等边三角形EFG的两面投影。
●利用正垂面和正平面的投影特性做题。
4、判断点K和直线MS是否在?MNT平面上？填写“在”或“不在”。
●若点位于平面内的任一直线，则点在该平面内。
●若一直线通过平面内的两点，则该直线在该平面内。
点K不在?MNT平面上。
直线MS不在?MNT平面上。
5、判断点A、B、C、D是否在同一平面上？填写“在”或“不在”。
●不在同一直线的三个可确定一个平面，再看另外一个点是否在此平面上即可判断。
四点不在同一平面上。
6、作出ABCD的?EFG的正面投影。
●利用点和直线在平面上的几何条件来作图。
7、补全平面图形PQRST的两面投影。
●解题要点：利用点和直线在平面上的几何条件来作图。
8、已知圆心位于点A、 30的圆为侧平面，作圆的三面投影。
●利用侧平圆的投影特性做题。
9、已知圆心位于点B、?30的圆处于左前到右后的铅垂面上，作圆的三面投影（投影椭圆用四心圆近似法作出）
●利用铅垂面的投影特性、圆的投影特性；四心圆近似法作椭圆具体见教P23。
第10页平面的投影（二）直线与平面及两平面的相对位置（一）
1、求?ABC对V面的倾角β。
●解题要点：利用一次换面可将一般位置平面变换为投影面垂直面。
2、求ABCD的真形。
●利用两次换面可将一般位置平面变换为投影面平行面。
3、正平线AB是正方形ABCD的边，点C在点B的前上方，正方形对V面的倾角β＝45°，补全正方形的两面投影。
●利用正平线AB反映实长，再根据直角投影定理以及经一次换面将可将一般位置平面投影面垂直面。
4、作直线CD与?LMN的交点，并表明可见性。
●从铅垂面LMN在水平投影面积聚为一直线入手,先利用公有性得到交点的一个投影,再根据从属关系求出交点的另一个投影。可见性判断可用重影点法进行判断；简单时可用直观法。
5、作出侧垂线AB与CDEF的交点，并表明可见性。
●从直线AB为侧垂线在侧面投影面积聚为一个点入手，先利用公有性得到交点的一个投影,再根据从属关系求出交点的另一个投影。可见性判断可用重影点法进行判断；
简单时可用直观法。
6、作?EFG与PQRS的交线，并表明可见性。
●铅垂面PQRS与一般平面相交，从铅垂面的水平投影积聚为一条直线入手,先利用公有性得到交线的一个投影,再根据从属关系求出交线的另一个投影。本题可见性判断可用直观法。
7、作正垂面M与ABCD的交线，并表明可见性。
●正垂面MV与一般平面相交，从正垂面的正面投影积聚为一条直线入手,先利用公有性得到交线的一个投影,再根据从属关系求出交线的另一个投影。本题可见性判断可用直观法。
8、作?ABC与圆平面的交线，并表明可见性。
●利用圆平面为正平圆，?ABC为铅垂面，此两平面相交的交线在水平投影面积聚为一个点,再根据从属关系求出交线的另一个投影。本题可见性判断可用直观法。
9、作△EFG与MNPQ的交线，并表明可见性。
●利用?EFG，MNPQ都为正垂面，此两平面相交的交线在正投影面积聚为一个点,再根据从属关系求出交线的另一个投影。本题可见性判断可用直观法。
第11页直线与平面及两平面的相对位置（一）用换面法求解点、直线、平面之间的定位和度量问题
1、作水平面P、平面ABCD、平面EFGD的共有点。
●先分别求水平面P与其余两平面的交线，再求两条交线的交点即可。
2、已
知Δ
BCD
和
PQRS的两面投影，并知ΔBCD上的点A的正面投影a’，在ΔBCD上作直线AE
4.
5. 6.
7.
第20页由立体图画组合体三视图的徒手草图
（槽和孔是通槽和通孔，曲面是圆柱面）
1 2 3
4 5 6
7 8
第21页由立体图画组合体的三视图（比例1：1）
1、
2、
3、
4、
第22页补画视图中所缺图线1、
2、
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