Euler Vase : 10 Steps (with Pictures) - Instructables

本说明书旨在帮助您在加州圣路易斯奥比斯波的SLO MakerSpace开始木工作业。

这个项目的灵感来源于Geometric Faced Vase“通过Faustwoodworks..

Check out his Instructable at:

//www.smiletrl.com/id/Geometric-Faced-Vases/

标题“欧拉花瓶”是指欧拉特征背后的数学，它描述了顶点，边缘和面之间的关系。我们将在步骤5（可选）中讨论此类讨论。

Your kit should include one block of wood, and a plastic tube. Don't be distressed if the tubes look ugly. Only one of them will be used, and it will be out of sight in the hole.

第1步：将木块切割成尺寸

Your block starts about 3 1/2" squared, and approximately 10" to 12" in length.

You need to cut this down to a manageable size so we can shape it on the band saw. First, attach a shop vacuum to the tube opening under the bandsaw table, and turn the shop vacuum on. Next, grab a push stick and a push block.

Align the fence at the correct distance. I chose to remove about 3/4" from each side. The less you remove, the bigger your vase will be. Larger blocks are more difficult to manage on the belt sander, and take much longer to shape. Remember that you can have a vase that is narrow in one axis, and wide in another.

将刀片防护装置放在你的挡块上方约四分之一英寸处，以便它能穿过锯子。

真空，围栏，刀片护罩和推块到位后，推动块。SLOW DOWN NEAR THE END OF THE CUT!慢点走，慢点走，直到你完成切割的时候，街区几乎停了下来。如果你在切割结束时用力过猛，你的手可能会向刀片猛拉。我们不想发生这种事。如果你在切口末端轻轻推，就没有问题。幸运的是，推杆给你一个额外的12英寸的停车距离。

完成第一次切割后，关闭带锯，等待刀片完全停止，然后再取出工件。把曲子翻到一边，再抓住你的棍子，做第二次也是最后一次。

完成后，关掉带锯。断开真空软管并用它吸干带锯上和周围的多余灰尘。

Now that you've cut the width. You're ready to cut it to length.

第二步：把这块切到一定长度

我选了9英寸。你可以精确地测量它，或者用你的直觉。用锯子切。记住，手不要放在禁区内。用橙色夹子从侧面夹住木材，或者从上面夹住，或者两者都可以。木锯应受到约束，使其不会滑动到轨道的末端，并且两个轴应设置为零度。

Hold onto your stump. You may want to use it later to test wood stains and finishes.

第3步：制作洞

使用钻头压机中的Forstner位进行孔。Forstner位是在钻机附近的黑色金属柜中。确保件夹在钻头压机上。使用带有夹子的垂直支架或副手的副手，螺栓和螺栓均匀。调整螺栓在握住黑色处理时最容易用扁平螺丝刀。注意：如果您只需用手握住块，每次踩到福尔斯特纳的柜台时都会凿孔的边缘。慢慢下降并经常拉出，让芯片清除。如果你想制作更深的洞，你可以切换到铁锹钻头下降甚至更远。完成后，请扫除或真空真空。

第四步：塑造脸型

这是必须有趣的步骤，但也许是最具挑战性的。沙面朝下以创造艺术形状。使用皮带砂光机或打磨盘 - 但首先 - 设置一个系统以去除灰尘。在桑德的一侧，你将看到几英寸宽的两个圆孔。将其连接到商店VAC或灰尘收集器并打开它。现在你准备好打开桑德。

请不要戴手套。我们不想让手套夹在任何活动部件里。我推荐安全护目镜（相对于安全眼镜），因为它们更能防止灰尘吹进眼睛。

如果您更喜欢，也可以抓住一次性防尘罩。

当你砂，使用适度的压力和移动件来回通过皮带。如果你推得太用力，那块会很快失去控制的！急的时候不要撒沙。试着不要摇摆或转动的一块，因为这将产生弯曲的脸。这个花瓶有31个平面。如果你需要更清楚地看到每一张脸，你可以跪下来把你的头和眼睛放在同一水平的皮带上（这是护目镜和防尘面具的帮助）。

避免在太平洋的角度下放置任何两个面。当您在灯中将其转动时，我们希望面孔之间的边缘可见。如果在转动它时有两面“混合在一起”，请考虑通过在边缘之间挤压在一起，直到它们消失在一个较大的脸部之间。您还可以更改一个或两个面的角度，产生更清晰的边缘。如果任何角落出现太突出或太尖锐，您可以通过打开该角落或边缘来创建新的脸。如果你看到一张脸太小并吸引眼睛，你可以做两件事：你可以通过打磨周围的脸来消除那张脸，或者你可以把那只小脸压入砂光机上放大，直到它看起来很适合它在。

您还可以使用肉制素作为皮带砂光机的替代品。（见图片）

This is the most tedious step, and you may find quickly that the picture you had in your head doesn't match the shape in your hands, but don't worry. It takes a while to get used to this method of shaping. If you start getting frustrated, take a break. Take your block home with you and look at it in your spare time. Think about how you want it to look. When you come back the next day, you'll know where you need to sand next.

Remember: This step isn't engineering - it's art. Have fun.

第五步：欧拉特性的数学（可选）

标题“欧拉花瓶”是指顶点，边缘和面之间的数学关系。无论您选择如何塑造花瓶的平面，欧拉特征x都将始终相同。

X = V - E + F = 2 where V is the number of vertices, E is the number of edges, and F is the number of faces. For this vase, X = 2, the same Euler Characteristic. You can count the edges and faces you just sanded to verify this for yourself. Use pieces of tape to mark which faces/edges/vertices you count as you go, record the number, then remove the tape and start again. You can pretend the hole isn't there and count the top as one face, or you can subdivide the cylindrical portion into faces and edges and vertices and count them. However, if you make your vase into a "doughnut" by drilling all the way through, then the Euler characteristic becomes zero! Zero is the Euler characteristic for all toruses, such as doughnuts and coffee mugs. For more information on topology, check out "A History of Mathematics" by Carl B Boyer. Call Number 510.9 in Adult Non-Fiction at the San Luis Obispo County Library.

步骤6：修改对象（可选）

此步骤提供了对前面步骤中不希望出现的结果的建议更正：

摆动件：如果你在底部打磨一个面太远，而工件变得不稳，你可以用锯子夹住它，从底部切下一些。我选择这样做，并扩大我的洞在顶部从⅞” 使用新的forstner钻头调整至1英寸。

孔洞或裂缝：我的那块碎木头上有一个小洞和一条小裂缝。我用木油灰把它们都补上了。存放在金属车间的黄色防火柜内。涂腻子要戴手套。把木腻子塞进洞里或缝里。然后用油灰刀把它弄平，把多余的刮掉。

第七步：切断管子

这个花瓶本身不防水。如果你直接倒入，水会渗入谷粒并从谷底流出。因此，您将使用我们提供的塑料管之一。找到一个最适合你的洞和削减它的长度。您的工具箱应包括一个用于7/8“孔、1”孔和1+1/8“孔的工具箱。如果你的洞有不同的尺寸，请告诉我们，我们会从库存中找到合适的直径。如果你把多余的管子都还给我们，那就可以帮我们为下一个人做药箱了。

Measure the depth of the hole in the wood. If the tape measure is too wide to fit, grab a screwdriver and use your thumb to compare against the tape measure.

在桌上看到背后的标签金属抽屉select a 3D printed tube of the correct diameter. The tube you choose should be just wide enough to slide down the hole easily. Use a fine-blade hacksaw with a mitre box to cut it to length. You may choose to subtract about an inch if you want some of the wood inside the hole to be visible. Fine blades are for metals or hard materials. This tube is soft. However, in our case we need a fine blade because we are cutting through a very thin wall tube. While using a hand-saw, where every stroke is controlled, you can place your fingers close to the blade when you grip your plastic. A tight clamp will crush the tube, use care and control when handling and cutting the tubes.

第8步：平滑脸部

我们穿上砂光机的皮带具有非常粗糙的颗粒，而异形侧面并不顺利。从往复带砂光机下的抽屉中抓住一些高砂纸。更高的数字意味着更平滑的完成。我使用了150个砂砾。

戴手套以保护表面免受手中的油脂。

不要肆无忌惮地砂，或者你将在面部之间取下酥脆边缘。为了保持边缘，用一只手将纸张握住纸张，用另一只手将纸张压入桌子，直到它搁置平坦并固定在其一个脸上。然后按到表中时拖动/推开。几次通过后，切换到下一个面部。

Step 9: Apply a Finish

我使用了可以在金属店的黄色橱柜中找到的聚氨酯。请准备工作站，不要弄脏我们的桌子。我使用了一块来自胡同的刨花板。

戴上塑料手套。

Use a can-key or a flat-head screwdriver to remove the lid. Use a rag to apply the finish to the piece. Roll the piece around to make sure it spreads evenly in the hole. Leave the piece drying in an upright position out of the way so others can use the shop.

Replace the lid and use a rubber mallet (not a hammer) to seal the top. Rinse the rag in the closet in the hallway, then discard rag in the red bin under the metal shop sign. Dispose of your gloves.

在您离开之前，在一张纸或一块纸张上写一张纸张，您的姓名，您的联系信息（电话和电子邮件）以及您将重新收集的时间。将笔记放在花瓶旁边，所以没有人会移动它或抛出它。