机械计算器是精确而迷人的装置，你可能不会想到它们能适合3D打印，但一位YouTuber已经证明，口袋大小的单元可以完全由塑料耗材制成。YouTuber 3D all Workshop 在最近的一段视频中详细介绍了他的工作过程，但仅限于一个小型构造。如果你熟悉掌上机械计算器的圣杯——Curta，也被称为“胡椒磨”，你已经对这款3D打印计算器的工作原理有了基本了解。
Mechanical calculators are precise, fascinating gadgets that you wouldn’t think would take well to being 3D printed, but a YouTuber has proved that a pocket-sized unit can be made purely from plastic filament. YouTuber 3D all Workshop detailed his working, but limited, build in a recent video. If you’re familiar with the holy grail of palm-sized mechanical calculators, the Curta, also known as the “pepper mill,” you already have a working understanding of how this 3D-printed calculator works.
正如视频所述，Workshop 的3D打印机械计算器与 Curta 一样，依赖于一种已有200多年历史的部件——莱布尼茨步进鼓（Leibniz stepped drum），以其发明者德国哲学家兼数学家戈特弗里德·威廉·莱布尼茨命名。与许多其他机械计算器一样，该计算器核心机制的核心概念是莱布尼茨鼓的不同长度齿。鼓上有九个齿，分别代表一到九的数值，而零设置则不激活任何齿。
As detailed in the video, Workshop’s 3D-printed mechanical calculator, like the Curta, relies on a more than 200-year-old component known as the Leibniz stepped drum, named for its inventor, German philosopher and mathematician Gottfried Wilhelm Leibniz. The core concept of the calculator’s central mechanism, like that of many other mechanical calculators, is the Leibniz drum’s teeth of different lengths. There are nine teeth per drum, representing values one through nine, while a zero setting engages none of them.
Workshop 的3D打印计算器可以接受 1 到 999 的输入，每个数字对应一个鼓。你使用杠杆将齿轮沿鼓向上移动，使其仅激活所需的齿数。相同的概念也用于 Curta 的输入，只是精度更高——使用机加工铝材而非3D打印耗材的一个主要优势。由于想保持3D打印计算器的掌上尺寸，YouTuber 被迫限制其功能。它可以进行加法，而多轮加法的功能使其也能通过多次相同数字的加法来实现乘法。
Workshop’s 3D printed calculator can take inputs from 1 to 999, with one drum per digit. You use a lever to move a gear up the drum so that it only activates as many teeth as are needed for a particular number. The same concept is used to input values into the Curta, just in a much more precise manner - one of the big benefits of using machined aluminum over 3D printing filament. As a result of wanting to keep the 3D printed calc’s build palm-sized, the YouTuber was forced to restrict what it’s able to do. It can do addition, and the addition of a multi-wheel enables it to also do multiplication by simply performing multiple sequences of adding the same number.
Curta 也以类似方式进行乘法，要求用户输入基数和需要乘以的次数，然后通过加法完成乘法。
The Curta does multiplication in a similar manner, requiring a user to input their base number and the number of times they want to multiply by addition.
与Curta不同，Workshop的计算器既不能减法，也不能除法——正如其创作者所解释的那样，根本没有足够的空间把所有那些繁琐的零件装进一个掌心大小的设备。它需要多大才能加入这些功能尚不清楚，但如果3倍尺寸的3D打印Curta能给我们一个参考——其创作者说尺寸增大是必要的——那它可能会相当大。将尺寸缩小到Workshop的微型3D打印计算器，意味着一定会出现许多问题，而且确实如此。
Unlike the Curta, Workshop’s calculator can’t subtract, nor can it divide - as its creator explains, there simply wasn’t the room to get all those fiddly bits into a palm-sized device. It’s not clear how large it would have to be to add those functions, but if the 3x-sized 3D printed Curta is any indication - its creator said the increased size was necessary - it’d probably be quite large. Scaling down to Workshop’s tiny 3D printed calculator means plenty of issues were bound to arise, and they definitely did.
“问题很多，”他指出，并解释说“即使是打印时最细微的不一致也会导致问题。”如果你曾使用过3D丝材打印机，你就会知道这种不一致经常出现。齿轮因3D打印公差过紧而卡住，而间隙（配合机械部件之间的空隙）可能会导致鼓面不同步。零件在重新设计过程中不断断裂，甚至使用计算器时的振动也足以干扰其组件。
“There were a lot of problems,” he noted, explaining that “even the tiniest inconsistencies when printing can cause problems.”If you’ve ever used a 3D filament printer, you know how often such inconsistencies pop up. Gears kept binding because of tight 3D-printing tolerances, while backlash (the play between mating mechanical parts) could throw the drums out of sync. Pieces kept breaking during redesigns, and even the vibrations from picking up and using the calculator were enough to disrupt its components.
该YouTuber在两个月的项目中经历了大约100次设计迭代，最终通过定制设计的3D打印弹簧和棘轮机构解决了问题，防止间隙导致鼓面不同步。总而言之，最终成品共包含109个独立零件，打印耗时17小时，使用了90克丝材。尽管在YouTube上多次呼吁Workshop发布甚至出售他的设计，他仍未将其公开，因此没有人能经历一次长达一天的打印工作，来短暂体验这个装置。
The YouTuber went through roughly 100 design iterations over the two-month project, finally addressing the problems with custom-designed 3D-printed springs and a ratchet mechanism that kept backlash from throwing the drums out of sync. All said, the final build ended up with 109 separate pieces, took 17 print-hours to complete, and used 90g of filament. Despite multiple calls on YouTube for 3D all Workshop to publish, or even sell, his design, he has yet to make it available, so no struggling through a day-long print job for a potentially brief moment playing with this one.
与此同时，你可以3D打印巨型Curta，或者如果你手头有几千美元想要花掉，试着去获得一台原装机。®
In the meantime, you could 3D print the giant Curta, or if you have a couple grand lying around begging to be spent, try to get your hands on an original. ®