多加一个齿轮，输出会变慢吗？Does an extra gear slow the output?
12 齿主动轮带动 24 齿输出轮。在两者之间加一个惰轮，再数转了几圈。把输出转多少和朝哪转分开记录。
A 12-tooth driver turns a 24-tooth output. Add one gear between them, then count turns. Track how far the output turns separately from which way it turns.
01预测Predict
02动手试Try
先不加惰轮，让主动轮转一圈。再加上惰轮重复一次。输入始终顺时针转。
Turn the driver once without an idler. Add the idler and repeat. The input always turns clockwise.
用滑块或方向键每次走四分之一圈。Home 归零，End 转满一圈。Use the slider or its arrow keys to step by a quarter turn. Home returns to zero. End completes one turn.
切换排列会从零开始新的一圈。已完成的结果保留在下表中。Changing the arrangement starts a fresh turn. Your completed results stay in the comparison below.
| 排列Arrangement | 输出圈数Output turns | 输出方向Output direction |
|---|---|---|
| 无惰轮No idler | ||
| 一个惰轮One idler |
03解释Explain
加一个惰轮，速比的大小不变。每次啮合，一个齿推动邻轮的一个齿。12 齿主动轮转一圈，就有 12 个齿经过第一个啮合点。
惰轮把同样的 12 个齿送过第二个啮合点。24 齿的输出轮因此前进 24 齿中的 12 齿，也就是半圈。
转多少
惰轮本身比主动轮转得少，但下一次啮合不会再叠加同样的减速。每一次啮合都有自己的齿数比。
Adding one idler leaves the speed-ratio magnitude unchanged. Each meshing tooth pushes one tooth of its neighbor. One full turn of the 12-tooth driver moves 12 teeth past the first contact.
The idler moves those same 12 teeth past the second contact. The 24-tooth output therefore advances 12 of its 24 teeth. That is half a turn.
Magnitude
The idler turns less than the driver, but the next mesh does not add the same reduction again. Each mesh has its own tooth-count ratio.
惰轮的齿数一次作除数、一次作乘数，所以相互抵消。输入每秒 1 圈时，两种排列的输出都是每秒 0.5 圈。
朝哪转
每一次外啮合都会反转方向。没有惰轮时反转一次，输出逆时针；有一个惰轮时反转两次，输出顺时针。方向变了，大小仍是 ½。
The idler's tooth count appears once as a divisor and once as a multiplier, so it cancels. At a steady input speed of 1 turn per second, the output makes 0.5 turns per second in either arrangement.
Direction
Every external gear mesh reverses direction. With no idler, one reversal makes the output turn counterclockwise. With one idler, two reversals make it turn clockwise. Direction changes. The magnitude stays at ½.
“惰轮改变了 ___，而输出仍然转 ___，因为 ___。”“The idler changes ___, while the output still turns ___ because ___.”
迁移：换一个新情形Transfer question
这个模型的适用范围Where this model applies
本课使用理想的刚性外齿轮：齿距相同、轴固定、不打滑。惰轮是单独一根轴上的一个齿轮。齿数是为教学选的示例值。
省略了摩擦、齿隙、轮齿变形、轴承阻力和惯性。加入惰轮会增加损耗并影响加速，真实电机在负载增加时可能变慢。本图固定了主动轮的运动，所以演示的是几何速比，不是功率损失或电机性能。
如果中间轴上锁着两个不同的齿轮（复合轮系），需要另一种算法。这里的抵消只适用于单个简单惰轮。
This lesson uses ideal, rigid external gears with the same tooth spacing, fixed shafts, and no slipping. The idler is one gear on its own shaft. Tooth counts are illustrative teaching choices.
Friction, backlash, tooth flex, bearing drag, and inertia are omitted. An added idler can increase losses and affect acceleration. A real motor may slow under extra load. This figure holds the driver's motion fixed, so it demonstrates the geometric ratio, not power loss or motor performance.
A compound train with two different gears locked to the same intermediate shaft needs a different calculation. The cancellation shown here applies to a single simple idler.
离线可用。用 Tab 切换控件，空格勾选复选框，方向键调节进度滑块。没有快捷键会干扰你的写作。Works offline. Use Tab to reach controls, Space to toggle the checkbox, and arrow keys on the progress slider. No keyboard shortcuts override your writing.
2D 示意图。齿轮大小与齿数成比例，径向标记让不满一圈的转动也看得见。2D schematic. Gear size follows tooth count. Radial marks make partial turns visible.