Lesson 3: An Engineering Introduction to Machines–Gears ALTERNATE (December 12)

This SUPPLEMENTAL assignment is for ONLY for the students who have more than one engineering class with this teacher.

Objectives: (1) To introduce students to the basic concepts of machines, as used by engineers; and (2) to specifically learn the most basic principles of how the movement of gears is regulated in a mechanical pendulum clock.

The main lesson for this day involves various types of gears and gear trains.  One of the examples cited is a mechanical clock.  The purpose of this SUPPLEMENT is to address other principles of the mechanical clock that enable it to work as a time piece.

The essential parts of a clock are as follows:

  1. Power Source, which is usually a weight descending and powered by gravity.  An alternate power source, used in many clocks is a coiled spring, which must be periodically wound.
  2. The gear train.
  3. The time indicators, usually by means of at least an hour and minute hand.
  4. The movement regulator, which is usually an escapement and  pendulum.


As weights descend, they rotate a wheel or gear

The weight acts as an energy storage device so that the clock can run for relatively long periods of time unattended. When you “wind” a weight-driven clock, you pull on a cord that lifts the weight. That gives the weight “potential energy” in the Earth’s gravitational field. The clock uses that potential energy as the weight falls to drive the clock’s mechanism.1


gear train for mechanical clock

You can create a high-ratio gear train that causes the drum to make perhaps one turn every six to 12 hours. This would give you a clock that you only had to rewind once a week or so. The gear ratio between the weight drum and the escapement gear might be something like 500:1, as shown in the diagram above.


Clock Gear Math2

Here is what we are trying to do:

  • Make a device where the minute shaft makes one revolution every 3600 seconds.  That’s it.

  • Early clocks behaved this way with just a minute hand.  It wasn’t until much later that clocks were made with hour and second hands.
  • Ignore the second and hour hands for a moment to make the calculations easier.  Other hands are merely gear ratios to the minute hand.
  • In our example the minute hand is the shaft with the 90 tooth gear.
  • This shaft makes one rotation every 3600 seconds or once an hour.



An Escapement, in mechanics, is a device that permits controlled motion, usually in steps. In a watch or clock, it is the mechanism that controls the transfer of energy from the power source to the counting mechanism. The classic form for a timepiece, which made the mechanical clock possible, was the verge escapement, probably invented in 13th-century Europe. 3


The pendulum is the device that  allows the whole timekeeping mechanism to advance so the second hand moves one second on the dial (and only one second) in a time of one second. That’s what the pendulum does. As it swings from side to side, it rocks a lever called an escapement that locks and then unlocks the part of the mechanism driven by the falling weight. (Think of it this way: the mechanism is locked and the escapement releases it so it can move—in other words, lets it escape—once per second.) It’s this repeated locking and unlocking that makes the tick-tock sound you can hear. Since (in theory, at least) a pendulum of a certain length always takes the same amount of time to swing back and forth, the pendulum is what keeps the clock to time. The escapement mechanism that the pendulum regulates also (cleverly) keeps it moving back and forth by repeatedly giving it a slight nudge—an extra injection of energy to counteract friction and drag. 4


The workings of a mechanical clock is not exactly the easiest machine to visualize and understand.   Use other sourced if necessary to answer the following:

(1) Please write a paragraph or two about each major component of the mechanical clock, as reflected above.  Explain how that component of the clock works.

(2) write another paragraph or two putting them all together.  How is each component connected?  How does it interact with the other components?

(3) Hand in your assignment to the teacher at least 15 minutes before the end of class  Be prepared to verbally summarize your answers to him.

  1.   How stuff works (https://electronics.howstuffworks.com/gadgets/clocks-watches/clock2.htm)
  2.   from Gary’s Clocks website (http://garysclocks.sawdustcorner.com/clock-gear-math.html)
  3. Encyclopedia Britaninica (https://www.britannica.com/technology/escapement)
  4.   Explain that stuff website (https://www.explainthatstuff.com/how-pendulum-clocks-work.html)