Gear Clock

view, and play with, the insides of a clock

Have you ever got into trouble for taking apart a clock to see how it works? I know somebody who did, a long time ago; more than once. ;)

This gadget illustrates the functioning of a central part of a mechanical clock — the gear train. The focus is on achieving the right ratios between the clock hands' rotation speeds, while showing how, and that this can be done in different combinations.

You can change the placement of the gears. When you move one, the positions and/or sizes of several gears change. I like to do this and lay them out in different ways. Sometimes I try to make it so that all gears have same size teeth.

In understanding something, I want to know what's essential vs accidental. Here, you get some indication of that by changing between 4-wheel and 8-wheel clocks, and by changing the layout.

So, was I the one breaking up clocks? Well, no, but the boy who was curious enough to do it (hello, Mino) got a head start in understanding how devices work, and in using that knowledge. Now, I am beginning to understand how clocks work, too, after playing with this gadget. :)

cris p

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This gadget allows one to observe how the rotations of the clock hands are achieved by their being attached to linked gears. The gear ratios are such that the clock hands' relative rotation speeds are the correct ones for a working clock.

The gadget simulates the transmission of motion from a driving clock hand to the others. The user can drive the motion from any of the clock hands, using the mouse.

A number of selectable options give control over what's displayed and how.


Different examples of gear and tooth count configurations are available. For each, one can select whether to spread them out or keep the clock hands on the same axis.

The layouts can be edited, by moving gears to new positions. (When the mouse pointer is over a gear: mouse button down, move to desired position, button up to commit.)

Drawing styles
They help the user notice various aspects of the gear train's functioning.

The gears are colored in a graded sequence, in transmission order. There are options to choose the highlighting of different parts of the gear train.

The initial points of contact are marked on each gear. That allows one to count how many times a gear turns, and to see when the initial points meet again.

Next to the each initial contact point mark, there is also an arrow, indicating the normal direction of rotation. When one gear turns in the direction indicated by the arrow, all of them turn as their arrows show. When one gear turns in the opposite direction, all of them do the same.


Causes the clock to run by itself. Normally, it will be in sync with the computer's time; when "x 10" or "x 60" is also selected, the gadget's speed will increase 10 or 60 times.
It automatically spreads out (when checking) or packs (when unchecking) the gears. There are two spread out layouts possible, selected randomly.
4 / 8 wheels
Switches between a predefined gear train configuration containing 4 wheels and one containing 8 wheels. The 4-wheel one is simpler, but the differences between gears are greater.
meshing / pinions / wheels
These control what is highlighted. When none is selected, the gears are drawn normally, some of them obscuring parts of others. When one of these options is selected, the corresponding parts are drawn normally, and the rest is transparent, faded out.
This simulates a force opposing the one that makes the gears turn. As a result, the selected clock hand can move slower than the mouse pointer when it's moved with the mouse.

Dig Deeper

What makes the gears turn?

In this gadget, it's the user's moving a clock hand; or, when set on 'auto', some mysterious internal fire :).

In a physical clock, there has to be an energy source, and a way of passing it to the first gear. The energy source can be a dropping weight or a wound up spring. (I'll add one of these to the gadget later.)

Since electrical clocks: batteries, connected to a special kind of motor.

Why are there 4 gears highlighted when the mouse is over a gear?

The 4 highlighted gears are the ones whose placement will change when the first gear is moved.

The first affected is the position of the center of the gear handled directly with the mouse (gear 1). Then, there is another gear (gear 2) that turns around the same axis, jointly with the first one; its center moves to the same new position. Now, gear 1 is meshed with a third gear (3), and gear 2 with gear 4.

By design, the centers of gears 3 and 4 do not move. But when gear 1 is moved, the distance between the centers of gears 1 and 3 changes, so their sizes (and their teeth's sizes) have to change, too; same for the pair of gears 2 and 4.

The exception to this is when gear 1 or 2 doesn't mesh with other gears (so, only 3 gears highlighted), or when gear 1 does not have a coaxial buddy (only 2 gears highlighted); this happens at the ends of the gear train.

Why does friction slow down the turning of the hours hand but not the seconds hand?

When the hours hand turns once around the dial, the seconds hand turns 720 times. (Why not 3600? — there are 3600 seconds in an hour. Because the hours hand moves 5 times more for one hour compared to the seconds hand for 1 second. 720 = 3600 / 5)

When friction is present, you need energy to do the turning; 720 times more energy to turn the hours hand once, compared to the energy to turn the seconds hand once.

Spending more energy over the same [angular] distance requires proportionally more force. To turn the hours hand just as fast as you would turn the seconds hand, you need to apply 720 times that force. If we want to simulate real behavior, it's reasonable to assume that the operator doesn't have that much more force available, so the hours hand cannot be turned so fast.

(Think about bicycles with gears, too.)

What's special about 4 wheels and 8 wheels? Why not 6?

We want the three clock hands to turn in the same direction. Look at the direction of rotation (indicated by arrows) of each gear: wheels 1, 3, . . . turn in one direction, and wheels 2, 4, . . . turn in the other.

So we can't have exactly 3 (or 5, 7, . . .) wheels between the seconds and minutes hands, or between the minutes and hours hands.

Given that transmission ratios can be achieved in many different ways, with different gear and tooth counts and sizes, are the actual clocks' gear train designs mostly accidental?

In a physical clock or watch, there are constraints that make many other choices (besides even wheel count and transmission ratios) non-accidental.

We only addressed 2D kinematics here (and minimal dynamics when friction is on). There are many other considerations: 3D, all dynamics issues, economics, durability, aesthetics, ergonomics, tradition . . .

Not much is accidental.

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