## 21: Daniel's Independent Double-Escape Wheel Escapement

This escapement brings together the best of the Chronometer and the Swiss Lever. The Swiss Lever is essentially self-starting. The Chronometer is more efficient and its escape wheel is not lubricated. The combination is the best of both worlds.

Take the Chronometer's escape wheel, duplicate it, flip it over (to create a mirror image of it), and place it next to the other with a gap of half an inch. Draw a horizontal line, rotate it by 45º, and place it over the center of each escape wheel. Rotate it by 90º, and place it over the center of each escape wheel.

You need to find the radius of the impulse pallet's circle (X), as for the Chronometer. If the escape wheel rotates 18º (24º less 3º twice for drop) during impulse, you could draw the following triangles:

This calculation is similar to the one on page 68. It could also be calculated using a different method, and one formula:

X = Ö [ 32 + 4.5962 - (2)(3)(4.596)(cos9) ] = 1.699

Draw a circle with a radius of 1.699 inches and place its center on the point where lines (1) and (2) intersect.

Draw a horizontal line, (3), through the impulse pallet's circle center. Rotate line (3) counterclockwise by 31º (to the point where the pallet circle and the escape wheel's circle meet) to get line (4). Rotate line (3) clockwise by 31º to get line (6). In order for the pallet to be inside the escape circle path, rotate line (4) counterclockwise by 3º to get line (5), and rotate line (6) clockwise by 3º to get line (7). This way the pallets would rotate by 3º inside the path of the escape wheel at the moment when the escape wheel is released.

The upper locking pallet should have a width equal to the gap between the escape wheels and should have a "V" shape to allow for a draw angle of 10º. Place the pallet 7º above the horizontal line, shown by the point where lines (8) and (9) intersect.

The lower locking pallets have flat locking faces, however. Rotate the left escape wheel counterclockwise by 4º and place one lower locking pallet next to the escape tooth, below the pallet's circle center, giving the pallet 1º of lock and a draw angle of 8º. Rotate the right escape wheel clockwise by 4º and place the other lower locking pallet next to the escape tooth, as shown below, giving the pallet 1º of lock and a draw angle of 8º.

Notice that the sum of 10º for upper draw and 8º for lower draw gives 18º for total draw: this is similar, if only slightly more than the 15º for draw designed into the Swiss Lever pallets.

The locking pallets must be placed into position before you could locate their circle center. The upper locking pallet lies 7º above the horizontal line. The lower locking pallets each lie 38º below the horizontal line, so there are 45º between the upper and lower pallets. Place the locking pallet's circle center 16º below the horizontal line, as shown by the point where lines (10) and (11) intersect. The axis of rotation is important because the displacement of each pallet should be the same during rotation.

Before drawing the roller jewel that moves the locking pallets from side to side, you need to find the distance from the roller jewel's circle center to the locking pallets' circle center. I will call this distance "D."

 D = L + 3.25 = (3.25 tan 16) + 3.25 = 4.182 inches

 R will be the roller jewel's circle radius. R sin 30 = G sin 3    (i) 0.5 R = 0.052 G R = 0.105 G R cos 30 + G cos 3 = 4.182    (ii) 0.866 R + 0.999 G = 4.182 0.866 (0.105 G) + 0.999 G = 1.089 G 1.089 G = 4.182 G = 3.839 R = 3.839 x 0.105 = 0.402 (3.839 + 0.403) - 4.182 = 0.060

Draw the roller jewel's circle with a radius of 0.402 inches, and place it such that its center lies on the center of the impulse pallet's circle. Draw the pallet fork with a radius of 3.839 inches from the locking pallets' circle center to the entrance corner of the fork horn: the roller jewel would have a depth of 0.06 inches inside the pallet fork. I have not included the locking pallets' circle in this drawing, but it would be needed for a simulation.

In this drawing, I have rotated the locking pallets clockwise by 3º and the impulse pallet / roller table assembly counterclockwise by 30º. The left escape wheel has just been released by the impulse pallet and is detained by a lower locking pallet. The right escape wheel is detained by the upper locking pallet.

This drawing reveals how complicated the design is. Notice how the escape wheel and the impulse pallet appear to roll together, instead of sliding across one another, and therefore why the escape wheels and the pallets need not be lubricated.

There are several differences between my drawing and the original specifications. I made these changes in order to enhance the actions of the escapement during the simulation. The gap between the escape wheels was not drawn in proportion to the original, but the only effects this had were to change the impulse pallet's circle radius and the diameter of the upper locking pallet. The convenience of using the gap of half an inch, in allowing me to use the "snap to grid" function in the computer's software, outweighed the compulsion to draw it as closely to the original as possible. Furthermore, I chose an angle of 60º for the rotation of the roller jewel during engagement with the pallet fork. The original design called for 24º, but increasing the angle also increases the depth of the roller jewel inside the fork: by exaggerating the actions of the escapement, the actions become more easily visible during the simulation. Other side effects of increasing this angle from 24º to 60º are that the pallet fork becomes longer and the roller jewel's circle radius becomes smaller by half. The depth increases by a factor of three.

This example demonstrates how creating your own drawings would allow you to change the variables and observe the consequences. The idea is not necessarily to create the drawing as closely to the original specifications as possible, but rather to make changes and to experiment. You may be able to improve a design or even invent an all-original design.

Go to Chapter 22