13: Drawing the Pallets

The first tooth was drawn next to line (2), which had an angle of 30 relative to the vertical line (1). The 30 angle was chosen so that there would be a 2.5 tooth span between the pallets for a 15 tooth wheel. The angle between lines (2) and (4) was 90 so that the angle between the force exerted by the escape tooth and the force that acted to rotate the pallet would be 90.

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Rotate line (1) clockwise by 30 to get line (9). Rotate line (9) by 90 to get line (10). Place line (10) onto the point where line (9) intersects the edge of the six inch circle. The point where lines (1), (4) and (10) intersect will be the pallet's circle center.

If you rotate line (2) counterclockwise by 2, you would see that the escape wheel's impulse face occupies a span of 2 of escape wheel rotation. (The impulse face also provides 3 of lift and lock.)

Since the escape wheel rotates by 12 per beat and you want 2 for drop and 2 for the escape tooth's impulse face, the pallet should occupy a span of 8. Rotate line (9) counterclockwise by 4 to get line (11). Rotate line (9) clockwise by 4 to get line (12). Repeat with line (2) to get lines (13) and (14):

Rotate line (2) counterclockwise by 45 to get line (15). Notice that it is at an angle half way between the escape circle's radius and the pallet circle's radius, shown by lines (2) and (4) respectively:

Rotate line (13) clockwise by 15 to get line (16), and place it onto the point where lines (13) and (15) intersect. Line (16) will be the pallet's locking face, and it will have a draw angle of 15. Duplicate line (16) and place it onto the point where lines (14) and (15) intersect: lines (16) and (17) are parallel. Rotate line (17) by 90 to get line (18) and place it in a suitable position along lines (16) and (17). The pallet is now recognizable. You could place a small line at the point where lines (2) and (15) intersect: this small line would show the mid-point of the pallet.

Once you finish the entry pallet, group the lines and duplicate them. Rotate the second pallet clockwise by 60 because that is the angle between lines (2) and (9), and then place the pallet on the exit side such that the mid-point of the impulse face lies on the point where lines (9) and (10) intersect. Most watches have different pallets, but an escapement using the same pallet on both sides can be designed, and using the same pallets makes manufacture easier.

It will be necessary to draw the pallet circle to perform a simulation. The circle must be larger than the drawing of the pallets, so I chose a six inch diameter circle, placed a horizontal and a vertical line in it, grouped the circle and the lines, and then placed them such that the circle center would lie on the point where lines (1), (4) and (10) intersect.

To draw the pallet arms, you could use circles, stretched and shaped to give the outline you desire. It should be obvious by looking at the drawing below that the design is of equidistant impulse.

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