Recoil escapements commonly are to be found in collections as simple, domestic pendulum-clocks. In America, the infant clockmaking industry almost exactly identified its beginning with that of mass-production techniques. Therefore, it is understandable that even tolerably old American clocks were mass-produced; and most of them were designed for use on tables or shelves, so they are small or moderate in size. Their mechanisms tend to exhibit near-standard characteristics of robust escapements, relatively short pendulums, and long escape-arcs for assured performance under conditions of casual handling and unstable alignment. Geometrically, the escapement of a typical specimen is very likely to appear as a square configuration in which the escape wheel occupies a corner diagonally opposite the corner which coincides with pallet-arbor axis; and the impulse-faces of the pallets are located at the remaining two corners of the reference square.

Unique limitations are to be found in the square recoil-escapement, and some advantages, too. As a special case, the square geometry lends itself to fairly straightforward analysis; and a layout method is offered for planar-pallets systems which provides convergent accuracy towards the order of precision that is required when escape wheels with high tooth-counts are employed.. The limitations and advantages are discussed in appropriate places, and it is emphasized that correct center-distances must be known and used. Of vital importance is the fact that escape wheels are obliged to have tooth-counts that identify with a specific sequence in which the numbers progress in steps of four tooth-units, I.e.: 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, etc.

The use of conjugate pallet-profiles, long ignored or misused in the clockmaking craft, is discussed; and four dimensioned examples are diagrammed. The profile-pairs are classed in terms of the vigor of their recoil functions, and their optimum curvatures are presented as circular-arc approximations dimensioned by radii and center-locations. It is suggested that a planar exit-pallet paired with an appropriate convex entry-pallet is the best practical choice for the constructions of small, moderately coarse-pitched escapements.

The geometrical constants, the dimensions, and the tables supplied should enable careful clockmakers to design and fabricate valid working escapements for their pendulum timepieces.

Notes and references include bibliographical data and complementary information; they are appended at the end of the paper.

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