**2. Constructive geometry and basic principles**

**Figure 1** shows all components of chronometer escapement mechanism. Escapement wheel (1) receives the energy from twisted mainspring and is mashed with the last gear of the chronometer main gear train [5]. Balance wheel (B) performs torsion oscillations with a rotational motion about the axis of the helical spring (S), while the rotation of escapement wheel is blocked by the locking pallet (10) until the discharging pallet (5) pushes the gold spring (9) supported by the horn of detent (11) [5, 7]. Discharging event occurs during the period of time in which balance wheel (B) rotates in positive (counterclockwise) direction. As the

balance moves, the discharging pallet (5) on the balance staff engages the gold spring (9) and moves the detent blade (8) until the locking stone (10) releases the wheel tooth. At that precise moment, one tooth of the escapement wheel drops (escapes) and the next in advance engages the impulse pallet (3), which is a jewel fastened into the impulse roller [1, 5]. As the balance wheel proceeds, the wheel tooth continues to push the pallet (3), and after the short movement, the detent (8) is released and drops back to rest. Now, in the rest position, detent locking stone

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**Figure 1.** All parts of Thomas Earnshaw's chronometer detent escapement mechanism.

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**Figure 1.** All parts of Thomas Earnshaw's chronometer detent escapement mechanism.

The detent or chronometer escapement is considered the most accurate of the balance wheel escapements and it was used in marine chronometers [1]. In 1748, Pierre Le Roy invented the early form of it. He created a pivoted detent type of escapement [2, 3]. Around 1775, John Arnold invented the first effective design of detent escapement. In 1780, Arnold's escapement was modified by Thomas Earnshaw [3, 4]. If watches or clocks had been equipped with free harmonic oscillators, they would have performed harmonic oscillations with constant frequency. But real watch balance wheels always perform dumped and driven oscillations. Thomas's modification

**1.** Impulsive: It maintains the balance wheel oscillations and keeps its amplitude constant

Important characteristics of Thomas Earnshaw's chronometer detent escapement mechanism

**1.** Balance wheel (oscillator) is almost free from the escapement influence and thus independent from the interference by the main gear train. In accordance to this, Thomas Earnshaw's escapement belongs to the escapement group named as "detached." Balance wheel coupled with detached escapement performs almost free harmonic oscil-

**2.** Escapement wheel is locked on a stone (jewel) carried in a detent. Impulse is given by the teeth of the escapement wheel (when a tooth is unlocked) to a pallet on the balance staff in every alternate swing of the balance wheel. Instead as a pivoted lever, the detent is designed and constructed as a blade spring and consequently does not require lubrication

**3.** Geometry and kinematics of the escapement teeth and impulse pallet are designed in such a way that they also do not need lubrication. This feature is of greatest importance for the stability of the balance wheel oscillations and uniform chronometer's going rate [5].

**Figure 1** shows all components of chronometer escapement mechanism. Escapement wheel (1) receives the energy from twisted mainspring and is mashed with the last gear of the chronometer main gear train [5]. Balance wheel (B) performs torsion oscillations with a rotational motion about the axis of the helical spring (S), while the rotation of escapement wheel is blocked by the locking pallet (10) until the discharging pallet (5) pushes the gold spring (9) supported by the horn of detent (11) [5, 7]. Discharging event occurs during the period of time in which balance wheel (B) rotates in positive (counterclockwise) direction. As the

to the chronometer escapement was very close to previously mentioned ideal [5]. Two different but equally important functions are accomplished by escapement:

**2.** Regulative: It regulates the speed of the watch main movement [5, 6].

**2. Constructive geometry and basic principles**

[5, 6].

46 Modeling and Computer Simulation

lations [5].

[1, 5].

are:

balance moves, the discharging pallet (5) on the balance staff engages the gold spring (9) and moves the detent blade (8) until the locking stone (10) releases the wheel tooth. At that precise moment, one tooth of the escapement wheel drops (escapes) and the next in advance engages the impulse pallet (3), which is a jewel fastened into the impulse roller [1, 5]. As the balance wheel proceeds, the wheel tooth continues to push the pallet (3), and after the short movement, the detent (8) is released and drops back to rest. Now, in the rest position, detent locking stone (10) is ready to lock the nest tooth. The wheel tooth continues to push on the pallet (3) until the tooth drops off, and the appropriate tooth is locked on the detent locking stone (10) [5, 7]. On its return, the balance wheel (B) rotates clockwise and comes against the gold (passing) spring (9) through the discharging pallet (5) again but on the opposite site [2, 5]. However, as the balance wheel (B) proceeds, instead of lifting the detent (8), the passing spring (9) gives way, and as the balance continues rotation, the passing spring (9) is released. This is particularly important for the proper operation of the escapement since no push or impulse is given to the locking stone (10) and discharge roller (4) during the clockwise rotation of the balance wheel (B) [5]. Escapement working cycle can repeat endlessly long. This was the explanation of basic working principles of Thomas Earnshaw's chronometer detent escapement mechanism.

length of detent line is assumed to be *l*

impulse pallet circle *D*<sup>i</sup>

by dynamical analysis [5].

given beneath:

**1.** Escapement wheel

**3.** Balance wheel and discharge roller

**4.** Balance wheel thermal compensation

**2.** Impulse roller

**3. Making of 3D model and assembly**

<sup>d</sup> *=* 130 mm. The distance between the point *E* (center

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is determined by geometrical construction in SolidWorks sketch, as

Modeling, Motion Study, and Computer Simulation of Thomas Earnshaw's Chronometer Detent…

of escapement wheel) and detent line should be a bit longer than the radius of escapement wheel and it is presumed to be *l =* 65 mm. For the reason of safe mashing between impulse pallet and escapement teeth, the impulse pallet drop of at least 1° on each side of the pallet must be defined, and as a result, the escapement wheel rotates by 22° [5]. The diameter of the

well as *D*d (diameter of the discharge pallet's circle—the assumption is that it rotates by 30° during discharge) and *R* (length of the detent—the assumption is that it rotates by 2*°* during discharge). The position p and length q of the locking pallet can be found from the disposition

There is no need for lubrication of the escapement wheel of Thomas Earnshaw's chronometer escapement and that is its biggest advantage over all other watch escapements. Balance's impulse pallet and the escape tooth roll together, so there is less friction (they not slide across one another) [2, 5]. Lubricant viscosity changes due to the temperature changes (it can even dry up), and the ability of chronometer escapement to run dry can result in more consistent timekeeper [5, 7]. The constructive geometry of this mechanism can be modified and adapted

Since the constructive geometry and basic principles have been explained so far, now, 3D modeling can be easily conducted. Making of 3D model and assembly was completed in

As it is known, when using some of the programs for 3D modeling, all parts of one assembly must be modeled separately. In this case, all parts of chronometer detent escapement mechanism were created according to the constructive geometry that is previously explained and applied in sketches definition. The set of SolidWorks commands named "Features" was used for part modeling. Commands such as "Extruded Boss/Base," "Revolved Boss/Base," "Lofted Boss/Base," and "Swept Boss/Base" were used for material adding, while commands such as "Extruded Cut," "Revolved Cut," "Lofted Cut," and "Swept Cut" were used to remove the material in various ways. Part modeling includes the specification of materials and physical properties that are principally important for dynamical analysis and appropriate motion study of a mechanism as a whole. **Figure 3** [5] shows the modeling of escapement wheel. All other components are modeled in the same way; they are shown in **Figure 4** and their list is

"SolidWorks 2016" and the procedure will be explained in continuance.

of the escapement tooth and detent angular displacement [1, 5].

Some of the parameters of escapement constructive geometry (**Figure 2**) are known, some of them can be acquired willingly, and the rest must be rigidly established [5, 7].

Commonly, the escapement wheel has 15 teeth that are at mutual angular distance out of 24°, even though the wheels of 12, 14, and 16 teeth can be found often. The angle between *EO* and detent line is 45°, the diameter of escapement wheel is assumed to be *d*<sup>E</sup> *=* 120 mm, and the

**Figure 2.** Constructive geometry of Thomas Earnshaw's chronometer detent escapement mechanism.

length of detent line is assumed to be *l* <sup>d</sup> *=* 130 mm. The distance between the point *E* (center of escapement wheel) and detent line should be a bit longer than the radius of escapement wheel and it is presumed to be *l =* 65 mm. For the reason of safe mashing between impulse pallet and escapement teeth, the impulse pallet drop of at least 1° on each side of the pallet must be defined, and as a result, the escapement wheel rotates by 22° [5]. The diameter of the impulse pallet circle *D*<sup>i</sup> is determined by geometrical construction in SolidWorks sketch, as well as *D*d (diameter of the discharge pallet's circle—the assumption is that it rotates by 30° during discharge) and *R* (length of the detent—the assumption is that it rotates by 2*°* during discharge). The position p and length q of the locking pallet can be found from the disposition of the escapement tooth and detent angular displacement [1, 5].

There is no need for lubrication of the escapement wheel of Thomas Earnshaw's chronometer escapement and that is its biggest advantage over all other watch escapements. Balance's impulse pallet and the escape tooth roll together, so there is less friction (they not slide across one another) [2, 5]. Lubricant viscosity changes due to the temperature changes (it can even dry up), and the ability of chronometer escapement to run dry can result in more consistent timekeeper [5, 7]. The constructive geometry of this mechanism can be modified and adapted by dynamical analysis [5].
