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

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

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 given beneath:


(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.

Some of the parameters of escapement constructive geometry (**Figure 2**) are known, some of

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

them can be acquired willingly, and the rest must be rigidly established [5, 7].

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


All parts named above have been assembled in one functional mechanism in accordance with kinematical principles and constructive geometry that has been previously explained.

Complex assemblies contain many different parts, which can be the components of some other assemblies, so-called sub-assemblies [5]. When adding a part to an assembly, the bond between them is made and when user opens the assembly in SolidWorks, one can identify the

component file as a part of assembly. Changes in components manifest in the very assembly and parts are linked by command "Mate" that creates geometric tie between components. Mates define the allowable directions of linear or rotational motion of the components. They can be moved within its degrees of freedom, visualizing the assembly's behavior [8, 9]. Complete chronometer detent escapement modeled in "SolidWorks 2016" is shown on **Figure 5** [5].

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**1.** Standard mates define geometrical links between components (parallel, tangent, concentric, coincident, perpendicular, distance, or angle). For example, a concentric mate forces two cylindrical mates to become concentric, while a coincident mate forces two planar

There are three categories of mates—standard, advanced, and mechanical.

**Figure 4.** Components of chronometer detent escapement mechanism.

faces to become coplanar [8].

**Figure 3.** Escapement wheel modeled in SolidWorks 2016.

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**Figure 4.** Components of chronometer detent escapement mechanism.

**5.** Helical spring

**7.** Detent

**6.** Gold (Passing) spring

50 Modeling and Computer Simulation

**8.** Locking pallet (Jewel stone)

**9.** Discharging pallet (Jewel stone)

**11.** Chronometer mechanism frame [5, 8].

**Figure 3.** Escapement wheel modeled in SolidWorks 2016.

All parts named above have been assembled in one functional mechanism in accordance with

Complex assemblies contain many different parts, which can be the components of some other assemblies, so-called sub-assemblies [5]. When adding a part to an assembly, the bond between them is made and when user opens the assembly in SolidWorks, one can identify the

kinematical principles and constructive geometry that has been previously explained.

**10.** Impulse pallet (Jewel stone)

component file as a part of assembly. Changes in components manifest in the very assembly and parts are linked by command "Mate" that creates geometric tie between components. Mates define the allowable directions of linear or rotational motion of the components. They can be moved within its degrees of freedom, visualizing the assembly's behavior [8, 9]. Complete chronometer detent escapement modeled in "SolidWorks 2016" is shown on **Figure 5** [5].

There are three categories of mates—standard, advanced, and mechanical.

**1.** Standard mates define geometrical links between components (parallel, tangent, concentric, coincident, perpendicular, distance, or angle). For example, a concentric mate forces two cylindrical mates to become concentric, while a coincident mate forces two planar faces to become coplanar [8].


The assembling of Thomas Earnshaw's chronometer detent escapement was done only by using standard mates. This access describes the real process of the mechanism assemblage [5]. Firstly, chronometer frame is set as an immovable part of mechanism. Then, balance and escapement wheels are linked to the frame (axles of balance and escapement wheel are concentric with related bearings). On the inner surface of the balance wheel are thoroughly adhered two thermal compensation pieces. Helical spring is attached to the balance wheel and the frame (coincident mate is used), so its axis and axis of balance wheel are collinear. Detent assembly is made by linking detent blade to the detent foot so it can rotate about

detent foot axle. Eventually, mechanism is completed by adding three pallets–the locking, the impulse, and the discharging jewel stones [1, 5, 8]. Chronometer detent escapement mecha-

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**Figure 6.** Horizontal and isometric projection of Thomas Earnshaw's chronometer detent escapement mechanism.

nism is shown in **Figure 6** in horizontal and isometric projection [5].

**Figure 5.** The assembly of Thomas Earnshaw's chronometer detent escapement mechanism.

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**2.** Advanced mates include limit, symmetry, width, path, profile center, and linear/linear coupler. For instance, profile center mate automatically center-aligns geometric profiles to each other and fully defines the components. A path mate constrains a selected point on a component to a path that has been defined by selecting one or more entities in the

**3.** Mechanical mates contain gear, screw, hinge, slot, rack and pinion, cam-follower, and universal joint mates. For example, a hinge mate limits the movement between two components to one rotational degree of freedom. Gear mates force two components to rotate relative to one another about selected axes. A cam-follower mate is a type of tangent or coincident mate and it allows the user to mate a cylinder, plane, or point to a series of

The assembling of Thomas Earnshaw's chronometer detent escapement was done only by using standard mates. This access describes the real process of the mechanism assemblage [5]. Firstly, chronometer frame is set as an immovable part of mechanism. Then, balance and escapement wheels are linked to the frame (axles of balance and escapement wheel are concentric with related bearings). On the inner surface of the balance wheel are thoroughly adhered two thermal compensation pieces. Helical spring is attached to the balance wheel and the frame (coincident mate is used), so its axis and axis of balance wheel are collinear. Detent assembly is made by linking detent blade to the detent foot so it can rotate about

**Figure 5.** The assembly of Thomas Earnshaw's chronometer detent escapement mechanism.

assembly [8].

52 Modeling and Computer Simulation

tangent extruded faces [8, 9].

**Figure 6.** Horizontal and isometric projection of Thomas Earnshaw's chronometer detent escapement mechanism.

detent foot axle. Eventually, mechanism is completed by adding three pallets–the locking, the impulse, and the discharging jewel stones [1, 5, 8]. Chronometer detent escapement mechanism is shown in **Figure 6** in horizontal and isometric projection [5].
