**4. Motion study**

SolidWorks motion studies are graphical simulations of motion for assembly models. Motion studies do not change an assembly model or its properties, but they simulate and animate the motion that is prescribed for a model. Motion study has a timeline-based interface named "Motion Manager" that includes animation, basic motion, and motion analysis [8, 9].

of spring force expression (*e*), and exponent of damper force expression (*d*) [8, 10]. Spring property manager was used for the simulation of helical spring (**Figures 4** and **5**), gold (passing) spring (**Figures 4**–**6**), and detent blade (**Figures 4**–**7**), and parameters settings for

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**5.** Contact must be defined in a motion study to prevent parts from penetrating each other during motion [8]. Forces can be generated between contacting components, or components can be constrained to touch continually [5]. In the motion study of this mechanism are shown four different contacts: between discharging pallet and gold spring, escapement wheel teeth and impulse pallet, detent, and gold spring and between escapement wheel teeth and locking pallet [5, 8]. Static and kinetic friction coefficients simulate dry friction, since the lubrication of escapement wheel teeth is not needed. The escapement wheel is

**6.** Force/Torque property manager applies forces, moments, or torques with uniform distribution to faces, edges, reference points, vertices, and beams in any direction for use in structural studies [8]. Forces can be defined by type, parameter values, and mathematical expressions [9]. The escapement wheel receives the energy from the twisted chronometer's

The motion manager tree (on the left) is divided involves used simulation elements (forces, motors, and springs), components entities that appear in SolidWorks Feature Manager design tree, orientation, and camera views settings [9]. The timeline is located to the right of the motion manager design tree. It displays the times and types of animation events in the motion study and it is divided by vertical grid lines corresponding to numerical markers showing the time [8, 9]. Key points represent a beginning or end of a change in animation position or other attributes at a given time. In other words, a key point is the entity that corresponds to define assembly component positions, visual properties, or simulation element states. Key frame defines the portion of the timeline that separates key points (it can be any length of time). Change bars are horizontal bars connecting key points and they indicate a change between key points (component motion, animation duration, and simulation element property changes) [5, 8, 9]. As it was previously mentioned, standard mates were used for the assemblage of chronometer escapement components since these mates do not change physical properties of assembly

The working cycle of Thomas Earnshaw's chronometer detent escapement mechanism is

**1.** Rotation of the escapement wheel is blocked by the detent locking pallet. Balance wheel

**2.** Discharging event is taking place. Discharging pallet engages the gold spring and moves the detent blade until the moment when locking stone releases the wheel tooth [5].

**3.** Impulse event is starting to occur. Tooth of the escapement wheel drops (escapes) and engages the impulse pallet. The balance wheel proceeds counter clockwise, and the wheel

made of steel and all pallets are made of ruby (corundum) [8, 9].

mainspring and the constant torque out of *M =* 25 N acts on it [5].

the simulation are shown in **Table 1** [5].

in dynamical analysis.

divided into six steps that are shown in **Figure 8** [5]:

rotates counter clockwise [5, 7].

tooth continues to push the pallet [5, 7].

Animation is available in core of SolidWorks, and it can be used to animate the simple motion of assemblies by adding motors to drive the motion of one or more parts of an assembly or by prescribing the positions of assembly components at various times using set key points. Animation uses interpolation to define the motion of assembly components between key points [8].

Basic motion is available in the core of SolidWorks and it can be used for the approximation of the effects of motors, springs, contact, and gravity. Even though the mass is taken into consideration, computation is relatively fast [8, 9].

Motion analysis is available with the SolidWorks application "Motion TM" add-in to SolidWorks Premium. It is used accurately for simulations and analyses of the effects of motion elements (dampers, forces, springs, and friction) on an assembly. Motion analysis uses computationally strong kinematic solvers and accounts for material properties as well as mass and inertia in the computations [9].

The graphics section for SolidWorks motion study of Thomas Earnshaw's chronometer detent mechanism is split horizontally into upper and lower area and it is shown on **Figure 7** [5]. Assembly of the mechanism as a whole is in the upper area and the lower area is divided into three segments: timeline with key points and time bar on the right, the motion manager toolbar across the top, and the motion manager design tree on the left [5, 8, 9].

The motion manager toolbar contains some of the following property managers:


of spring force expression (*e*), and exponent of damper force expression (*d*) [8, 10]. Spring property manager was used for the simulation of helical spring (**Figures 4** and **5**), gold (passing) spring (**Figures 4**–**6**), and detent blade (**Figures 4**–**7**), and parameters settings for the simulation are shown in **Table 1** [5].

**4. Motion study**

54 Modeling and Computer Simulation

SolidWorks motion studies are graphical simulations of motion for assembly models. Motion studies do not change an assembly model or its properties, but they simulate and animate the motion that is prescribed for a model. Motion study has a timeline-based interface named

Animation is available in core of SolidWorks, and it can be used to animate the simple motion of assemblies by adding motors to drive the motion of one or more parts of an assembly or by prescribing the positions of assembly components at various times using set key points. Animation uses interpolation to define the motion of assembly components between key points [8].

Basic motion is available in the core of SolidWorks and it can be used for the approximation of the effects of motors, springs, contact, and gravity. Even though the mass is taken into

Motion analysis is available with the SolidWorks application "Motion TM" add-in to SolidWorks Premium. It is used accurately for simulations and analyses of the effects of motion elements (dampers, forces, springs, and friction) on an assembly. Motion analysis uses computationally strong kinematic solvers and accounts for material properties as well as

The graphics section for SolidWorks motion study of Thomas Earnshaw's chronometer detent mechanism is split horizontally into upper and lower area and it is shown on **Figure 7** [5]. Assembly of the mechanism as a whole is in the upper area and the lower area is divided into three segments: timeline with key points and time bar on the right, the motion manager

**1.** Gravity (property manager) is a simulation element that moves components around an assembly by inserting a simulated gravitational force. Gravity parameters are direction reference and numeric gravity value, but only one of these definitions can be used in any simulation [8, 9]. Gravity has been eliminated from dynamical analysis of escapement

**2.** Damper (property manager) is consisted of linear and torsional damper and it simulates the effects of energy dissipation [8]. This motion study does not deal with dumpers separately, since the dumping characteristics have already been included into the spring simulation [5].

**3.** Motors are motion study elements that move components in an assembly by simulating the effects of various types of motors. Motors can be rotary and linear [8]. This function was not used in the motion study of Thomas Earnshaw's chronometer detent escapement

**4.** Springs are simulation elements that move components around an assembly by simulating the effects of various types of springs. They can be linear and torsional springs [8]. Parameters are spring constant (*k*), damping constant (*c*), free length (angle *φ*), exponent

toolbar across the top, and the motion manager design tree on the left [5, 8, 9].

The motion manager toolbar contains some of the following property managers:

mechanism, since it does not affect the performance of the mechanism [8].

"Motion Manager" that includes animation, basic motion, and motion analysis [8, 9].

consideration, computation is relatively fast [8, 9].

mass and inertia in the computations [9].

mechanism [5].


The motion manager tree (on the left) is divided involves used simulation elements (forces, motors, and springs), components entities that appear in SolidWorks Feature Manager design tree, orientation, and camera views settings [9]. The timeline is located to the right of the motion manager design tree. It displays the times and types of animation events in the motion study and it is divided by vertical grid lines corresponding to numerical markers showing the time [8, 9].

Key points represent a beginning or end of a change in animation position or other attributes at a given time. In other words, a key point is the entity that corresponds to define assembly component positions, visual properties, or simulation element states. Key frame defines the portion of the timeline that separates key points (it can be any length of time). Change bars are horizontal bars connecting key points and they indicate a change between key points (component motion, animation duration, and simulation element property changes) [5, 8, 9].

As it was previously mentioned, standard mates were used for the assemblage of chronometer escapement components since these mates do not change physical properties of assembly in dynamical analysis.

The working cycle of Thomas Earnshaw's chronometer detent escapement mechanism is divided into six steps that are shown in **Figure 8** [5]:


**Figure 7.** Motion study of Thomas Earnshaw's chronometer detent escapement mechanism.


The amplitude of the balance wheel oscillation must achieve the value of nearly 270**°** to each side of its center equilibrium position. This amplitude can be achieved by choosing the proper value of the escapement wheel torque [5]. The center equilibrium position should be chosen in such a way to deliver impulses to the impulse pallet symmetrically and that can be achieved

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**Figure 8.** Six steps (a–f) of working cycle of Thomas Earnshaw's chronometer detent escapement mechanism.

by the adjustment of the helical spring free angle [1, 5].

**Table 1.** Parameters settings for the motion manager spring function.

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**4.** The detent is released by the discharging pallet and drops back to rest. The escapement wheel tooth continues to push on the pallet until the tooth drops off, and the appropriate tooth is locked on the detent locking stone. Impulse event is finished. The balance wheel

**5.** The balance wheel rotates clockwise and comes against the passing spring through the discharging pallet again, but on the opposite site. However, instead of lifting the detent, the passing spring gives way. As the balance wheel continues rotation the passing spring

**6.** The balance wheel reaches its amplitude position and begins to rotate counter clockwise. Mechanism has just finished the complete working cycle and is ready to repeat the new

reaches its amplitude position and begins to rotate clockwise [5].

cycle, which is effectively equivalent to the previous one [7].

**Figure 7.** Motion study of Thomas Earnshaw's chronometer detent escapement mechanism.

**Table 1.** Parameters settings for the motion manager spring function.

Helical spring 180 0.1 0.02 1 1 Gold spring 0 15.0 0.05 1 1 Detent blade 0 0.05 0.0001 1 1

**φ [deg] k [mm/deg] c [N mm/(deg/s)] e d**

is released [5, 7].

56 Modeling and Computer Simulation

**Figure 8.** Six steps (a–f) of working cycle of Thomas Earnshaw's chronometer detent escapement mechanism.

The amplitude of the balance wheel oscillation must achieve the value of nearly 270**°** to each side of its center equilibrium position. This amplitude can be achieved by choosing the proper value of the escapement wheel torque [5]. The center equilibrium position should be chosen in such a way to deliver impulses to the impulse pallet symmetrically and that can be achieved by the adjustment of the helical spring free angle [1, 5].
