Motion Study Analysis of Internal Geneva Mechanism

Aim:- Motion Study Analysis of Internal Geneva Mechanism using Solidworks.

Objective:-

1. To create 3D models for driver and driven wheels.

2. To perform motion analysis by rotating the driver wheel at 10rpm.

3. To obtain the following plots: Contact force (between driving and the driven wheel) as a function of time; Angular Displacement of the driven wheel.

4. To compare Angular Velocity of the driver wheel for 10RPM and 20 RPM.

5. To compare the contact forces with and without "Precise contact".

Introduction:-

The Geneva drive or Maltese cross is a gear mechanism that translates a continuous rotation movement into intermittent rotary motion.

The rotating drive wheel is usually equipped with a pin that reaches into a slot located in the other wheel (driven wheel) that advances it by one step at a time. The drive wheel also has an elevated circular blocking disc that "locks" the rotating driven wheel in position between steps.

External Geneva Drive

In this most common arrangement of the Geneva drive, the driven wheel has four slots and thus advances the drive by one step at a time (each step being 90 degrees) for each full rotation of the master wheel. If the steered wheel has n slots, it advances by 360°/n per full rotation of the propeller wheel. It can be built smaller and can withstand higher mechanical stresses. Because the mechanism needs to be well lubricated, it is often enclosed in an oil capsule.

Internal Geneva Drive

An internal Geneva drive is a variant of the design. The axis of the drive wheel of the internal drive can have a bearing only on one side. The angle by which the drive wheel has to rotate to effect one step rotation of the driven wheel is always smaller than 180° in an external Geneva drive and always greater than 180° in an internal one, where the switch time is, therefore, greater than the time the driven wheel stands still.

Spherical Type Geneva Mechanism

In this type of mechanism, the Geneva cross is in Spherical shape and the cam drives are connected externally, which is extremely rare. The driver and driven wheel are on perpendicular shafts. The duration of the dwell is exactly 180 degrees of driver rotation.

ADVANTAGES OF GENEVA MECHANISM

1. Geneva mechanism may be the simplest and least Expensive of all intermittent motion mechanisms.

2. They come in a wide variety of sizes, ranging from those used in instruments, to those used in machine tools to index spindle carriers weighing several tons.

3. They have good motion curves characteristics compared to ratchets but exhibit more “jerk” or instantaneous change in acceleration than better cam systems

4. Geneva maintains good control of its load at all times since it is provided with locking ring surfaces.

DISADVANTAGES OF GENEVA MECHANISM

1. Geneva is not a versatile mechanism.

2. All Geneva acceleration curves start and end with finite acceleration & deceleration. This means they produce a jerk.

APPLICATIONS & USES

1. Modern film projectors may also use an electronically controlled indexing mechanism or stepper motor, which allows for fast-forwarding the film.

2. Geneva wheels having the form of the driven wheel were also used in mechanical watches, but not in a drive, rather limit the tension of the spring, such that it would operate only in the range where its elastic force is nearly linear.

3. Geneva drive include the pen change mechanism in plotters, automated sampling devices

4. Indexing tables in assembly lines, tool changers for CNC machines, and so on.

5. The Iron Ring Clock uses a Geneva mechanism to provide intermittent motion to one of its rings.

3D Models and 2D Drawings:-

Driver Wheel:-

Driven Wheel:-

Assembly:-

Motion Analysis:-

Study 1- Driver Wheel at 10 RPM with PRECISE Contacts(60FPS)

Plots/Graphs:-

Contact force (between driving and the driven wheel) as a function of time

On observing the reaction force plot, we can see that a common pattern(from 0 seconds to 6 seconds) is repeating.

Initially, at 0 seconds the pin of the driver wheel starts entering the slot of the driven wheel and a small peak in the graph at that point represents minute force (pin hits one of the faces of the slot).

As the pin moves into the slot, force reduces gradually.

At 2 seconds the pin reaches the end of the slot, the curve in the graph being flat. Here, the pin reaches a certain length into the slot, that length is equal to the distance of the center of the pin and the axis of the driving wheel.

Around 4 seconds, a small peak occurs representing contact of the pin with the outer face of the slot and the graph flattens because the pin rotates idly not being in contact with any of the slots.

At 6 second, there is a high peak of force which represents the pin entering the other slot. At this point the pin suddenly hits the face of the slot, hence a large force occurs.

After this, the cycle repeats and continues.

Angular Displacement of the driven wheel

In the angular displacement plot, we can see that a common pattern(from 0 seconds to 6 seconds) is repeating.

Initially, at 0 seconds the pin of the driver wheel starts entering the slot of the driven wheel.

As the pin moves into the slot, the angular displacement of the wheel increases gradually.

At 2 seconds the pin reaches the end of the slot. Here, the pin reaches a certain length into the slot, which is equal to the distance of the center of the pin and the axis of the driving wheel.

After 4 seconds, the graph starts to gradually flatten. At this point, the pin is coming out of the slot.

After that, the graph flattens because the pin rotates idly not being in contact with any of the slots.

At 6 seconds, the graph again gradually rises which represents the pin entering the other slot.

After this, the cycle repeats and continues.

Angular Velocity of the driver wheel

On analysing the angular velocity graph, we can see that a common pattern(from 0 seconds to 6 seconds) is repeating.

The initial angular velocity of the driver wheel is 60 deg/sec as per the graph.

Initially, at 0 seconds the pin of the driver wheel enters the slot of the driven wheel and a small peak in the graph at that point represents that the pin hits one of the faces of the slot. And then the graph gradually starts descending.

As the pin moves into the slot, angular velocity reduces gradually due to friction between the pin and the slot(considering the force required by the pin to move the driven wheel of some amount of weight).

At 2 seconds the pin reaches the end of the slot, the graph being flat for an instant because for a minute amount of time the pin does not rotate the driven wheel. Here, the pin reaches to a certain length into the slot, that length is equal to the distance of the centre of the pin and the axis of the driving wheel.

After that, a gradual rise in the graph is visible representing that the pin again starts moving the driven wheel.

After 4 seconds, the graph flattens suddenly because at this point the pin comes out of the slot, rotating idly not being in contact with any of the slots. Therefore, the driven wheel does not rotate for a while till the pin enters the other slot.

As soon as the pin hits one of the faces of the slot, a sudden rise in the graph occurs because the driven wheel gets a jerk start by the pin. Moreover, on observing animation carefully, we see that the driven wheel slightly rotate opposite to its direction of motion due to its weight and vibrations. Therefore, the pin hits the slot.

After this, the cycle repeats and continues.

Study 2- Driver Wheel at 10 RPM with NOT PRECISE Contacts(60FPS)

Plots/Graphs:-

Contact force (between driving and the driven wheel) as a function of time

On observing the reaction force plot, we can see that a common pattern(from 0 seconds to 6 seconds) is repeating.

Initially, at 0 seconds the pin of the driver wheel starts entering the slot of the driven wheel and a small peak in the graph at that point represents minute force (pin hits one of the faces of the slot).

As the pin moves into the slot, force reduces gradually.

At 2 seconds the pin reaches the end of the slot, the curve in the graph being flat. Here, the pin reaches to a certain length into the slot, that length is equal to the distance of the centre of the pin and the axis of the driving wheel.

Around 4 seconds, a small peak occurs representing contact of the pin with the outer face of the slot and the graph flattens because the pin rotates idly not being in contact with any of the slots.

At 6 second, there is a high peak of force which represents the pin entering the other slot. At this point the pin suddenly hits the face of the slot, hence large force occurs.

After this, the cycle repeats and continues.

Angular Displacement of the driven wheel

In angular displacement plot, we can see that a common pattern(from 0 seconds to 6 seconds) is repeating.

Initially, at 0 seconds the pin of the driver wheel starts entering the slot of the driven wheel.

As the pin moves into the slot, the angular displacement of the wheel increases gradually.

At 2 seconds the pin reaches the end of the slot. Here, the pin reaches to a certain length into the slot, which is equal to the distance of the centre of the pin and the axis of the driving wheel.

After 4 seconds, the graph starts to gradually flatten. At this point, the pin is coming out of the slot.

After that, the graph flattens because the pin rotates idly not being in contact with any of the slots.

At 6 second, the graph again gradually rises which represents the pin entering the other slot.

After this, the cycle repeats and continues.

Angular Velocity of the driver wheel

On analysing the angular velocity graph, we can see that a common pattern(from 0 seconds to 6 seconds) is repeating.

The initial angular velocity of the driver wheel is 60 deg/sec as per the graph.

Initially, at 0 seconds the pin of the driver wheel enters the slot of the driven wheel and a small peak in the graph at that point represents that the pin hits one of the faces of the slot. And then the graph gradually starts descending.

As the pin moves into the slot, angular velocity reduces gradually due to friction between the pin and the slot(considering the force required by the pin to move the driven wheel of some amount of weight).

At 2 seconds the pin reaches the end of the slot, the graph being flat for an instant because for a minute amount of time the pin does not rotate the driven wheel. Here, the pin reaches to a certain length into the slot, that length is equal to the distance of the centre of the pin and the axis of the driving wheel.

After that, a gradual rise in the graph is visible representing that the pin again starts moving the driven wheel.

After 4 seconds, the graph flattens suddenly because at this point the pin comes out of the slot, rotating idly not being in contact with any of the slots. Therefore, the driven wheel does not rotate for a while till the pin enters the other slot.

As soon as the pin hits one of the faces of the slot, a sudden rise in the graph occurs because the driven wheel gets a jerk start by the pin. Moreover, on observing animation carefully, we see that the driven wheel slightly rotate opposite to its direction of motion due to its weight and vibrations. Therefore, the pin hits the slot.

After this, the cycle repeats and continues.

Study 3- Driver Wheel at 20 RPM with Precise Contacts(120FPS)

Plots/Graphs:-

Contact force (between driving and the driven wheel) as a function of time

On observing the reaction force plot, we can see that a common pattern(from 0 seconds to 3 seconds) is repeating.

Initially, at 0 seconds the pin of the driver wheel hits the face of the slot and starts entering into it and a small peak in the graph at that point represents minute force.

As the pin moves into the slot, force reduces gradually.

At 1 second the pin reaches the end of the slot, the curve in the graph being flat. Here, the pin reaches to a certain length into the slot, that length is equal to the distance of the centre of the pin and the axis of the driving wheel.

Around 2 seconds, a small peak occurs representing contact of the pin with the outer face of the slot and after that, suddenly the graph drops because the pin leaves the slot and starts rotating idly not being in contact with any of the slots.

At 3 seconds, there is a high peak of force which represents the pin entering the other slot. At this point the pin suddenly hits the face of the slot, hence large force occurs. The reason for this peak is the slight opposite rotation of the driven wheel due to its own weight and vibration in the mechanism.

This cycle repeats and continues.

Note:- The major peaks(at 3,6,9,12,15 and 18 seconds) are not exactly the same because there are vibrations in the mechanism and also at that every instance, the driven wheel slightly rotates opposite to its actual rotation(counter-clockwise) due to which the pin strikes the face of the slot. The slight opposite rotation of the driven is not the same for every instance, hence variable peaks are observed.

Angular Displacement of the driven wheel

In the angular displacement plot, we can see that a common pattern(from 0 seconds to 10 seconds) repeats twice. This means 2 revolutions were taken by the driven wheel. Therefore, the pin enters and leaves the slots 8 times in 20 seconds in total.

The graph between 0 to 3 seconds represents the pin entering and leaving the slot.

Initially, the pin of the driver wheel starts entering the slot of the driven wheel.

As the pin moves into the slot, the angular displacement of the wheel increases gradually.

At 1 second the pin reaches the end of the slot. Here, the pin reaches a certain length into the slot, which is equal to the distance of the centre of the pin and the axis of the driving wheel.

After 2 seconds, the graph starts to gradually flatten. At this point, the pin is coming out of the slot.

After that, the graph flattens because the pin rotates idly not being in contact with any of the slots. Hence, no displacement is observed for that little time.

After 3 seconds, the graph again gradually rises which represents the pin entering the other slot.

After this, the cycle repeats and continues.

Angular Velocity of the driver wheel

On analyzing the angular velocity graph, we can see that a common pattern(from 0 seconds to 3 seconds) is repeating.

The initial angular velocity of the driver wheel is 119 deg/sec as per the graph approximately.

Initially, the pin of the driver wheel enters the slot of the driven wheel and then the graph gradually starts descending.

As the pin moves into the slot, angular velocity reduces gradually due to friction between the pin and the slot(considering the force required by the pin to move the driven wheel of some amount of weight).

When the pin reaches the end of the slot, the graph falls for an instance because for a minute amount of time the pin does not rotate the driven wheel. Here, the pin reaches a certain length into the slot, that length is equal to the distance of the centre of the pin and the axis of the driving wheel.

After that, a gradual rise in the graph is visible representing that the pin again starts moving the driven wheel.

Finally, the graph flattens suddenly because at this point the pin comes out of the slot, rotating idly not being in contact with any of the slots. Therefore, the driven wheel does not rotate for a while till the pin enters the other slot.

As soon as the pin hits one of the faces of the slot, a sudden rise in the graph occurs because the driven wheel gets a jerk start by the pin. Moreover, on observing animation carefully, we see that the driven wheel slightly rotates opposite to its direction of motion due to its weight and vibrations. Therefore, the pin hits the slot.

After this, the cycle repeats and continues.

At 20 RPM, there are 6 cycles in this graph whereas for 10 RPM there were only 3 cycles. Therefore, on increasing the revolutions per minute of the motor, the number of cycles increases for a fixed time plot for both the cases.

Motion Analysis Simulation:-

Google Drive Link - https://drive.google.com/drive/folders/1Jbh1As8v42Es4SDrZbE98u3CkRlLrV3v?usp=sharing

It contains graphs and spreadsheets for comparisons.

Conclusion:-

1. On comparing graphs for 10 RPM with precise contacts(study1) and without precise contacts(study2), the values for precise contacts in much greater than not precise contacts. Therefore, using precise contacts the results are quite accurate or precise.

2. On selecting "Precise contact", calculation of contacts is done using the equations that represent the solid bodies. If we clear the "Precise contact", the calculation of contacts is done approximately using the geometry of many-sided polygons. When we select Use Precise Contact, the computed contact is analytically correct, but the computation can take longer than an approximate solution.

3. On increasing the number of revolutions per minute for the motor, the number of cycles increases which can be seen in comparing the graphs of 10 RPM and 20 RPM.

4. After comparing contact forces for precise and not precise contacts in spreadsheets, we observed that maximum forces for "precise contacts" are greater than "not precise contacts". In a precise contacts graph, the maximum force is 1.7232E+03 newton at 6.033 seconds whereas for not precise contacts is 1.6356+03 newton at 6.00 seconds.

Reference:-

https://en.wikipedia.org/wiki/Geneva_drive

Tags - #genevamechanism #geneva #mechanics #analysis #simulation #mbd #motionanalysis #multibodydynamics