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Chain & Sprocket SimulationChain & Sprocket SimulationChain & Sprocket SimulationChain & Sprocket SimulationChain & Sprocket SimulationChain & Sprocket SimulationChain & Sprocket SimulationChain & Sprocket SimulationChain & Sprocket SimulationChain & Sprocket SimulationChain & Sprocket SimulationChain & Sprocket SimulationChain & Sprocket SimulationChain & Sprocket SimulationChain & Sprocket SimulationChain & Sprocket Simulationusingusingusingusingusingusingusingusing

CATIA V5 DMU CATIA V5 DMU CATIA V5 DMU CATIA V5 DMU CATIA V5 DMU CATIA V5 DMU CATIA V5 DMU CATIA V5 DMU KinematicsKinematicsKinematicsKinematicsKinematicsKinematicsKinematicsKinematicsCATIA V5 DMU CATIA V5 DMU CATIA V5 DMU CATIA V5 DMU CATIA V5 DMU CATIA V5 DMU CATIA V5 DMU CATIA V5 DMU KinematicsKinematicsKinematicsKinematicsKinematicsKinematicsKinematicsKinematics(Revised 27SEP09)(Revised 27SEP09)(Revised 27SEP09)(Revised 27SEP09)(Revised 27SEP09)(Revised 27SEP09)(Revised 27SEP09)(Revised 27SEP09)

Website = http://bndtechsource.ucoz.com Prepared by: Bill Harbin –Technical Director 27-Sep-09

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� The following licenses are required to � The following licenses are required to

simulate Chain & Sprocket movement with CATIA V5 DMU Kinematics: CATIA V5 DMU Kinematics:

� Digital Mockup + DMU Kinematics� Digital Mockup + DMU Kinematics� Mechanical Design + Part Design� Mechanical Design + Assembly Design� Mechanical Design + Assembly Design

Prepared by: Bill Harbin –Technical Director 27-Sep-09

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� The end result we are trying to achieve is � The end result we are trying to achieve is

to simulate the movement of a bicycle chain around the sprockets.chain around the sprockets.

Prepared by: Bill Harbin –Technical Director 27-Sep-09

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� There are certain known values when � There are certain known values when

you begin your simulation.19 T

Sprocket Center Curve

Links19 T

Sprocket Center Curve

40 T11 T

Adjustable Sprocket

11 T

Adjustable Sprocket

Drive Sprocket

Prepared by: Bill Harbin –Technical Director 27-Sep-09

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� Known values:� Known values:

� Sprocket sizes (number of teeth)� Sprocket placement (center to center)� Sprocket placement (center to center)� Sprocket adjustability (lower derailleur)� Link size (12.7mm)� Link size (12.7mm)� Total Number of Links (106)

� These values will help set up the � These values will help set up the Sprocket Center Curve.

Prepared by: Bill Harbin –Technical Director 27-Sep-09

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� To accurately simulate the chain movement around � To accurately simulate the chain movement around

the sprockets, you must first understand the chordal relationship of the Link to the Sprocket.chordal relationship of the Link to the Sprocket.

Each Link moves around the Sprocket with a fixed length.

Prepared by: Bill Harbin –Technical Director 27-Sep-09

Each Link moves around the Sprocket with a fixed length.This is the Chord of the Angular rotation of the Sprocket.

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� The Chord length is not the same as the Arc length.� The Chord length is not the same as the Arc length.

Ex. Arc Length = 12.713Ex. Chord Length = 12.7

This may seem insignificant, but CATIA is very exacting.

Prepared by: Bill Harbin –Technical Director 27-Sep-09

This may seem insignificant, but CATIA is very exacting.

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� Time for some trigonometry...� Time for some trigonometry...

Ex. 40T Drive Sprocket:

360O /40 = 9O

12.7

6.35 360O /40 = 9O

Chord Length = 12.7

Radius = x

Sin-1 (6.35/x) = 4.5O

6.35

Sin-1 (6.35/x) = 4.5O

x = (6.35/sin4.5O)

x = 80.934mm

Circ = 2ππππR = 508.523mm

9O

4.5OCirc = 2ππππR = 508.523mm

Arc Length =

508.523/40 = 12.713066

Sprkt Ctr Curve =

4.5

x

Prepared by: Bill Harbin –Technical Director 27-Sep-09

Sprkt Ctr Curve =

106*12.713066 = 1347.585mm

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R80.934

R38.58

Sprocket Center Curve Length= 1347.585

R22.539

R22.539

Prepared by: Bill Harbin –Technical Director 27-Sep-09

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� Here are the Joints and Commands to run the � Here are the Joints and Commands to run the

Simulation (Laws come later).

Sprockets

Links

Sprockets

Links

Prepared by: Bill Harbin –Technical Director 27-Sep-09

Links

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� The Gear Joints for the Sprockets will begin with � The Gear Joints for the Sprockets will begin with

the normal ratio (ex. 40T/19T=2.105).

40T Drive Sprocket

19T Sprocket

SprocketSprocket

11T Sprocket

11T Sprocket

Prepared by: Bill Harbin –Technical Director 27-Sep-09

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� The Link Shuttle is created with two Links (Inner & � The Link Shuttle is created with two Links (Inner &

Outer). These two links will run along the Sprocket Center Curve and the Sprocket Tracking Curve.Center Curve and the Sprocket Tracking Curve.

Sprocket Tracking Curve

Link Tracking Curve

Sprocket Tracking Curve

Inner Link Shuttle PointInner Link Shuttle Point

Outer Link Shuttle Point

Prepared by: Bill Harbin –Technical Director 27-Sep-09

Sprocket Center Curve

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� There will be four Joints in the Link Shuttle .� There will be four Joints in the Link Shuttle .

2) Slide-Curve Joint• Inner Link Tracking CurveTracking Curve

• Sprocket Tracking Curve

1) Point-Curve Joint• Point on Inner Link

3) Point-Curve Joint• Point on Outer LinkInner Link

• Sprocket Center Curve

4) Revolute Joint• Inner Link

Outer Link• Sprocket Center Curve

Prepared by: Bill Harbin –Technical Director 27-Sep-09

• Inner Link• Outer Link

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dimensions.This dimension should This dimension should be exactly the same as the Link dimension.

Prepared by: Bill Harbin –Technical Director 27-Sep-09

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� Check Link roller-to-roller centerline dimensions � Check Link roller-to-roller centerline dimensions

(for both Links).This dimension should This dimension should be exactly the same as the Sprocket dimension.

Prepared by: Bill Harbin –Technical Director 27-Sep-09

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� Check Drive Sprocket tooth centerline to the � Check Drive Sprocket tooth centerline to the

Sprocket Center Curve.They should

intersect exactly.

Prepared by: Bill Harbin –Technical Director 27-Sep-09

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� Check Link roller centerline to the Sprocket Center � Check Link roller centerline to the Sprocket Center

Curve.They should

intersect exactly.

Prepared by: Bill Harbin –Technical Director 27-Sep-09

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� Create a Law Sketch 954x954 (106x9O).� Create a Law Sketch 954x954 (106x9O).

This Law will be applied to the Drive Chain Sprocket for Chain Sprocket for rotation angle.

Prepared by: Bill Harbin –Technical Director 27-Sep-09

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� Apply the Law to the Gear Command.� Apply the Law to the Gear Command.

c) Pick the Law Sketch.

a) Double pick the Command.

Law Sketch.

b) Pick Link.

d) Pick OK.

Prepared by: Bill Harbin –Technical Director 27-Sep-09

d) Pick OK.

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� Apply a Formula to the Shuttle Command.� Apply a Formula to the Shuttle Command.

a) Double pick the Command.

c) Hold cursor over Formula.

b) Right click inside the Command value box.

over Formula.

d) Drop cursor onto Edit.

Prepared by: Bill Harbin –Technical Director 27-Sep-09

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� Apply a Formula to the Shuttle Command (cont’d).� Apply a Formula to the Shuttle Command (cont’d).

The start point of the Sprocket Center Curve a) Type this value with

1344.896mm+’Chain 2\Commands\Chain Wheel Rotation\Angle1’*80.93389225mm

The start point of the Sprocket Center Curve is 1344.896 from the Link Shuttle Point.

a) Type this value with mm followed by +

b) Pick the Drive Sprocket Command.

d) Type the Radius d) Type the Radius value followed by mm.

c) Double pick this text to place it into the Formula. e) Pick Ok.

Prepared by: Bill Harbin –Technical Director 27-Sep-09

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� Apply a Formula to the Shuttle Command (cont’d).� Apply a Formula to the Shuttle Command (cont’d).

You will get this Syntax Warning.Syntax Warning.

-Do not be alarmed. -It is telling you that you must be precise when converting angular measurement to length measurement. measurement to length measurement. -This is why it is important to add the mm to your Formula. Else it will assume meters!

Prepared by: Bill Harbin –Technical Director 27-Sep-09

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� Run the Kinematic with Laws.� Run the Kinematic with Laws.

Pick Simulation with Laws Icon.with Laws Icon.

When you run the simulation, When you run the simulation, the Links should end exactly

where they began.

Prepared by: Bill Harbin –Technical Director 27-Sep-09

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� Return the Kinematic Simulation to the beginning.� Return the Kinematic Simulation to the beginning.

If you toggle between the start between the start and the end, the Links should appear not to

move.move.

Return the Kinematic Simulation to the beginningSimulation to the beginning

Prepared by: Bill Harbin –Technical Director 27-Sep-09

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� Check the Links as they travel across the other � Check the Links as they travel across the other

Sprockets. (19T Sprocket shown)There may be an angular There may be an angular mismatch as the Link

meets the Sprocket tooth.

This problem is easily This problem is easily corrected by using the compass, while current in the CatProduct, to rotate the Sprocket to the

0.557 deg

Prepared by: Bill Harbin –Technical Director 27-Sep-09

the Sprocket to the correct position.

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� A different challenge arises as you rotate the � A different challenge arises as you rotate the

Sprocket further around.Notice the angle is closing

This means the Sprocket is Notice the angle is closing

as you rotate.

This means the Sprocket is rotating faster than the

Link is moving.

0.202 deg

Prepared by: Bill Harbin –Technical Director 27-Sep-09

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� A different challenge arises as you rotate the � A different challenge arises as you rotate the

Sprocket further around.Notice the angle is closing

The reason for this is the Notice the angle is closing

as you rotate.

The reason for this is the smaller radius on this Sprocket results in a larger Arc Length.

0.202 deg

Prepared by: Bill Harbin –Technical Director 27-Sep-09

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� Time for some more trigonometry...� Time for some more trigonometry...

Ex. 19T Drive Sprocket:

360O /19 = 18.947O

12.7

6.35 360O /19 = 18.947O

Chord Length = 12.7

Radius = x

Sin-1 (6.35/x) = 9.4735O

6.35

Sin-1 (6.35/x) = 9.4735O

x = (6.35/sin9.4735O)

x = 38.58mm

Circ = 2ππππR = 242.403mm

18.947O

9.4735OCirc = 2ππππR = 242.403mm

Arc Length =

242.403/19 = 12.75805x

Prepared by: Bill Harbin –Technical Director 27-Sep-09

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� Adjust the Gear Ratio.� Adjust the Gear Ratio.

To correct the problem of different Arc Lengths, simply divide the Drive Sprocket Arc Length by the 19T Sprocket Arc length, then multiply the current Gear Ratio by that value.length, then multiply the current Gear Ratio by that value.

12.713/12.758 = .996472801Current Gear Ratio = Current Gear Ratio = 40/19 = 2.105263158New Gear Ratio = 2.105263158* .996472801 = 2.097837476 2.105263158* .996472801 = 2.097837476

The same technique can be applied to the 11T gears.

Prepared by: Bill Harbin –Technical Director 27-Sep-09

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� Adjust the Gear Ratio.� Adjust the Gear Ratio.

12.713/12.758 = .996472801Current Gear Ratio = Double pick the Current Gear Ratio = 40/19 = 2.105263158New Gear Ratio = 2.105263158* .996472801 = 2.097837476

Double pick the Gear Joint to edit the ratio.

Prepared by: Bill Harbin –Technical Director 27-Sep-09

The same technique can be applied to the 11T gears.

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� Congratulations!! Now the real work begins...� Congratulations!! Now the real work begins...

Prepared by: Bill Harbin –Technical Director 27-Sep-09

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� Complete the chain with all 106 Links!� Complete the chain with all 106 Links!

Prepared by: Bill Harbin –Technical Director 27-Sep-09

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� Complete the chain with all 106 Links!� Complete the chain with all 106 Links!

Here is where we left off.we left off.

Each new Link will have two joints.1) Point-Curve Joint1) Point-Curve Joint

• Point on Link• Sprocket Center Curve

2) Revolute Joint• Inner Link• Inner Link• Outer Link

Prepared by: Bill Harbin –Technical Director 27-Sep-09

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� Complete the chain with all 106 Links!� Complete the chain with all 106 Links!

Add the remaining 104 Links and Joints…Links and Joints…

And here is where you will get to.

Prepared by: Bill Harbin –Technical Director 27-Sep-09

you will get to.Good Luck!

BND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSourceBND TechSource� Conclusion: � Conclusion:

This explanation of how we created our bicycle chain simulation put together at the bicycle chain simulation put together at the request of our users.

� If you have a request, please visit our free � If you have a request, please visit our free website at http://bndtechsource.ucoz.com

Prepared by: Bill Harbin –Technical Director 27-Sep-09