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Pulley

Pulley component for use with Rope, Chain, or Cable components

The Pulley component models a simplified 3-D pulley and must be connected to Rope, Chain, or Cable components. Various use cases are shown below.

 

Details

Parameters

Connections

Details

Connecting Ropes

When connecting Rope/Chain/Cable components to a Pulley:

1. Make sure the required options, Pulley on end a or Pulley on end b (found under Connections parameters) are checked on the connecting Rope/Chain/Cable components before making the connection to the Pulley.

2. A connection between a Rope/Chain/Cable component and a Pulley requires both the Multibody ports and the 1-D Translational ports:

3. Make sure that the arrows on the Pulley components and the corresponding Rope/Chain/Cable components point in the same direction.

Rope Arrangement

When connecting a Rope/Chain/Cable components to a Pulley, there are always two possible solutions:

To change the selected solution, check the option Use alternative configuration on the Pulley component.

Frame Offset

The Add frame offset option adds a rigid body offset to the pulley frame mass and inertia. When enabled, a simple visualization for the pulley frame is be added using an additional visualization parameter.

The frame geometry is defined by the 2-vector parameter rf in the rotation plane of the pulley.

For example, if e^axis=0,0,1 (or local z axis), then the first element of rf is in local x and the second in local y. Below the frame visualization is shown for e^axis=0,0,1 and rf=1.5R,R, where R is the pulley radius.

If e^axis=0,1,0 (or local y axis), then the first element of rf is in local z and the second in local x. Below, the frame visualization is shown for the same offset as the previous case but with e^axis=0,1,0.

If e^axis=1,0,0 (or local x axis), then the first element of rf is in local y and the second in local z.

Locked Pulley

Use the option Locked (found in the Settings parameter group) to enable/disable an internal rotational degree of freedom for the rotation of the pulley with respect to its holder.

Fixed or Floating Pulleys

The Pulley component can be uses as a fixed or floating pulley depending on the model configuration.

                       

The pulley frame (frame_c) must be given appropriate initial conditions (position and orientation). This can be done either through other system components with defined initial conditions, or by a Free Motion component as shown above.

Slippage

Simplified rope slippage is included by enabling the include slippage option (found in the Slippage parameter group) . The relationship between high tension (T2 ) and low tension (T1) sides is given by the Euler equation

T2=T1expμβ

where β is the contact angle and μ is the coefficient of friction.

The actual implementation has two modifications compared to the above: 1) Friction smoothing to avoid numerical instability, 2) option for additional full turns:

T2=T1expμtanhvrelv0β+2nTurnsπ

where vrelt is the relative rope/pulley sliding velocity, v0 is velocity threshold parameter for smoothing friction, and nTurns is the number of additional full turns of rope around the pulley.

Test Mode

The test mode helps arrange the Pulley components in a model before connecting Rope/Chain/Cable components. In this mode, which is activated by setting the Boolean parameter Test mode to true, all geometric parameters can be adjusted and inspected in the 3-D playback window.

Parameters

Settings

Name

Default

Description

Modelica ID

e^axis

0,0,1

Unit vector (w.r.t. local frame) defining the axis of the rotation for the pulley.

e_axis

Locked

false

When checked (true), frame_c (holder) is disabled.  Refer to the Section Fixed or Floating Pulleys above.

locked

Use alternative configuration

false

Choose between two possible solutions for the rope/pulley configuration.  Refer to the section Rope Arrangement above.

useAltConfig

Pulley

Name

Condition

Default

Units

Description

Modelica ID

R

 

0.2

m

Pitch radius of the pulley

R

m

 

1

kg

Pulley mass (excluding the holder)

m

Use cylindrical geometry

 

true

 

When checked (true) pulley inertia is calculated assuming a uniform thin-disk geometry

useCylindricalGeometry

I

Use cylindrical geometry is false

 

kgm2

Pulley rotational inertia

Inertia

Rope

Name

Default

Units

Description

Modelica ID

λ

0

kgm

Linear density

lambda

Turns

0

 

Number of additional full turns

nTurns

Use tension correction

false

 

When checked (true) additional torque is applied to the pulley to enforce torque = tension x radius even when the rope is not in the plane of the pulley.

useTensionCorrection

Frame

Name

Condition

Default

Units

Description

Modelica ID

mf

Locked=false

1

kg

Frame (holder) mass

mf

If

Locked=false

 

kgm2

Frame (holder) rotational inertia

Inertiaf

Add frame offset

 

false

 

When checked (true), a rigid body frame is added to the pulley frame to move the connection point away from the center

addFrameOffset

rf

Add frame offset=true

0,R

m

Offset in the pulley plane. If the rotational axis is local X, the offset is local Y,Z. Offset for other choices for the rotation axis follow the right-hand rule.

rf

Slippage

Name

Condition

Default

Units

Description

Modelica ID

Include slippage

 

false

 

Enable slippage calculations. When checked (true) rope can slide on the pulley depending on the tension, contact angle, and the coefficient of friction.

includeSlippage

μ

Include slippage = true

0.1

 

Rope/Pulley coefficient of friction

mu

v0

Include slippage = true

0.01

ms

Smoothing function scale, i.e. tanhvrelv0

v0

Initial Conditions

Name

Default

Units

Description

Modelica ID

ICθ,ω

Ignore

 

Indicates whether MapleSim ignores, tries to enforce, or strictly enforces the rotational initial conditions

MechRotTree

θ0

0

rad

Initial rotation of the joint at the start of the simulation, expressed about the e^axis axis

InitAng

ω0

0

rads

Initial angular velocity of the the joint at the start of the simulation, expressed about the e^axis

IntAngVel

Visualization

Name

Condition

Default

Units

Description

Modelica ID

Show pulley

 

true

 

Show pulley visualization

showPulley

Show frame

Locked=falseAdd frame offset=true

true

 

Show pulley frame visualization

showFrame

Show rope

 

true

 

Show rope visualization

showRope

Transparent pulley

Show pulley=true

false

 

Select this option to make the pulley transparent

transparent_pulley

Transparent frame

Locked=falseAdd frame offset=trueShow frame=true

false

 

Select this option to make the frame transparent

transparent_frame

Transparent rope

Show rope=true

false

 

Select this option to make the rope transparent

transparent_rope

radius

Show rope=trueShow pulley=true

0.02

m

This radius is only used for visualization

radius

ndiv

Show rope=true

0

 

Number of segments used for rope visualization

nDiv

Pulley color

Show pulley=true

blue

 

Pulley color

color_pulley

Frame color

Locked=falseAdd frame offset=trueShow frame=true

orange

 

Frame color

color_frame

Color based on tension

Show rope=truendiv>0

false

 

Color based on tension

colorMode

Rope color 1

Show rope=true

gray

 

Rope color 1

color

Rope color 2

Color based on tension=true

red

 

Rope color 2

color2

τmin

Color based on tension=true

0

N

Minimum Tension: color 1

minTension

τmax

Color based on tension=true

1000

N

Maximum Tension: color 2

maxTension

Setup

Name

Default

Description

Modelica ID

Test mode

false

Use this option to test the pulley configuration.  All rope connections and internal dynamics are switched off when in test mode

testMode

Connections

Name

Condition

Description

Modelica ID

framea

side=A

2-Vector multibody frame for Rope/Chain/Cable connection on side a

frame_a

frameb

side=B

2-Vector multibody frame for Rope/Chain/Cable connection on side b

frame_b

framec

Locked = false

Multibody frame for the pulley holder

frame_c

framed

 

Multibody frame for the pulley rigid body

frame_d

flangea

Fixed end a=falsePulley on end a=true

Side a 1-D translational flange for rope flow

flange_a

flangeb

Fixed end b=falsePulley on end b=true

Side b 1-D translational flange for rope flow

flange_b

flangec

Locked=false

1-D rotational flange for pulley rotation

flange_c

See Also

Cable

Chain

Pulley

Rope

Winch

Winch3D

Ropes and Pulleys Library Overview