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
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=1.5⁢R,−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=T1⁢exp⁡μ⁢β
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=T1⁢exp⁡μ⁢tanh⁡vrelv0⁢β+2⁢nTurns⁢π
where vrel⁡t 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.
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
Choose between two possible solutions for the rope/pulley configuration. Refer to the section Rope Arrangement above.
useAltConfig
Condition
Units
R
0.2
m
Pitch radius of the pulley
1
kg
Pulley mass (excluding the holder)
Use cylindrical geometry
true
When checked (true) pulley inertia is calculated assuming a uniform thin-disk geometry
useCylindricalGeometry
I
Use cylindrical geometry is false
kg⁢m2
Pulley rotational inertia
Inertia
Rope
λ
0
kgm
Linear density
lambda
Turns
Number of additional full turns
nTurns
Use tension correction
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
mf
Locked=false
Frame (holder) mass
If
Frame (holder) rotational inertia
Inertiaf
Add frame offset
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
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.
Include slippage
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
0.01
ms
Smoothing function scale, i.e. tanh⁡vrelv0
Initial Conditions
ICθ,ω
Ignore
Indicates whether MapleSim ignores, tries to enforce, or strictly enforces the rotational initial conditions
MechRotTree
θ0
rad
Initial rotation of the joint at the start of the simulation, expressed about the e^axis axis
InitAng
ω0
rads
Initial angular velocity of the the joint at the start of the simulation, expressed about the e^axis
IntAngVel
Visualization
Show pulley
Show pulley visualization
showPulley
Show frame
Locked=false∧Add frame offset=true
Show pulley frame visualization
showFrame
Show rope
Show rope visualization
showRope
Transparent pulley
Show pulley=true
Select this option to make the pulley transparent
transparent_pulley
Transparent frame
Locked=false∧Add frame offset=true∧Show frame=true
Select this option to make the frame transparent
transparent_frame
Transparent rope
Show rope=true
Select this option to make the rope transparent
transparent_rope
radius
Show rope=true∨Show pulley=true
0.02
This radius is only used for visualization
ndiv
Number of segments used for rope visualization
nDiv
Pulley color
blue
color_pulley
Frame color
orange
color_frame
Color based on tension
Show rope=true∧ndiv>0
colorMode
Rope color 1
gray
color
Rope color 2
Color based on tension=true
red
color2
τmin
N
Minimum Tension: color 1
minTension
τmax
1000
Maximum Tension: color 2
maxTension
Setup
Test mode
Use this option to test the pulley configuration. All rope connections and internal dynamics are switched off when in test mode
testMode
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=false∨Pulley on end a=true
Side a 1-D translational flange for rope flow
flange_a
flangeb
Fixed end b=false∨Pulley on end b=true
Side b 1-D translational flange for rope flow
flange_b
flangec
1-D rotational flange for pulley rotation
flange_c
See Also
Cable
Chain
Winch
Winch3D
Ropes and Pulleys Library Overview
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