Constant Velocity Joint

Joint that enforces a constant-velocity kinematic constraint between two shafts

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Libraries:
Simscape / Multibody / Joints

Description

The Constant Velocity Joint block enforces a constant-velocity (CV) kinematic constraint between its base and follower frames, whose origins are coincident throughout the simulation. Specifically, if the Z-axes of the base and follower frames are both fixed with respect to a common reference frame, the Z-components of the two frames' angular velocities with respect to the common reference frame are equal.

The block has two degrees of freedom that allow the Z-axes of the base and follower frames to be arbitrarily oriented relative to each other. The figure shows an example.

The black and red frames indicate the base and follower frames of the block. The azimuth rotation about the Z-axis of the base frame locates the plane in which the bend angle occurs. The bend angle about the resulting Y-axis, the red Y-axis, specifies the orientation of the Z-axis of the follower frame with respect to the Z-axis of the base frame.

The block has two parameterizations, Rotation Sequence (faster simulation) or Quaternion (allows zero bend angle), to specify the internal states of the joint. Use the rotation-sequence parameterization whenever possible because a simulation with this parameterization is generally faster than a simulation with the quaternion parameterization. See Internal State for more information.

You can specify the desired initial states of the joint with the parameters under State Targets, such as the position and velocity of the azimuth and bend angle.

The block has a variety of sensing abilities. You can sense the azimuth, bend angle, and their time derivatives throughout the simulation. Furthermore, you can sense the forces and torques that act in the joint, such as constraint forces and total torque. For more information, see Composite Force/Torque Sensing section.

Faults

Using mode faults, you can change the joint modes during a simulation without modifying the model design. The fault injection overrides the mode setting. For example, if a joint has the Mode parameter set to Locked and the Fault behavior parameter set to Disengaged, the joint becomes disengaged.

To add a mode fault to a joint block, click on the joint block, in the Simscape Block tab, and the Faults section, click Fault > Add Fault. Alternatively, you can click the joint block, hover over the ellipsis to open the action bar, and click the Add a fault on the block icon . You can add multiple faults to a joint block, but the joint block can have only one active fault during a simulation.

As you add faults, in the Property Inspector, under the Fault section, specify the behavior and the trigger type of the fault. To define the fault behavior, click the link next to the Fault Behavior. This joint supports Locked, Normal, or Disengaged mode. The joint blocks support these trigger types: Always on, Timed, Manual, and Conditional. For more details of these trigger types, see Set Fault Triggers. To trigger a conditional fault, you can use Simulink signals, Simscape language blocks, and MATLAB workspace variables. To set the active fault for a block, use the Fault Table. For more details, see Access the Fault Table and Fault Dashboard.

To enable fault simulation, in the Simscape Block tab and the Faults section, turn on the Fault Simulation button. The fault simulation is on when the button is green and the status is on. The simulation logs the trigger status data. To view the data, use the Simulation Data Inspector. Also, you can see the fault status and a summary of the triggered faults in the Fault Dashboard. To open the Fault Dashboard, in the Simscape Block tab, click Faults > Fault Dashboard.

To create and modify faults, you can also use Simscape™ and Simulink^® fault functions. For more details, see the function section of the Simulink Fault Controls and Simscape Faults Interface.

Examples

Modeling Constant Velocity Joints - Power Take-Off Shaft

A Power Take-Off (PTO) shaft, a device for transferring power from tractor engines to auxiliary equipment such as soil tillers and wood chippers. The model includes two PTO subsystems identical in every sense but their joints. One contains universal (U) joints, the other constant-velocity (CV) joints.

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Ports

Frame

B — Base frame

frame

Port associated with the base frame of the joint block. In typical applications where a CV joint couples two shafts, the Z-axis of base frame is aligned with the driving shaft.

F — Follower frame

frame

Port associated with the follower frame of the joint block. In typical applications where a CV joint couples two shafts, the Z-axis of follower frame is aligned with the driven shaft.

Input

Mode Configuration

mode — Joint mode control

physical signal

Input port that controls the mode of the joint. The signal must be a unitless scalar. The joint mode is normal when the input signal is 0, disengaged when the input signal is -1, and locked when the input signal is 1. You can change the mode at any time during the simulation.

The table shows how the position and velocity of the joint change during transitions between modes.

Transitions	Position	Velocity
Normal to Locked	The joint position retains the current value and remains constant after the transition.	The joint velocity becomes zero and remains constant after the transition.
Normal to Disengaged	The joint position retains the current value but can change in any direction after the transition.	The joint velocity retains the current value but can change in any direction after the transition.
Locked to Normal	The joint position retains the current value but can change in the directions aligned with the joint degrees of freedom (DOFs) after the transition.	The joint velocity remains at zero but can change in the directions aligned with the joint DOFs after the transition.
Locked to Disengaged	The joint position retains the current value but can change in any direction after the transition.	The joint velocity remains at zero but can change in any direction after the transition.
Disengaged to Normal	For the directions aligned with the joint DOFs, the joint positions initially take values calculated by using Newton's method and can change thereafter. In the constrained directions, the joint positions become zero and remain constant after the transition.	For the directions aligned with the joint DOFs, the joint velocities initially take values calculated by using Newton's method and can change thereafter. In the constrained directions, the joint velocities become zero and remain constant after the transition.
Disengaged to Locked	For the directions aligned with the joint DOFs, the joint positions initially take values calculated by using Newton's method and remain constant after the transition. In the constrained directions, the joint positions become zero and remain constant after the transition.	The joint velocity becomes zero and remains constant after the transition.

Dependencies

To enable this port, under Mode Configuration, set Mode to Provided by Input.

Output

qb — Bend angle

scalar

Bend angle of the CV joint, returned as a scalar. This quantity is the angle between the Z-axes of the base and follower frames of the block.

Dependencies

To enable this port, under Constant Velocity Primitive (CV) > Sensing > Bend Angle, select Position.

wb — Velocity of bend angle

scalar

Velocity of the bend angle of the CV joint, returned as a scalar. This quantity equals the time derivative of the signal output from port qb.

Dependencies

To enable this port, under Constant Velocity Primitive (CV) > Sensing > Bend Angle, select Velocity.

bb — Acceleration of bend angle

scalar

Acceleration of the bend angle of the CV joint, returned as a scalar. This quantity equals the second time derivative of the signal output from port qb.

Dependencies

To enable this port, under Constant Velocity Primitive (CV) > Sensing > Bend Angle, select Acceleration.

qa — Azimuth

scalar

Azimuth of the CV joint, returned as a scalar. This quantity is the angle of the rotation about the Z-axis of the base frame. The rotation locates the plane in which the bend angle occurs.

Dependencies

To enable this port, under Constant Velocity Primitive (CV) > Sensing > Azimuth, select Position.

wa — Velocity of azimuth

scalar

Velocity of the azimuth of the CV joint, returned as a scalar. This quantity equals the time derivative of the signal output from port qa.

Dependencies

To enable this port, under Constant Velocity Primitive (CV) > Sensing > Azimuth, select Velocity.

ba — Acceleration of azimuth

scalar

Acceleration of the azimuth of the CV joint, returned as a scalar. This quantity equals the second time derivative of the signal output from port qa.

Dependencies

To enable this port, under Constant Velocity Primitive (CV) > Sensing > Azimuth, select Acceleration.

Composite Force/Torque Sensing

fc — Constraint force, N

physical signal

Physical signal port that outputs the constraint forces that act across the joint. These forces maintain the translational constraints of the joint. The output has a 3-by-1 vector format and represents the force components along the x, y, and z axes of the resolution frame. For more information, see Force and Torque Sensing.

Dependencies

To enable this port, under Composite Force/Torque Sensing, select Constraint Force.

tc — Constraint torque, N*m

physical signal

Physical signal port that outputs the constraint torques that act across the joint. These torques maintain the rotational constraints of the joint. The output has a 3-by-1 vector format and represents the torque components about the x, y, and z axes of the resolution frame. For more information, see Force and Torque Sensing.

Dependencies

To enable this port, under Composite Force/Torque Sensing, select Constraint Torque.

ft — Total force, N

physical signal

Physical signal port that outputs the total force that acts across the joint. The total force is the sum of the of all forces transmitted between the connected frames through the joint. The output has a 3-by-1 vector format and represents the force components along the x, y, and z axes of the resolution frame.

To demonstrate the total force acting on a joint, the figure shows a model using a Prismatic Joint block.

The total force includes the actuator force (F_A), internal force (F_I), and constraint forces (F_C). For more information, see Force and Torque Sensing.

Dependencies

To enable this port, under Composite Force/Torque Sensing, select Total Force.

tt — Total torque, N*m

physical signal

Physical signal port that outputs the total torque that acts across the joint. The total torque is the sum of all torques transmitted between the connected frames through the joint. The torque includes the actuation, internal, limit, and constraint torques. The output has a 3-by-1 vector format and represents the torque components about the x, y, and z axes of the resolution frame. For more information, see Force and Torque Sensing.

Dependencies

To enable this port, under Composite Force/Torque Sensing, select Total Torque.

Parameters

Constant Velocity Primitive (CV)

Internal State — Internal state parameterization of joint

Rotation Sequence (faster simulations) (default) | Quaternion (allows zero bend angle)

Choose the parameterization to specify the internal states of the joint.

Rotation Sequence (faster simulations)

The Constant Velocity Joint block uses the Z-Y-Z rotation sequence parameterization. The angle of the second Z-axis rotation is the negative of the angle of the first Z-axis rotation.

Use this method whenever possible because a simulation with this parameterization is generally faster than a simulation with the quaternion parameterization. However, the Z-Y-Z rotation sequence parameterization has a kinematic singularity when the bend angle is zero. If zero bend angle is required, set Internal State to Quaternion (allows zero bend angle).

Quaternion (allows zero bend angle)

The Constant Velocity Joint block uses the quaternion parameterization. To enforce the CV kinematic constraint, the fourth component of the quaternion, the Z-component of the vector part, is always zero.

Use this method when zero bend angle is required. This method does not have a kinematic singularity at zero bend angle but has a kinematic singularity when the bend angle is 180 degrees. A simulation with this parameterization is generally slower than a simulation with the Z-Y-Z parameterization.

State Targets > Specify Position Target — Whether to specify position target

off (default) | on

Select this parameter to enable parameters for specifying the position target of the joint.

State Targets > Specify Position Target > Priority — Priority level of position target

High (desired) (default) | Low (approximate)

Set the priority level of the position target. See Guiding Assembly for more information.

Dependencies

To enable this parameter, under Constant Velocity Primitive (CV) > State Targets, select Specify Position Target.

State Targets > Specify Position Target > Value — Angles to specify position target

Bend Angle Only (default) | Bend Angle and Azimuth

Whether to specify the position target of the CV joint at the start of simulation using only the bend angle or the bend angle and the azimuth.

Dependencies

To enable this parameter, under Constant Velocity Primitive (CV) > State Targets, select Specify Position Target.

State Targets > Specify Position Target > Value > Bend Angle — Bend angle to specify

45 deg (default)

Specify the bend angle of the CV joint.

Dependencies

To enable this parameter, under Constant Velocity Primitive (CV) > State Targets, select Specify Position Target.

State Targets > Specify Position Target > Value > Azimuth — Azimuth to specify

0 deg (default)

Specify the azimuth of the CV joint.

Dependencies

To enable this parameter, under Constant Velocity Primitive (CV) > State Targets > Specify Position Target > Value, select Bend Angle and Azimuth.

State Targets > Specify Velocity Target — Whether to specify velocity target

off (default) | on

Select this parameter to enable parameters for specifying the velocity target of the joint.

State Targets > Specify Velocity Target > Priority — Priority level of velocity target

High (desired) (default) | Low (approximate)

Set the priority level of the velocity target. See Guiding Assembly for more information.

Dependencies

To enable this parameter, under Constant Velocity Primitive (CV) > State Targets, select Specify Velocity Target.

State Targets > Specify Velocity Target > Value — Parameters to specify velocity target

Bend Angle Only (default) | Bend Angle and Azimuth

Whether to specify the velocity target of the CV joint at the start of simulation using only the bend angle or the bend angle and the azimuth.

Dependencies

To enable this parameter, under Constant Velocity Primitive (CV) > State Targets, select Specify Velocity Target.

State Targets > Specify Velocity Target > Value > Bend Angle — Bend angle velocity to specify

0 deg/s (default)

Specify the bend angle velocity of the CV joint.

Dependencies

To enable this parameter, under Constant Velocity Primitive (CV) > State Targets, select Specify Velocity Target.

State Targets > Specify Velocity Target > Value > Azimuth — Azimuth velocity to specify

0 deg/s (default)

Specify the azimuth velocity of the CV joint.

Dependencies

To enable this parameter, under Constant Velocity Primitive (CV) > State Targets > Specify Velocity Target > Value, select Bend Angle and Azimuth.

Sensing > Bend Angle > Position — Whether to sense bend angle

off (default) | on

Select this parameter to enable the port qb.

Sensing > Bend Angle > Velocity — Whether to sense velocity of bend angle

off (default) | on

Select this parameter to enable the port wb.

Sensing > Bend Angle > Acceleration — Whether to sense acceleration of bend angle

off (default) | on

Select this parameter to enable the port bb.

Sensing > Azimuth > Position — Whether to sense azimuth

off (default) | on

Select this parameter to enable the port qa.

Sensing > Azimuth > Velocity — Whether to sense velocity of azimuth

off (default) | on

Select this parameter to enable the port wa.

Sensing > Azimuth > Acceleration — Whether to sense acceleration of azimuth

off (default) | on

Select this parameter to enable the port ba.

Mode Configuration

Mode — Joint mode

Normal (default) | Locked | Disengaged | Provided by Input

Joint mode for the simulation, specified as one of these values:

Mode	Description
Locked	Locked mode constrains all the degrees of freedom (DOFs) for the joint. The locked joint maintains its initial assembly position with zero velocity during the simulation. The joint block can sense forces or torques in accordance with the settings of the Internal Mechanics, Limits, and Actuation parameters.
Normal	Normal mode enables the DOFs and the constraints of the joint work as intended during the simulation.
Disengaged	Disengaged mode releases the joint from all constraints throughout the simulation. The settings for Internal Mechanics, Limits, and Actuation parameters do not affect the disengaged joint. All output ports output zero.
Provided by Input	The Provided by Input option allows you to specify the joint mode by using an input signal. For more information, see the port mode in the Input section.

Composite Force/Torque Sensing

Direction — Measurement direction

Follower on Base (default) | Base on Follower

Measurement direction, specified as one of these values:

• Follower on Base — The block senses the force and torque that the follower frame exerts on the base frame.

• Base on Follower — The block senses the force and torque that the base frame exerts on the follower frame.

This parameter affects only the output signals under the Composite Force/Torque Sensing section. Reversing the direction changes the sign of the measurements. For more information, see Force and Torque Measurement Direction.

Resolution Frame — Frame used to resolve measurements

Base (default) | Follower

Frame used to resolve the measurements, specified as one of these values:

• Base — The block resolves the measurements in the coordinates of the base frame.

• Follower — The block resolves the measurements in the coordinates of the follower frame.

This parameter affects only the output signals under the Composite Force/Torque Sensing section.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2015a

R2025a: Model mode faults

You can now model mode faults for all the joint blocks. Using the faults, you can change the joint modes during a simulation without changing the model design. For more information, see the Faults section in the description.