# Universal Joint

Joint that allows for transfer of rotary motion between unaligned shafts

Libraries:
Simscape / Multibody / Joints

## Description

The Universal Joint block models a coupling between two spinning shafts. The two shafts align with the z-axes of the base and follower frames and rotate at the same average angular velocity. However, the relative velocities of the shafts fluctuate if the shafts are not aligned. The fluctuation increases as the bend angle increases. This joint constrains the origins of the two frames to be coincident.

The joint has two revolute primitives that represent two sequential rotations. The rotations specify the orientation of the follower frame with respect to the base frame. The first rotation is about the x-axis of the follower frame, and the second rotation is about the y-axis of the follower frame generated after the first rotation, as shown in the image.

To specify the target of the initial state for a joint primitive, use the parameters under State Targets. The targets are specified in the base frame. You can also set the priority levels for the targets. If the joint is not able to satisfy all the state targets, the priority level determines which targets to satisfy first and how closely to satisfy them. For an example, see the Guiding Assembly section of How Multibody Assembly Works.

To model damping and the spring behavior for a joint primitive, use the parameters under Internal Mechanics. Use the Damping Coefficient parameter to model energy dissipation and the Spring Stiffness parameter to model energy storage. Joint springs attempt to displace the joint primitive from its equilibrium position, and joint dampers act as energy dissipation elements. The springs and dampers are strictly linear.

To specify the limits of a joint primitive, use the parameters under Limits. The lower and upper bounds define the width of the free region. The block applies a force to accelerate the joint position back to the free region when the position exceeds the bounds. The block uses a smoothed spring-damper method to compute the force. For more information about the smoothed spring-damper method, see the Description section of the Spatial Contact Force block.

The Force, Torque, and Motion parameters in the Actuation section control the motion of the joint primitives during simulation. For more information, see Specifying Joint Actuation Inputs. Additionally, the joint block has ports that output sensing data, such as position, velocity, acceleration, force, and torque, that you can use to perform analytical tasks on a model. For more information, see Sensing and Force and Torque Sensing.

To specify the joint mode configuration, use the Mode parameter. For more details, see Mode Configuration under the Ports and Parameters sections.

## Ports

### Frame

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Base frame of the joint block.

Follower frame of the joint block.

### Input

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X Revolute Primitive (Rx)

Physical signal input port that accepts the actuation torque for the joint primitive. The block applies this torque equally and oppositely to both the base and follower frames of the joint primitive. The torque is about the x-axis of the base frame. The x-axes of the follower and base frames align with each other during simulation.

#### Dependencies

To enable this port, under X Revolute Primitive (Rx) > Actuation, set Torque to `Provided by Input`.

Physical signal input port that accepts the motion profile for the joint primitive. The block uses this signal to determine the rotation of the follower frame with respect to the base frame about the x-axis of the base frame. The signal must also contain the first and second derivatives of the rotation.

#### Dependencies

To enable this port, under X Revolute Primitive (Rx) > Actuation, set Motion to `Provided by Input`.

Y Revolute Primitive (Ry)

Physical signal input port that accepts the actuation torque for the joint primitive. The block applies this torque equally and oppositely to both the base and follower frames of the joint primitive. The torque is about the y-axis of the base frame. The y-axes of the follower and base frames align with each other during simulation.

#### Dependencies

To enable this port, under Y Revolute Primitive (Ry) > Actuation, set Torque to `Provided by Input`.

Physical signal input port that accepts the motion profile for the joint primitive. The block uses this signal to determine the rotation of the follower frame with respect to the base frame about the y-axis of the base frame. The signal must also contain the first and second derivatives of the rotation.

#### Dependencies

To enable this port, under Y Revolute Primitive (Ry) > Actuation, set Motion to `Provided by Input`.

Mode Configuration

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.

TransitionsPositionVelocity
Normal to LockedThe 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 DisengagedThe 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 NormalThe 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 DisengagedThe 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 NormalFor 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 LockedFor 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

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X Revolute Primitive (Rx)

Physical signal port that outputs the position of the joint primitive. The value is the rotation angle of the follower frame with respect to the base frame about the x-axis of the base frame.

#### Dependencies

To enable this port, under X Revolute Primitive (Rx) > Sensing, select Position.

Physical signal port that outputs the angular velocity of the joint primitive. The value is the first derivative of the signal from the port .

#### Dependencies

To enable this port, under X Revolute Primitive (Rx) > Sensing, select Velocity.

Physical signal port that outputs the angular acceleration of the joint primitive. The value is the second derivative of the signal from the port .

#### Dependencies

To enable this port, under X Revolute Primitive (Rx) > Sensing, select Acceleration.

Physical signal port that outputs the actuator torque acting on the joint primitive.

#### Dependencies

To enable this port, under X Revolute Primitive (Rx) > Sensing, select Actuator Torque.

Physical signal port that outputs the lower-limit torque. The block applies this torque when the joint primitive position is less than the lower bound of the free region. The block applies this torque to both the base and follower frames of the joint primitive in order to accelerate the relative position back to the free region.

#### Dependencies

To enable this port, under X Revolute Primitive (Rx) > Sensing, select Lower-Limit Torque.

Physical signal port that outputs the upper-limit torque. The block applies this torque when the joint primitive position exceeds the upper bound of the free region. The block applies this torque to both the base and follower frames of the joint primitive in order to accelerate the relative position back to the free region.

#### Dependencies

To enable this port, under X Revolute Primitive (Rx) > Sensing, select Upper-Limit Torque.

Y Revolute Primitive (Ry)

Physical signal port that outputs the position of the joint primitive. The value is the rotation angle of the follower frame with respect to the base frame about the y-axis of the base frame.

#### Dependencies

To enable this port, under Y Revolute Primitive (Ry) > Sensing, select Position.

Physical signal port that outputs the angular velocity of the joint primitive. The value is the first derivative of the signal from the port .

#### Dependencies

To enable this port, under Y Revolute Primitive (Ry) > Sensing, select Velocity.

Physical signal port that outputs the angular acceleration of the joint primitive. The value is the second derivative of the signal from the port .

#### Dependencies

To enable this port, under Y Revolute Primitive (Ry) > Sensing, select Acceleration.

Physical signal port that outputs the actuator torque acting on the joint primitive.

#### Dependencies

To enable this port, under Y Revolute Primitive (Ry) > Sensing, select Actuator Torque.

Physical signal port that outputs the lower-limit torque. The block applies this torque when the joint primitive position is less than the lower bound of the free region. The block applies this torque to both the base and follower frames of the joint primitive in order to accelerate the relative position back to the free region.

#### Dependencies

To enable this port, under Y Revolute Primitive (Ry) > Sensing, select Lower-Limit Torque.

Physical signal port that outputs the upper-limit torque. The block applies this torque when the joint primitive position exceeds the upper bound of the free region. The block applies this torque to both the base and follower frames of the joint primitive in order to accelerate the relative position back to the free region.

#### Dependencies

To enable this port, under Y Revolute Primitive (Ry) > Sensing, select Upper-Limit Torque.

Composite Force/Torque Sensing

Physical signal port that outputs the constraint forces that act across the joint. The force maintains the translational constraints of the joint. For more information, see Measure Joint Constraint Forces.

#### Dependencies

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

Physical signal port that outputs the constraint torques that act across the joint. The torque maintains the rotational constraints of the joint. For more information, see Force and Torque Sensing.

#### Dependencies

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

Physical signal port that outputs the total force that acts across the joint. The total force is the sum of the forces transmitted from one frame to the other through the joint. The force includes the actuation, internal, limit, and constraint forces. See Force and Torque Sensing for more information.

#### Dependencies

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

Physical signal port that outputs the total torque that acts across the joint. The total torque is the sum of the torques transmitted from one frame to the other through the joint. The torque includes the actuation, internal, limit, and constraint torques. For more information, see Force and Torque Sensing.

#### Dependencies

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

## Parameters

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To edit block parameters interactively, use the Property Inspector. From the Simulink® Toolstrip, on the Simulation tab, in the Prepare gallery, select .

### X Revolute Primitive (Rx)

State Targets

Select this parameter to specify the position target of the x revolute primitive.

Priority level of the position target, specified as `High (desired)` or `Low (approximate)`. For more information, see the Guiding Assembly section of How Multibody Assembly Works..

#### Dependencies

To enable this parameter, select Specify Position Target.

Position target of the x revolute primitive, specified as a scalar with a unit of angle.

#### Dependencies

To enable this parameter, select Specify Position Target.

Select this parameter to specify the angular velocity target for the x revolute primitive.

Priority level of the angular velocity target, specified as ```High (desired)``` or `Low (approximate)`. For more information, see the Guiding Assembly section of How Multibody Assembly Works.

#### Dependencies

To enable this parameter, select Specify Velocity Target.

Angular velocity target of the x revolute primitive, specified as a scalar with a unit of angular velocity.

#### Dependencies

To enable this parameter, select Specify Velocity Target.

Internal Mechanics

Position where the spring torque is zero, specified as a scalar with a unit of angle.

Stiffness of the internal spring-damper force law for the x revolute primitive, specified as a scalar with a unit of torsional stiffness.

Damping coefficient of the internal spring-damper force law for the x revolute primitive, specified as a scalar with a unit of damping coefficient.

Limits

Select this parameter to specify the lower limit of the x revolute primitive.

Lower bound for the free region of the x revolute primitive, specified as a scalar with a unit of angle.

#### Dependencies

To enable this parameter, select Specify Lower Limit.

Stiffness of the spring at the lower bound, specified as a scalar with a unit of torsional stiffness.

#### Dependencies

To enable this parameter, select Specify Lower Limit.

Damping coefficient at the lower bound, specified as a scalar with a unit of damping coefficient.

#### Dependencies

To enable this parameter, select Specify Lower Limit.

Region to smooth the spring and damper torques, specified as a scalar with a unit of angle.

The block applies the full value of the lower-limit torque when the penetration reaches the width of the transition region. The smaller the region, the sharper the onset of forces and the smaller the time step required of the solver. In the tradeoff between simulation accuracy and simulation speed, reducing the transition region improves accuracy and expanding it improves speed.

#### Dependencies

To enable this parameter, select Specify Lower Limit.

Select this parameter to specify the upper limit of the x revolute primitive.

Upper bound for the free region of the x revolute primitive, specified as a scalar with a unit of angle.

#### Dependencies

To enable this parameter, select Specify Upper Limit.

Stiffness of the spring at the upper bound, specified as a scalar with a unit of torsional stiffness.

#### Dependencies

To enable this parameter, select Specify Upper Limit.

Damping coefficient at the upper bound, specified as a scalar with a unit of damping coefficient.

#### Dependencies

To enable this parameter, select Specify Upper Limit.

Region to smooth the spring and damper torques, specified as a scalar with a unit of angle.

The block applies the full value of the upper-limit torque when the penetration reaches the width of the transition region. The smaller the region, the sharper the onset of forces and the smaller the time step required of the solver. In the tradeoff between simulation accuracy and simulation speed, reducing the transition region improves accuracy and expanding it improves speed.

#### Dependencies

To enable this parameter, select Specify Upper Limit.

Actuation

Option to provide the actuator torque for the joint primitive, specified as one of these values:

Torque SettingDescription
`None`No actuator torque.
`Provided by Input`The input port tx specifies the actuator torque for the x revolute primitive.
`Automatically Computed`The block computes the torque automatically. If you set this parameter to `Automatically Computed`, you do not need to set Motion to `Provided by Input` for the for the same joint primitive. The automatically computed torque may satisfy a motion input somewhere else in the mechanism.

Option to provide the motion for the joint primitive, specified as one of these values:

Motion SettingDescription
`Automatically computed`The block computes and applies the joint primitive motion based on model dynamics.
`Provided by Input`The input port qx specifies the motion for the x revolute primitive.

### Y Revolute Primitive (Ry)

State Targets

Select this parameter to specify the position target of the y revolute primitive.

Priority level of the position target, specified as `High (desired)` or `Low (approximate)`. For more information, see the Guiding Assembly section of How Multibody Assembly Works.

#### Dependencies

To enable this parameter, select Specify Position Target.

Position target of the y revolute primitive, specified as a scalar with a unit of angle.

#### Dependencies

To enable this parameter, select Specify Position Target.

Select this parameter to specify the angular velocity target for the y revolute primitive.

Priority level of the angular velocity target, specified as ```High (desired)``` or `Low (approximate)`. For more information, see the Guiding Assembly section of How Multibody Assembly Works.

#### Dependencies

To enable this parameter, select Specify Velocity Target.

Angular velocity target of the y revolute primitive, specified as a scalar with a unit of angular velocity.

#### Dependencies

To enable this parameter, select Specify Velocity Target.

Internal Mechanics

Position where the spring torque is zero, specified as a scalar with a unit of angle.

Stiffness of the internal spring-damper force law for the y revolute primitive, specified as a scalar with a unit of torsional stiffness.

Damping coefficient of the internal spring-damper force law for the y revolute primitive, specified as a scalar with a unit of damping coefficient.

Limits

Select this parameter to specify the lower limit of the y revolute primitive.

Lower bound for the free region of the y revolute primitive, specified as a scalar with a unit of angle.

#### Dependencies

To enable this parameter, select Specify Lower Limit.

Stiffness of the spring at the lower bound, specified as a scalar with a unit of torsional stiffness.

#### Dependencies

To enable this parameter, select Specify Lower Limit.

Damping coefficient at the lower bound, specified as a scalar with a unit of damping coefficient.

#### Dependencies

To enable this parameter, select Specify Lower Limit.

Region to smooth the spring and damper torques, specified as a scalar with a unit of angle.

The block applies the full value of the lower-limit torque when the penetration reaches the width of the transition region. The smaller the region, the sharper the onset of forces and the smaller the time step required of the solver. In the tradeoff between simulation accuracy and simulation speed, reducing the transition region improves accuracy and expanding it improves speed.

#### Dependencies

To enable this parameter, select Specify Lower Limit.

Select this parameter to specify the upper limit of the y revolute primitive.

Upper bound for the free region of the y revolute primitive, specified as a scalar with a unit of angle.

#### Dependencies

To enable this parameter, select Specify Upper Limit.

Stiffness of the spring at the upper bound, specified as a scalar with a unit of torsional stiffness.

#### Dependencies

To enable this parameter, select Specify Upper Limit.

Damping coefficient at the upper bound, specified as a scalar with a unit of damping coefficient.

#### Dependencies

To enable this parameter, select Specify Upper Limit.

Region to smooth the spring and damper torques, specified as a scalar with a unit of angle.

The block applies the full value of the upper-limit torque when the penetration reaches the width of the transition region. The smaller the region, the sharper the onset of forces and the smaller the time step required of the solver. In the tradeoff between simulation accuracy and simulation speed, reducing the transition region improves accuracy and expanding it improves speed.

#### Dependencies

To enable this parameter, select Specify Upper Limit.

Actuation

Option to provide the actuator torque for the joint primitive, specified as one of these values:

Torque SettingDescription
`None`No actuator torque.
`Provided by Input`The input port ty specifies the actuator torque for the y revolute primitive.
`Automatically Computed`The block computes the torque automatically. If you set this parameter to `Automatically Computed`, you do not need to set Motion to `Provided by Input` for the for the same joint primitive. The automatically computed torque may satisfy a motion input somewhere else in the mechanism.

Option to provide the motion for the joint primitive, specified as one of these values:

Motion SettingDescription
`Automatically computed`The block computes and applies the joint primitive motion based on model dynamics.
`Provided by Input`The input port qy specifies the motion for the y revolute primitive.

### Mode Configuration

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

ModeDescription
`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

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.

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.

## Version History

Introduced in R2012a