Rectangular Joint

Joint with two prismatic primitives

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Libraries:
Simscape / Multibody / Joints

Description

The Rectangular Joint block models a joint with two translational degrees of freedom. The joint enables the follower frame to execute a planar transformation with respect to the base frame through a sequence of two orthogonal translations. The figure shows the sequence in which the joint transformations occur at a given simulation time step.

The joint constrains the origin of the follower frame within the xy-plane of the base frame, and the axes of the follower frame are parallel with the corresponding axes of the base frame.

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.

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.

Ports

Frame

B — Base frame

frame

Base frame of the joint block.

F — Follower frame

frame

Follower frame of the joint block.

Input

X Prismatic Primitive (Px)

fx — Actuation force

physical signal

Physical signal input port that accepts the actuation force for the joint primitive. The block applies the force equally and oppositely to the base and follower frames of the joint along the x-axis of the base frame.

Dependencies

To enable this port, under X Prismatic Primitive (Px) > Actuation, set Force to Provided by Input.

px — Motion profile

physical signal

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

Dependencies

To enable this port, under X Prismatic Primitive (Px) > Actuation, set Motion to Provided by Input.

Y Prismatic Primitive (Py)

fy — Actuation force

physical signal

Physical signal input port that accepts the actuation force for the joint primitive. The block applies this force equally and oppositely to the base and follower frames of the joint along the y-axis of the base frame.

Dependencies

To enable this port, under Y Prismatic Primitive (Py) > Actuation, set Force to Provided by Input.

py — Motion profile

physical signal

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

Dependencies

To enable this port, under Y Prismatic Primitive (Py) > Actuation, set Motion to Provided by 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

X Prismatic Primitive (Px)

px — Position of primitive

physical signal

Physical signal port that outputs the position of the joint primitive. The value is the displacement of the follower frame with respect to the base frame in the x-direction of the base frame.

Dependencies

To enable this port, under X Prismatic Primitive (Px) > Sensing, select Position.

vx — Velocity of primitive

physical signal

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

Dependencies

To enable this port, under X Prismatic Primitive (Px) > Sensing, select Velocity.

ax — Acceleration of primitive

physical signal

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

Dependencies

To enable this port, under X Prismatic Primitive (Px) > Sensing, select Acceleration.

fx — Actuator force acting on joint primitive

physical signal

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

Dependencies

To enable this port, under X Prismatic Primitive (Px) > Sensing, select Actuator Force.

fllx — Lower-limit force

physical signal

Physical signal port that outputs the lower-limit force. The block applies this force when the joint primitive position is less than the lower bound of the free region. The block applies this force 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 Prismatic Primitive (Px) > Sensing, select Lower-Limit Force.

fulx — Upper-limit force

physical signal

Physical signal port that outputs the upper-limit force. The block applies this force when the joint primitive position exceeds the upper bound of the free region. The block applies this force 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 Prismatic Primitive (Px) > Sensing, select Upper-Limit Force.

Y Prismatic Primitive (Py)

py — Position of primitive

physical signal

Physical signal port that outputs the position of the joint primitive. The value is the displacement of the follower frame with respect to the base frame in the y-direction of the base frame.

Dependencies

To enable this port, under Y Prismatic Primitive (Py) > Sensing, select Position.

vy — Velocity of primitive

physical signal

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

Dependencies

To enable this port, under Y Prismatic Primitive (Py) > Sensing, select Velocity.

ay — Acceleration of primitive

physical signal

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

Dependencies

To enable this port, under Y Prismatic Primitive (Py) > Sensing, select Acceleration.

fy — Actuator force acting on joint primitive

physical signal

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

Dependencies

To enable this port, under Y Prismatic Primitive (Py) > Sensing, select Actuator Force.

flly — Lower-limit force

physical signal

Physical signal port that outputs the lower-limit force. The block applies this force when the joint primitive position is less than the lower bound of the free region. The block applies this force 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 Prismatic Primitive (Py) > Sensing, select Lower-Limit Force.

fuly — Upper-limit force

physical signal

Physical signal port that outputs the upper-limit force. The block applies this force when the joint primitive position exceeds the upper bound of the free region. The block applies this force 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 Prismatic Primitive (Py) > Sensing, select Upper-Limit Force.

Composite Force/Torque Sensing

fc — Constraint force

physical signal

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.

tc — Constraint torque

physical signal

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.

ft — Total force

physical signal

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.

tt — Total torque

physical signal

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

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

X Prismatic Primitive (Px)

State Targets

Specify Position Target — Whether to specify position target

off (default) | on

Select this parameter to specify the position target for the x prismatic primitive.

Priority — Priority level of position target

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

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.

Value — Position target

0 m (default) | scalar

Position target of the x prismatic primitive, specified as a scalar in units of length.

Dependencies

To enable this parameter, select Specify Position Target.

Specify Velocity Target — Whether to specify linear velocity target

off (default) | on

Select this parameter to specify the linear velocity target for the x prismatic primitive.

Priority — Priority level of linear velocity target

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

Priority level of the linear 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.

Value — Velocity target

0 m/s (default) | scalar

Linear velocity target for the x prismatic primitive, specified as a scalar in units of linear velocity.

Dependencies

To enable this parameter, select Specify Velocity Target.

Internal Mechanics

Equilibrium Position — Position where internal force is zero

0 m (default) | scalar

Position where the spring force is zero, specified as a scalar in units of length.

Spring Stiffness — Stiffness of force law

0 N/m (default) | scalar

Stiffness of the internal spring-damper force law for the joint primitive, specified as a scalar in units of linear stiffness.

Damping Coefficient — Damping coefficient of force law

0 N(m/s) (default) | scalar

Damping coefficient of the internal spring-damper force law for the joint primitive, specified as a scalar in units of linear damping coefficient.

Limits

Specify Lower Limit — Whether to specify lower position limit

off (default) | on

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

Bound — Lower bound of free region

-1 m (default) | scalar

Lower bound of the free region of the x prismatic primitive, specified as a scalar in units of length.

Dependencies

To enable this parameter, select Specify Lower Limit.

Spring Stiffness — Stiffness of spring at lower bound

1e6 N/m (default) | scalar

Stiffness of the spring at the lower bound, specified as a scalar in units of linear stiffness.

Dependencies

To enable this parameter, select Specify Lower Limit.

Damping Coefficient — Damping coefficient at lower bound

1e3 N/(m/s) (default) | scalar

Damping coefficient at the lower bound, specified as a scalar in units of linear damping coefficient.

Dependencies

To enable this parameter, select Specify Lower Limit.

Transition Region Width — Region to smooth spring and damper forces

1e-4 m (default) | scalar

Region to smooth the spring and damper forces, specified as a scalar in units of length.

The block applies the full value of the lower-limit force 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.

Specify Upper Limit — Whether to specify upper position limit

off (default) | on

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

Bound — Upper bound of free region

1 m (default) | scalar

Upper bound for the free region of the joint primitive, specified as a scalar in units of length.

Dependencies

To enable this parameter, select Specify Upper Limit.

Spring Stiffness — Stiffness of spring at upper bound

1e6 N/m (default) | scalar

Stiffness of the spring at the upper bound, specified as a scalar in units of linear stiffness.

Dependencies

To enable this parameter, select Specify Upper Limit.

Damping Coefficient — Damping coefficient at upper bound

1e3 N/(m/s) (default) | scalar

Damping coefficient at the upper bound, specified as a scalar in units of linear damping coefficient.

Dependencies

To enable this parameter, select Specify Upper Limit.

Transition Region Width — Region to smooth spring and damper forces

1e-4 m (default) | scalar

Region to smooth the spring and damper forces, specified as a scalar in units of length.

The block applies the full value of the upper-limit force 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

Force — Option to provide actuator force

None (default) | Provided by Input | Automatically Computed

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

Force Setting	Description
None	No actuator force.
Provided by Input	The input port fx specifies the actuator force for the x prismatic primitive.
Automatically Computed	The block automatically calculates the amount of force required to satisfy the motion inputs to the mechanism. If you set this parameter to Automatically Computed, you do not need to set Motion to Provided by Input for the same joint primitive. The automatically computed force may satisfy a motion input elsewhere in the mechanism.

Motion — Option to provide motion

Automatically Computed (default) | Provided by Input

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

Motion Setting	Description
Automatically Computed	The block computes and applies the joint primitive motion based on the model dynamics.
Provided by Input	The input port px specifies the motion for the joint primitive.

Y Prismatic Primitive (Py)

State Targets

Specify Position Target — Whether to specify position target

off (default) | on

Select this parameter to specify the position target for the y prismatic primitive.

Priority — Priority level of position target

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

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.

Value — Position target

0 m (default) | scalar

Position target of the y prismatic primitive, specified as a scalar in units of length.

Dependencies

To enable this parameter, select Specify Position Target.

Specify Velocity Target — Whether to specify linear velocity target

off (default) | on

Select this parameter to specify the linear velocity target for the y prismatic primitive.

Priority — Priority level of linear velocity target

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

Priority level of the linear 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.

Value — Velocity target

0 m/s (default) | scalar

Linear velocity target for the y prismatic primitive, specified as a scalar in units of linear velocity.

Dependencies

To enable this parameter, select Specify Velocity Target.

Internal Mechanics

Equilibrium Position — Position where internal force is zero

0 m (default) | scalar

Position where the spring force is zero, specified as a scalar in units of length.

Spring Stiffness — Stiffness of force law

0 N/m (default) | scalar

Stiffness of the internal spring-damper force law for the joint primitive, specified as a scalar in units of linear stiffness.

Damping Coefficient — Damping coefficient of force law

0 N(m/s) (default) | scalar

Damping coefficient of the internal spring-damper force law for the joint primitive, specified as a scalar in units of linear damping coefficient.

Limits

Specify Lower Limit — Whether to specify lower position limit

off (default) | on

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

Bound — Lower bound of free region

-1 m (default) | scalar

Lower bound of the free region of the y prismatic primitive, specified as a scalar in units of length.

Dependencies

To enable this parameter, select Specify Lower Limit.

Spring Stiffness — Stiffness of spring at lower bound

1e6 N/m (default) | scalar

Stiffness of the spring at the lower bound, specified as a scalar in units of linear stiffness.

Dependencies

To enable this parameter, select Specify Lower Limit.

Damping Coefficient — Damping coefficient at lower bound

1e3 N/(m/s) (default) | scalar

Damping coefficient at the lower bound, specified as a scalar in units of linear damping coefficient.

Dependencies

To enable this parameter, select Specify Lower Limit.

Transition Region Width — Region to smooth spring and damper forces

1e-4 m (default) | scalar

Region to smooth the spring and damper forces, specified as a scalar in units of length.

The block applies the full value of the lower-limit force 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.

Specify Upper Limit — Whether to specify upper position limit

off (default) | on

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

Bound — Upper bound of free region

1 m (default) | scalar

Upper bound for the free region of the joint primitive, specified as a scalar in units of length.

Dependencies

To enable this parameter, select Specify Upper Limit.

Spring Stiffness — Stiffness of spring at upper bound

1e6 N/m (default) | scalar

Stiffness of the spring at the upper bound, specified as a scalar in units of linear stiffness.

Dependencies

To enable this parameter, select Specify Upper Limit.

Damping Coefficient — Damping coefficient at upper bound

1e3 N/(m/s) (default) | scalar

Damping coefficient at the upper bound, specified as a scalar in units of linear damping coefficient.

Dependencies

To enable this parameter, select Specify Upper Limit.

Transition Region Width — Region to smooth spring and damper forces

1e-4 m (default) | scalar

Region to smooth the spring and damper forces, specified as a scalar in units of length.

The block applies the full value of the upper-limit force 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

Force — Option to provide actuator force

None (default) | Provided by Input | Automatically Computed

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

Force Setting	Description
None	No actuator force.
Provided by Input	The input port fy specifies the actuator force for the y prismatic primitive.
Automatically Computed	The block automatically calculates the amount of force required to satisfy the motion inputs to the mechanism. If you set this parameter to Automatically Computed, you do not need to set Motion to Provided by Input for the same joint primitive. The automatically computed force may satisfy a motion input elsewhere in the mechanism.

Motion — Option to provide motion

Automatically Computed (default) | Provided by Input

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

Motion Setting	Description
Automatically Computed	The block computes and applies the joint primitive motion based on the model dynamics.
Provided by Input	The input port py specifies the motion for the joint primitive.

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 R2012a

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.