Lead Screw Joint

Joint with coupled rotational and translational degrees of freedom

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Libraries:
Simscape / Multibody / Joints

Description

The Lead Screw Joint block represents a joint that has one degree of freedom and models a pair of coupled rotation and translation, as shown in the image.

During simulation, the joint constrains the z-axes of the base and follower frames to be aligned. The follower frame origin can translate along the base z-axis while the follower x-axis and y-axis rotate about the base frame z-axis. The translation is proportional to the rotation based on the value of the Lead and Direction parameters.

To specify the target of the initial state for the joint, use the parameters under State Targets. You can specify the targets based on the relative rotation or translation between the joint frames. To specify the joint mode configuration, use the Mode parameter. For more details, see Mode Configuration under the Ports and Parameters sections.

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.

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

Lead Screw with Friction

Models a lead screw with friction. The constraint force in the lead screw is measured and used to calculate the friction torque within the lead screw. A continuous stick-slip friction model is used to determine the coefficient of friction based on the relative rotational speed of the two parts connected by the lead screw.

• Open Model

Cartesian 3-D Printer

Models a Cartesian 3-D printer. The model allows you to specify the rotational motion of the motor on each axis to define a printing path. In this example, the printing head moves along the edges of two letters, S and M, using the predefined rotational motions.

• Open Model

Using the Lead Screw Joint Block - Linear Actuator

Illustrates the use of the Lead Screw Joint block to model a linear actuator. The Lead Screw Joint block converts rotational motion at the Revolute Joint block to translational motion at the four Cylindrical Joint blocks. The translational motion is specified as a motion input to a cylindrical joint and the necessary actuator torque is automatically computed at the revolute joint.

• Open Model

Ports

Frame

B — Base frame

frame

Base frame of the joint block.

F — Follower frame

frame

Follower frame of the joint block.

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

Rotation

q — Joint rotation

physical signal

Physical signal port that outputs the rotation angle of the follower frame with respect to the base frame.

Dependencies

To enable this port, under Sensing > Rotation, select Position.

w — First derivative of joint rotation

physical signal

Physical signal port that outputs the first derivative of the joint rotation.

Dependencies

To enable this port, under Sensing > Rotation, select Velocity.

b — Second derivative of joint rotation

physical signal

Physical signal port that outputs the second derivative of the joint rotation.

Dependencies

To enable this port, under Sensing > Rotation, select Acceleration.

Translation

p — Joint translation

physical signal

Physical signal port that outputs the joint translation of the follower frame with respect to the base frame.

Dependencies

To enable this port, under Sensing > Translation, select Position.

v — First derivative of joint translation

physical signal

Physical signal port that outputs the first derivative of the joint translation.

Dependencies

To enable this port, under Sensing > Translation, select Velocity.

a — Second derivative of joint translation

physical signal

Physical signal port that outputs the second derivative of the joint translation.

Dependencies

To enable this port, under Sensing > Translation, select Acceleration.

Composite Force/Torque Sensing

fc — Constraint force

physical signal

Physical signal port that outputs the constraint force that acts in 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 torque that acts in 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 in the joint. The total force is the sum of the forces transmitted from one frame to the other through the joint. For more information, see Force and Torque Sensing.

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 in the joint. The total torque is the sum of the torques transmitted from one frame to the other through the joint. 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.

Z Lead Screw Primitive (LSz)

Direction — Handedness of lead screw joint

Right-Hand (default) | Left-Hand

Handedness of the lead screw joint, specified as Right-Hand or Left-Hand. A right-handed joint translates a positive rotation into a positive linear movement, whereas a left-handed joint translates in a negative linear movement from a positive rotation.

Lead — Lead of lead screw joint

1 mm/rev (default) | scalar

Lead of the lead screw joint, specified as a scalar with a unit of length/angle. The lead refers to the distance the follower frame moves along the z-axis of the base frame with one complete turn of the follower frame.

State Targets

Specify Position Target — Whether to specify position target

off (default) | on

Select this parameter to enable parameters that specify the position target of the joint 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).

Dependencies

To enable this parameter, under State Targets, select Specify Position Target.

Based On — Motion type to use to specify position target

Translation (default) | Rotation

Motion type to use to specify the position target, specified as Translation or Rotation.

Dependencies

To enable this parameter, under State Targets, select Specify Position Target.

Value — Rotational position target

0 deg (default) | scalar with a unit of angle

Rotational position target, specified as a scalar with a unit of angle.

Dependencies

To enable this parameter, under State Targets > Specify Position Target > Based On, select Rotation.

Value — Translational position target

0 m (default) | scalar with a unit of length

Translational position target, specified as a scalar with a unit of length.

Dependencies

To enable this parameter, under State Targets > Specify Position Target > Based On, select Translation.

Specify Velocity Target — Whether to specify velocity target

off (default) | on

Select this parameter to enable parameters that specify the velocity target of the joint primitive.

Priority — Priority level of velocity target

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

Priority level of the velocity target, specified as High (desired) or Low (approximate).

Dependencies

To enable this parameter, under State Targets, select Specify Velocity Target.

Based On — Motion type to use to specify velocity target

Translation (default) | Rotation

Motion type to use to specify the velocity target, specified as Translation or Rotation.

Dependencies

To enable this parameter, under State Targets, select Specify Velocity Target.

Value — Angular velocity target

0 deg/s (default) | scalar with unit of angular velocity

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

Dependencies

To enable this parameter, under State Targets > Specify Position Target > Based On, select Rotation.

Value — Linear velocity target

0 m/s (default) | scalar with unit of linear velocity

Linear velocity target of the joint primitive, specified as a scalar with a unit of linear velocity.

Dependencies

To enable this parameter, under State Targets > Specify Position Target > Based On, select Translation.

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.