Prismatic Joint
Joint that allows relative motion along single axis
Libraries:
Simscape /
Multibody /
Joints
Description
The Prismatic Joint block models a connection that limits the relative motion between two frames to one translational degree of freedom. This type of motion is common in hydraulic or pneumatic cylinders.
The Prismatic Joint block has only one prismatic primitive, which is along the z-axis of the base frame. During simulation, the z-axes of the base and follower frames align, and the follower frame moves with respect to the base frame along the z-axis, as shown in the image.
Meanwhile, the x and y axes of the follower frame remain parallel to the x and y axes of the base frame, respectively.
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.
Examples
How to Build a Multibody in Simulink
Highlights key concepts and recommended steps for building a mechanical model using Simscape™ Multibody™. A simple design problem has been chosen to serve this purpose. The following section describes the design problem and subsequent sections discuss how to solve it.
Ports
Frame
B — Base frame
frame
Base frame of the joint block.
F — Follower frame
frame
Follower frame of the joint block.
Input
f — Actuation force
physical signal
Physical signal input port that accepts the actuation force for the joint primitive. The signal provides the value of the force that applies on both the base and follower frames of the joint primitive.
Dependencies
To enable this port, under Z Prismatic Primitive (Pz) > Actuation, set Force to Provided
by Input
.
p — Motion profile
physical signal
Physical signal input port that accepts the motion profile for the joint primitive. The signal provides the displacement of the follower frame with respect to the base frame along the joint primitive axis. Note that the signal must also contain the first and second derivatives of the displacement.
Dependencies
To enable this port, under Z Prismatic Primitive (Pz) > Actuation, set Motion to Provided
by Input
.
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
p — Position of primitive
physical signal
Physical signal port that outputs the position of the primitive. The value is the displacement of the follower frame with respect to the base frame.
Dependencies
To enable this port, under Z Prismatic Primitive (Pz) > Sensing, select Position.
v — Velocity of primitive
physical signal
Physical signal port that outputs the velocity of the primitive.
Dependencies
To enable this port, under Z Prismatic Primitive (Pz) > Sensing, select Velocity.
a — Acceleration of primitive
physical signal
Physical signal port that outputs the acceleration of the primitive.
Dependencies
To enable this port, under Z Prismatic Primitive (Pz) > Sensing, select Acceleration.
f — 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 Z Prismatic Primitive (Pz) > Sensing, select Actuator Force.
fll — Lower-limit force
physical signal
Physical signal port that outputs the lower-limit force. The block applies the force when the joint primitive position is less than the lower bound of the free region. The force applies to both the base and follower frames of the joint primitive to accelerate the position back to the free region.
Dependencies
To enable this port, under Z Prismatic Primitive (Pz) > Sensing, select Lower-Limit Force.
ful — Upper-limit force
physical signal
Physical signal port that outputs the upper-limit force. The block applies the force when the joint primitive position exceeds the upper bound of the free region. The force applies to both the base and follower frames of the joint primitive to accelerate the position back to the free region.
Dependencies
To enable this port, under Z Prismatic Primitive (Pz) > Sensing, select Upper-Limit Force.
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. The figure shows a crank-slider piston modeled using a Prismatic Joint block.
The total force that acts at the joint includes the actuator force (FA), internal force (FI), and constraint forces (FC). 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. The torque includes 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
Z Prismatic Primitive (Pz)
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.
State Targets > Specify Position Target > 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 Z Prismatic Primitive (Pz) > State Targets, select Specify Position Target.
State Targets > Specify Position Target > Value — Position target
0 m
(default) | scalar in units of length
Position target of the joint primitive, specified as a scalar in units of length.
Dependencies
To enable this parameter, under Z Prismatic Primitive (Pz) > State Targets, select Specify Position Target.
State Targets > 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.
State Targets > Specify Velocity Target > 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 Z Prismatic Primitive (Pz) > State Targets, select Specify Velocity Target.
State Targets > Specify Velocity Target > Value — Velocity target of joint primitive
0 m/s
(default) | scalar in units of linear velocity
Velocity target of the joint primitive, specified as a scalar in a unit of linear velocity.
Dependencies
To enable this parameter, under Z Prismatic Primitive (Pz) > State Targets, select Specify Velocity Target.
Internal Mechanics > Equilibrium Position — Position where internal force is zero
0 m
(default) | scalar in units of length
Position where the spring force is zero, specified as a scalar in units of length. The value specifies the position of the primitive.
Internal Mechanics > Spring Stiffness — Stiffness of force law
0 N/m
(default) | scalar in units of linear stiffness
Stiffness of the internal spring-damper force law for the joint primitive, specified as a scalar in units of linear stiffness.
Internal Mechanics > Damping Coefficient — Damping coefficient of force law
0 N(m/s)
(default) | scalar in units of linear damping coefficient
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 enable parameters that specify the lower limit of the joint primitive.
Limits > Specify Lower Limit > Bound — Lower bound of free region
-1 m
(default) | scalar in units of length
Lower bound of the free region of the joint primitive, specified as a scalar in units of length.
Dependencies
To enable this parameter, under Z Prismatic Primitive (Pz) > Limits, select Specify Lower Limit.
Limits > Specify Lower Limit > Spring Stiffness — Stiffness of spring at lower bound
1e6 N/m
(default) | scalar in units of linear stiffness
Stiffness of the spring at the lower bound, specified as a scalar in units of linear stiffness.
Dependencies
To enable this parameter, under Z Prismatic Primitive (Pz) > Limits, select Specify Lower Limit.
Limits > Specify Lower Limit > Damping Coefficient — Damping coefficient at lower bound
1e3 N/(m/s)
(default) | scalar in units of linear damping coefficient
Damping coefficient at the lower bound, specified as a scalar in units of linear damping coefficient.
Dependencies
To enable this parameter, under Z Prismatic Primitive (Pz) > Limits, select Specify Lower Limit.
Limits > Specify Lower Limit > Transition Region Width — Region to smooth spring and damper forces
1e-4 m
(default) | scalar in units of length
Region to smooth the spring and damper forces, specified as a scalar in units of length.
The block applies the full value of this 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 trade-off between simulation accuracy and simulation speed, reducing the transition region improves accuracy while expanding it improves speed.
Dependencies
To enable this parameter, under Z Prismatic Primitive (Pz) > Limits, select Specify Lower Limit.
Limits > Specify Upper Limit — Whether to specify upper position limit
off
(default) | on
Select this parameter to enable parameters for specifying the upper limit of the joint primitive.
Limits > Specify Upper Limit > Bound — Upper bound of free region
1 m
(default) | scalar in units of length
Upper bound for the free region of the joint primitive, specified as a scalar in units of length.
Dependencies
To enable this parameter, under Z Prismatic Primitive (Pz) > Limits, select Specify Upper Limit.
Limits > Specify Upper Limit > Spring Stiffness — Stiffness of spring at upper bound
1e6 N/m
(default) | scalar in units of linear stiffness
Stiffness of the spring at the upper bound, specified as a scalar in units of stiffness.
Dependencies
To enable this parameter, under Z Prismatic Primitive (Pz) > Limits, select Specify Upper Limit.
Limits > Specify Upper Limit > Damping Coefficient — Damping coefficient at upper bound
1e3 N/(m/s)
(default) | scalar in units of linear damping coefficient
Damping coefficient at the upper bound, specified as a scalar in units of linear damping coefficient.
Dependencies
To enable this parameter, under Z Prismatic Primitive (Pz) > Limits, select Specify Upper Limit.
Limits > Specify Upper Limit > Transition Region Width — Region to smooth spring and damper forces
1e-4 m
(default) | scalar in units of length
Region to smooth the spring and damper forces, specified as a scalar in units of length.
The block applies the full value of this 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 trade-off between simulation accuracy and simulation speed, reducing the transition region improves accuracy while expanding it improves speed.
Dependencies
To enable this parameter, under Z Prismatic Primitive (Pz) > Limits, select Specify Upper Limit.
Actuation > Force — Option to provide actuation force
None
(default) | Provided by Input
| Automatically Computed
Option to provide the actuation force for the joint primitive, specified as the values in the table.
Actuation Force Setting | Description |
---|---|
None | No actuation force. |
Provided by Input | Input port f specifies the actuation force for the joint primitive.. |
Automatically
computed | The block automatically calculates the amount of
force required to satisfy the motion inputs to the
mechanism. Note that if you set this parameter to
Automatically computed ,
it doesn’t mean that you must use Provided
by Input for the
Motion parameter for the same
joint primitive. The automatically computed force could
be to satisfy a motion input somewhere else in the
mechanism. |
Actuation > Motion — Option to provide actuation motion
Automatically
Computed
(default) | Provided by Input
Option to provide the actuation motion for the joint primitive, specified as the values in the table.
Actuation Motion Setting | Description |
---|---|
Automatically
computed | The block computes and applies the joint primitive motion based on model dynamics. |
Provided by Input | Input port p specifies the actuation motion for the joint primitive. |
Sensing > Position — Whether to sense joint primitive position
off (default) | on
Select this parameter to enable the output port p.
Sensing > Velocity — Whether to sense joint primitive velocity
off (default) | on
Select this parameter to enable port v.
Sensing > Acceleration — Whether to sense joint primitive acceleration
off (default) | on
Select this parameter to enable port a.
Sensing > Actuator Force — Whether to sense joint actuator force
off (default) | on
Select this parameter to enable port f.
Sensing > Lower-Limit force — Whether sense to lower-limit force
off (default) | on
Select this parameter to enable port fll.
Sensing > Upper-Limit force — Whether sense to upper-limit force
off (default) | on
Select this parameter to enable port ful.
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
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