Prismatic Joint


Symbol:
Identifier: Mechanics.MechanicsMBS.Joints.PrismaticJoint
Version: 3.9
File: MechanicsMBS.cat
Connectors: Kinetic MBS Connector ctr1 Connectable to kinematic MBS connector.
Kinematic MBS Connector ctr2 Connectable to kinetic MBS connectors.
Position: (see Table 1 in main chapter Initial Position of the Elements)
Parameters: Definition of Joint Direction
Axis of Translation axis Defaults to X-Axis.
Axis of Translation n Only visible if axis = Input.
Initial Values
Initial Rel. Displacement xRel0
Initial Rel. Velocity vRel0
Preset of Force (Drive) or Motion Quantities along the Axis of Translation
Preset of Drive kindD
  • "at 1D Connectors (or no Preset)"
  • "Force"
  • "Displacement"
  • "Velocity"
Force F Only visible if kindD=="Force"
Rel. Displacement Preset xRelPre Only visible if kindD=="Displacement"
Rel. Velocity Preset vRelPre Only visible if kindD=="Velocity"t
Friction: Consideration of Friction in Joint Direction
Consideration of Friction withFriction Defaults to false.
Rigid Friction with kindF Only visible if withFriction = true. Defaults to Continuous Transition.
Static Friction Coefficient mu0 Only visible if withFriction = true and kindF = Stick-Slip.
Sliding Friction Coefficient mu Only visible if withFriction = true.
Limit Velocity Difference dvL Only visible if withFriction = true and kindF = Continuous Transition.
End Stop: Consideration of an internal End Stop in Joint Direction
End Stop withStop Defaults to false.
End Stop 1 xRel1 Only visible if withStop = true.
End Stop 2 xRel2 Only visible if withStop = true.
Model mode Only visible if withStop = true. Defaults to Elastic End Stop.
Kind of Impact kind Only visible if withStop = true and mode = Rigid End Stop. Defaults to Plastic.
Coefficient of Restitution ci Only visible if withStop = true, mode = Rigid End Stop and kind = By Coefficient of Restitution.
Stiffness 1 k1 Only visible if withStop = true and mode = Elastic End Stop.
Stiffness 2 k2 Only visible if withStop = true and mode = Elastic End Stop.
Damping 1 b1 Only visible if withStop = true and mode = Elastic End Stop.
Damping 2 b2 Only visible if withStop = true and mode = Elastic End Stop.
Advanced: Advanced Settings for Joint Friction and End Stop
Advanced Settings adv Only visible if withStop = true and mode = Rigid End Stop or if withFriction = true.
Minimum Separation Force eps_Fi Only visible if withStop = true and mode = Rigid End Stop.
Maximum Velocity After Impact for Permanent Contact eps_dv Only visible if withStop = true and mode = Rigid End Stop.
Minimum Separation Impact eps_dI Only visible if withStop = true and mode = Rigid End Stop or withFriction = true and kindF = Stick-Slip.
Transition Shape of Force of Sliding Friction kindTrans Only visible if withFriction = true and kindF = Continuous Transition. Defaults to Gevrey Approach.
Shape Coefficient (Transition Shape) eps_sigma Only visible if withFriction = true and kindF = Continuous Transition.
Relative Minimum Difference of the Friction Forces dFfrel Only visible if withFriction = true and kindF = Stick-Slip.
Minimum Separation Velocity Difference eps_dvsl Only visible if withFriction = true and kindF = Stick-Slip.
Visualization: Color and Transparency
RGB Color color
Transparency alpha
Geometry (additional)
Length in Axis Direction l
Width w
Height h
Rel. Kinematic Results: Relative Motion Quantities in Joint Axis Direction
Rel. Displacement xRel
Rel. Velocity vRel
Rel. Acceleration aRel
Kinematic Results: (see Table 1in Joints Kinematic Results)
Kinetic Results: Internal Forces and Torques in Element Coordinates
Internal Force Fi
Internal Torque Ti
Magnitude of Normal Force FnAbs
Mass and Acceleration Force in the Direction of Translation Axis
Mass w.r.t. Axis of Translation m
Acceleration Force w.r.t. Axis of Translation Fa
Result Quantities if Joint Friction is considered
Internal Force due to Friction Ff Only visible if withFriction = true.
State of Friction sf Only visible if withFriction = true.
Power Loss due to Friction Pl Only visible if withFriction = true.
Result Quantities if an End Stop within the Joint is considered
Internal Force due to End Stop FStop Only visible if withStop = true.
State of End Stop stop Only visible if withStop = true.
  • Representiert einen translatorischen Freiheitsgrad um eine wählbare Achse
  • Optional mit Reibung und Endanschlägen
  • Der Antrieb kann durch translatorischen 1D-Modelle, Drehmomente oder Bewegungsgrößen definiert werden
  • Represents one translational degree of freedom about a selectable axis
  • Optionally with friction and end stops
  • Actuation can be defined by translational 1D models, torques or motion quantities

Description:

This element models an actuated prismatic joint. It represents one translational degree of freedom along a selectable axis. The prismatic joint generates two potential state variables for the relative displacement xRel and the relative velocity vRel along the selected axis. Both motion quantities are measured w.r.t. to the input frame at ctr1.

Additionally, the model is able to represent a motion preset along the DoF or a force preset in this direction. It it also possible to take friction along the translation axis into account.

The prismatic joint features two additional Linear Connectors connectable to elements of the Linear Mechanics library. Connector ctrT1 represents the mounting and connector ctrT2 represents the driving flange.

Parameters:

Position:

See Joints Parameters Position for more information.

It is possible to either choose the X-, Y- or Z-Axis as axis of translation or freely set the direction vector n of the axis (if axis = Input). Axis vector n is resolved in local coordinates and will be internally normalized.

Initial Values:

The initial motion quantities (joint states) are determined by the initial displacement xRel0 and the initial velocity vRel0.

Preset of Force (Drive) or Motion Quantities along Axis of Translation:

You can select between 4 possibilities of drive models (enumeration kindD):

  • kindD=="at 1D Connectors (or no Preset)": connect a drive model at the 1D-mechanical connectors ctrT1 and ctrT2
  • kindD=="Force": enter a driving force F (parameter
  • kindD=="Displacement": enter a displacement preset xRelPre, measured w.r.t. to the pin point frame atr ctr1
  • kindD=="Velocity": enter a velocity preset vRelPre, measured w.r.t. to the pin point frame atr ctr1

End Stop:

By default the joint models an unlimited degree of freedom. Optionally (withStop = true) the joint model is able to consider an internal end stop model for a limitation of the body motion. This can be selected in order to physically restrict the displacement xRel within the interval . The end stop can be modeled either as a rigid or as an elastic end stop. For a detailed description of the models and the corresponding parameters and advanced parameters, see the help chapter Mechanics Translation End Stop.

Note: This option is ponly available if there is no preset of motion quantities inside the element (kindD)

Friction:

Optional joint friction can be taken into account by the parameter withFriction. For a detailed description of the friction models, see the help Mechanics Translation Elastic Friction or ... Rigid Friction. These chapters describe also the corresponding parameters and advanced parameters of the friction models.

The parameter Fst, the Static friction force, for the friction models is computed by
where is the normalized axis of translation.

The Sliding friction force parameter Fsl is similarly computed by
.

Note: This option is ponly available if there is no preset of motion quantities inside the element (kindD)

Visualization:

This element type is represented by a cuboid in 3D View. Its shape is given by length parameters l, w and h.

Results:

Kinematic Results:

See Joints Results Kinematic Results for more information.

Relative Kinematic Results:

The displacement xRel along axis n gives the relative motion between two connected elements. Furthermore, the time derivatives of the relative displacement, i.e. the relative velocity vRel and the relative acceleration aRel are available as results.

Kinetic Results:

The internal force Fi and the internal torque Ti are computed in joint coordinates. FnAbs is the magnitude of normal force which is used for the calculation of friction force. The quantity m is the articulated mass of all subsequent bodies projected onto the axis n of translation. Subsequent is defined by means of the kinematic successor relationship of the MBS connection, i.e. those bodies are included that are connected to the kinematic MBS connector ctr2 by joints and bodies excluding connections by elastic bodies, constraints and force elements. The mass m is required to be non-zero otherwise an assertion is thrown. The articulated acceleration force Fa is the corresponding force with respect to the axis n of translation.

If end stop behavior is modeled the stop state stop and the internal stop force FStop are available as results, too. The internal stop force FStop is also included by the articulated acceleration force Fa.

If friction behavior is modeled the state of friction sf, the internal friction force Ff and the power loss Pl are available as results, too. The internal friction force Ff is also included by the articulated acceleration force Fa.

Remarks:

The assertion "Mass is zero." is thrown if no bodies with mass are connected to the kinematic MBS connector ctr2, i.e. the articulated mass m with respect to the axis n of translation is zero.