WOLFRAM SYSTEMMODELER

PrismaticWithLengthConstraint

Prismatic joint where the translational distance is computed from a length constraint (1 degree-of-freedom, no potential state)

Wolfram Language

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Click for copyable input
SystemModel["Modelica.Mechanics.MultiBody.Joints.Internal.PrismaticWithLengthConstraint"]
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Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

Joint where frame_b is translated along axis n which is fixed in frame_a. The two frames coincide when "s + s_offset = 0", where "s_offset" is a parameter with a zero default and "s" is the relative distance.

This variant of the prismatic joint is designed to work together with a length constraint in a kinematic loop. This means that the relative distance "s" of the joint is computed such that the length constraint is fulfilled.

Usually, this joint should not be used by a user of the MultiBody library. It is only provided to built-up the Modelica.Mechanics.MultiBody.Joints.Assemblies.JointXYZ joints.

In releases before version 3.0 of the Modelica Standard Library, it was possible to activate the force projection equation (= cut-force projected to the translation axis must be identical to the driving force of flange axis) via parameter axisForceBalance. This is no longer possible, since otherwise this model would not be "balanced" (= same number of unknowns as equations). Instead, when using this model in version 3.0 and later versions, the force in the length constraint component (Joints.SphericalSpherical or Joints.UniversalSpherical) must be calculated such that the driving force in direction of the translation axis is (RC shall be the name of the instance of PrismaticWithLengthConstraint):

    0 = RC.axis.f + RC.e*RC.frame_b.f;

If this equation is used, usually the force in the length constraint and the second derivative of the prismatic distance will be part of a linear algebraic system of equations. In some cases it is possible to solve this system of equations locally, i.e., provide the rod force directly as function of the prismatic constraint force. In any case, this projection equation or an equivalent one has to be provided via variable "constraintResidue" in the "Advanced" menu of "Joints.SphericalSpherical" or "Joints.UniversalSpherical".

Connectors (6)

frame_a

Type: Frame_a

Description: Coordinate system fixed to the component with one cut-force and cut-torque

frame_b

Type: Frame_b

Description: Coordinate system fixed to the component with one cut-force and cut-torque

axis

Type: Flange_a

Description: 1-dim. translational flange that drives the joint

bearing

Type: Flange_b

Description: 1-dim. translational flange of the drive bearing

position_a

Type: RealInput[3]

Description: Position vector from frame_a to frame_a side of length constraint, resolved in frame_a of prismatic joint

position_b

Type: RealInput[3]

Description: Position vector from frame_b to frame_b side of length constraint, resolved in frame_b of prismatic joint

Parameters (10)

animation

Value: true

Type: Boolean

Description: = true, if animation shall be enabled

length

Value:

Type: Position (m)

Description: Fixed length of length constraint

n

Value: {1, 0, 0}

Type: Axis ()

Description: Axis of translation resolved in frame_a (= same as in frame_b)

s_offset

Value: 0

Type: Position (m)

Description: Relative distance offset (distance between frame_a and frame_b = s(t) + s_offset)

s_guess

Value: 0

Type: Position (m)

Description: Select the configuration such that at initial time |s(t0)-s_guess| is minimal

boxWidthDirection

Value: {0, 1, 0}

Type: Axis ()

Description: Vector in width direction of box, resolved in frame_a

boxWidth

Value: world.defaultJointWidth

Type: Distance (m)

Description: Width of prismatic joint box

boxHeight

Value: boxWidth

Type: Distance (m)

Description: Height of prismatic joint box

positiveBranch

Value:

Type: Boolean

Description: Selection of one of the two solutions of the non-linear constraint equation

e

Value: Modelica.Math.Vectors.normalizeWithAssert(n)

Type: Real[3] ()

Description: Unit vector in direction of translation axis, resolved in frame_a

Components (2)

world

Type: World

Description:

box

Type: Shape

Description:

Used in Components (2)

JointUSP

Universal - spherical - prismatic joint aggregation (no constraints, no potential states)

JointSSP

Spherical - spherical - prismatic joint aggregation with mass (no constraints, no potential states)