Modelica.Mechanics.MultiBody.Joints.Internal

Components used for analytic solution of kinematic loops (use only if you know what you are doing)

Information

The models in this package should not be used by the user. They are designed to build up other models in the MultiBody library and some of them cannot be used in an arbitrary way and require particular knowledge how to set the options in the parameter menu. Don't use the models of this package.

Extends from Modelica.Icons.InternalPackage (Icon for an internal package (indicating that the package should not be directly utilized by user)).

Package Content

Name	Description
RevoluteWithLengthConstraint	Revolute joint where the rotation angle is computed from a length constraint (1 degree-of-freedom, no potential state)
PrismaticWithLengthConstraint	Prismatic joint where the translational distance is computed from a length constraint (1 degree-of-freedom, no potential state)
RollingConstraintVerticalWheel	Rolling constraint for wheel that is always perpendicular to x-y plane
InitPosition	Internal model to initialize r_rel_a for Joints.FreeMotionScalarInit
InitAngle	Internal model to initialize the angels for Joints.FreeMotionScalarInit
InitAngularVelocity	Internal model to initialize w_rel_b for Joints.FreeMotionScalarInit

Modelica.Mechanics.MultiBody.Joints.Internal.RevoluteWithLengthConstraint

Revolute joint where the rotation angle is computed from a length constraint (1 degree-of-freedom, no potential state)

Information

Joint where frame_b rotates around axis n which is fixed in frame_a. The two frames coincide when "phi + phi_offset = 0", where "phi_offset" is a parameter with a zero default and "phi" is the rotation angle.

This variant of the revolute joint is designed to work together with a length constraint in a kinematic loop. This means that the angle of the revolute joint, phi, 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 torque projection equation (= cut-torque projected to the rotation axis must be identical to the drive torque of flange axis) via parameter axisTorqueBalance. 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 torque in direction of the rotation axis is (RC shall be the name of the instance of RevoluteWithLengthConstraint):

0 = RC.axis.tau + RC.e*RC.frame_b.t;

If this equation is used, usually the force in the length constraint and the second derivative of the revolute angle 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 revolute constraint torque. 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".

Extends from Modelica.Mechanics.MultiBody.Interfaces.PartialTwoFrames (Base model for components providing two frame connectors + outer world + assert to guarantee that the component is connected).

Parameters

Name	Description
animation	= true, if animation shall be enabled
lengthConstraint	Fixed length of length constraint [m]
n	Axis of rotation resolved in frame_a (= same as in frame_b) [1]
phi_offset	Relative angle offset (angle = phi + from_deg(phi_offset)) [deg]
phi_guess	Select the configuration such that at initial time \|phi - from_deg(phi_guess)\| is minimal [deg]
Animation
if animation = true
cylinderLength	Length of cylinder representing the joint axis [m]
cylinderDiameter	Diameter of cylinder representing the joint axis [m]
cylinderColor	Color of cylinder representing the joint axis
specularCoefficient	Reflection of ambient light (= 0: light is completely absorbed)

Connectors

Name	Description
frame_a	Coordinate system a fixed to the component with one cut-force and cut-torque
frame_b	Coordinate system b fixed to the component with one cut-force and cut-torque
axis	1-dim. rotational flange that drives the joint
bearing	1-dim. rotational flange of the drive bearing
position_a[3]	Position vector from frame_a to frame_a side of length constraint, resolved in frame_a of revolute joint [m]
position_b[3]	Position vector from frame_b to frame_b side of length constraint, resolved in frame_b of revolute joint [m]

Modelica.Mechanics.MultiBody.Joints.Internal.PrismaticWithLengthConstraint

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

Information

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".

Extends from Modelica.Mechanics.MultiBody.Interfaces.PartialTwoFrames (Base model for components providing two frame connectors + outer world + assert to guarantee that the component is connected).

Parameters

Name	Description
animation	= true, if animation shall be enabled
length	Fixed length of length constraint [m]
n	Axis of translation resolved in frame_a (= same as in frame_b) [1]
s_offset	Relative distance offset (distance between frame_a and frame_b = s(t) + s_offset) [m]
s_guess	Select the configuration such that at initial time \|s(t0)-s_guess\| is minimal [m]
Animation
if animation = true
boxWidthDirection	Vector in width direction of box, resolved in frame_a [1]
boxWidth	Width of prismatic joint box [m]
boxHeight	Height of prismatic joint box [m]
boxColor	Color of prismatic joint box
specularCoefficient	Reflection of ambient light (= 0: light is completely absorbed)

Connectors

Name	Description
frame_a	Coordinate system a fixed to the component with one cut-force and cut-torque
frame_b	Coordinate system b fixed to the component with one cut-force and cut-torque
axis	1-dim. translational flange that drives the joint
bearing	1-dim. translational flange of the drive bearing
position_a[3]	Position vector from frame_a to frame_a side of length constraint, resolved in frame_a of prismatic joint [m]
position_b[3]	Position vector from frame_b to frame_b side of length constraint, resolved in frame_b of prismatic joint [m]

Modelica.Mechanics.MultiBody.Joints.Internal.RollingConstraintVerticalWheel

Rolling constraint for wheel that is always perpendicular to x-y plane

Information

Joint for a wheel rolling on the x-y plane of the world frame intended for an idealized wheelset. To meet this objective, the wheel always runs upright and enables no slip in the longitudinal direction of the wheel/ground contact.

On the contrary, the wheel can optionally slip in the lateral direction which is reasonable for the wheelset where just one of the wheels should be laterally constrained.

The frame frame_a is placed in the intersection of the wheel spin axis with the wheel middle plane and rotates with the wheel itself. A wheel body collecting the mass and inertia should be connected to this frame.

Note

To work properly, the gravity acceleration vector g of the world must point in the negative z-axis, i.e.

inner Modelica.Mechanics.MultiBody.World world(n={0,0,-1});

Parameters

Name	Description
radius	Wheel radius [m]
lateralSlidingConstraint	= true, if lateral sliding constraint taken into account, = false if lateral force = 0 (needed to avoid overconstraining if two ideal rolling wheels are connect on one axis)

Connectors

Name	Description
frame_a	Frame fixed in wheel center point. x-Axis: upwards, y-axis: along wheel axis

Modelica.Mechanics.MultiBody.Joints.Internal.InitPosition

Internal model to initialize r_rel_a for Joints.FreeMotionScalarInit

Information

Compute relative position vector r_rel_a from a position vector r_a_0 to a position vector r_b_0, resolved in frame given by an orientation object R_a.

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block).

Parameters

Name	Description
r_a_0[3]	[m]
r_b_0[3]	[m]
R_a

Connectors

Name	Description
r_rel_a[3]	[m]

Modelica.Mechanics.MultiBody.Joints.Internal.InitAngle

Internal model to initialize the angels for Joints.FreeMotionScalarInit

Information

Compute three rotational angles angle for a given rotational sequence sequence_start from a relative orientation from frame_a to frame_b.

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block).

Parameters

Name	Description
sequence_start	Sequence of angle rotations

Connectors

Name	Description
frame_a
frame_b
angle[3]	[rad]

Modelica.Mechanics.MultiBody.Joints.Internal.InitAngularVelocity

Internal model to initialize w_rel_b for Joints.FreeMotionScalarInit

Information

Compute relative angular velocity w_rel_b of an orientation object R_b relative to an orientation object R_a, resolved in orientation object R_b, i.e.

w_b_b = w_a_b + w_rel_b,

where

w_b_b ...... absolute angular velocity of frame_b resolved in frame_b,
w_a_b ...... absolute angular velocity of frame_a resolved in frame_b,
w_rel_b .... relative angular velocity resolved in frame_b.

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block).

Parameters

Name	Description
R_a
R_b

Connectors

Name	Description
w_rel_b[3]	[rad/s]

Automatically generated Thu Oct 1 16:07:54 2020.