JointUPS
Universal - prismatic - spherical joint aggregation (no constraints, no potential states)
Library
Modelica/Mechanics/MultiBody/Joints/Assemblies
Description
This component consists of a universal joint at frame_a,a spherical joint at frame_b and a prismatic joint along theline connecting the origin of frame_a and the origin of frame_b,see the default animation in the following figure (the axes vectorsare not part of the default animation):
This joint aggregation has no mass and no inertia andintroduces neither constraints nor potential state variables.It is especially useful to build up more complicated force elementswhere the mass and/or inertia of the force element shall be takeninto account.
The universal joint is defined in the following way:
- The rotation axis of revolute joint 1 is along parameter vector n1_a which is fixed in frame_a.
- The rotation axis of revolute joint 2 is perpendicular to axis 1 and to the line connecting the universal and the spherical joint.
The definition of axis 2 of the universal joint is performed accordingto the most often occurring case. In a future release, axis 2 mightbe explicitly definable via a parameter. However, the treatment is much morecomplicated and the number of operations is considerably higher,if axis 2 is not orthogonal to axis 1 and to the connecting rod.
Note, there is a singularity when axis 1 and the connecting line are parallelto each other. Therefore, if possible n1_a should be selected in such a way that itis perpendicular to nAxis_ia in the initial configuration (i.e., thedistance to the singularity is as large as possible).
An additional frame_ia is present. It is fixed on the lineconnecting the universal and the spherical joint at theorigin of frame_a. The placement of frame_ia on this lineis implicitly defined by the universal joint (frame_a and frame_ia coincidewhen the angles of the two revolute joints of the universal joint are zero)and by parameter vector nAxis_ia, an axis vector directedalong the line from the origin of frame_a to the spherical joint,resolved in frame_ia.
An additional frame_ib is present. It is fixed in the lineconnecting the prismatic and the spherical joint at theorigin of frame_b.It is always parallel to frame_ia.
Note, this joint aggregation can be used in cases wherein reality a rod with spherical joints at each end are present.Such a system has an additional degree of freedom to rotatethe rod along its axis. In practice this rotation is usuallyof no interest and is mathematically removed by replacing oneof the spherical joints by a universal joint.
The easiest way to define the parameters of this joint is by moving theMultiBody system in a reference configuration where all framesof all components are parallel to each other (alternatively,at least frame_a, frame_ia and frame_ib of the JointUSP jointshould be parallel to each other when defining an instance of thiscomponent).
Parameters
| Name | Label | Description | Data Type | Valid Values |
|---|---|---|---|---|
mo_animation | animation | = true, if animation shall be enabled | Scalar | true |
mo_showUniversalAxes | showUniversalAxes | = true, if universal joint shall be visualized with two cylinders, otherwise with a sphere (provided animation=true) | Scalar | true |
mo_n1_a | n1_a | Axis 1 of universal joint resolved in frame_a (axis 2 is orthogonal to axis 1 and to line from universal to spherical joint) | Vector of size 3 | |
mo_nAxis_ia | nAxis_ia | Axis vector along line from origin of frame_a to origin of frame_b, resolved in frame_ia | Vector of size 3 | |
mo_s_offset | s_offset | Relative distance offset (distance between frame_a and frame_b = s(t) + s_offset) | Scalar | |
mo_eAxis_ia | eAxis_ia | Unit vector from origin of frame_a to origin of frame_b, resolved in frame_ia | Vector of size 3 | |
mo_e2_ia | e2_ia | Unit vector in direction of second rotation axis of universal joint, resolved in frame_ia | Vector of size 3 | |
mo_e3_ia | e3_ia | Unit vector perpendicular to eAxis_ia and e2_ia, resolved in frame_ia | Vector of size 3 |
| Name | Label | Description | Data Type | Valid Values |
|---|---|---|---|---|
mo_sphereDiameter | sphereDiameter | Diameter of spheres representing the spherical joints | Scalar | |
mo_sphereColor | sphereColor | Color of spheres representing the spherical joints | Vector of size 3 | |
mo_axisDiameter | axisDiameter | Diameter of cylinder on the connecting line from frame_a to frame_b | Scalar | |
mo_axisColor | axisColor | Color of cylinder on the connecting line from frame_a to frame_b | Vector of size 3 | |
mo_specularCoefficient | specularCoefficient | Reflection of ambient light (= 0: light is completely absorbed) | Scalar | |
mo_cylinderLength | cylinderLength | Length of cylinders representing the two universal joint axes | Scalar | |
mo_cylinderDiameter | cylinderDiameter | Diameter of cylinders representing the two universal joint axes | Scalar | |
mo_cylinderColor | cylinderColor | Color of cylinders representing the two universal joint axes | Vector of size 3 |
| Name | Label | Description | Data Type | Valid Values |
|---|---|---|---|---|
mo_checkTotalPower | checkTotalPower | = true, if total power flowing into this component shall be determined (must be zero) | Scalar | true |
| Name | Label | Description | Data Type | Valid Values |
|---|---|---|---|---|
mo__nmodifiers | Number of Modifiers | Specifies the number of modifiers | Number | |
mo__modifiers | Modifiers | Add new modifier | Structure | |
mo__modifiers/varname | Variable name | Cell of strings | 's' | |
mo__modifiers/attribute | Attribute | Cell of strings | 'start' | |
mo__modifiers/value | Value |
Ports
| Name | Type | Description | IO Type | Number |
|---|---|---|---|---|
frame_a | implicit | Coordinate system fixed to the component with one cut-force and cut-torque | input | 1 |
frame_b | implicit | Coordinate system fixed to the component with one cut-force and cut-torque | output | 1 |
frame_ia | implicit | Coordinate system at origin of frame_a fixed at prismatic joint | input | 2 |
frame_ib | implicit | Coordinate system at origin of frame_b fixed at prismatic joint | output | 2 |
axis | implicit | 1-dim. translational flange that drives the prismatic joint | input | 3 |
bearing | implicit | 1-dim. translational flange of the drive bearing of the prismatic joint | output | 3 |