Multipoint Constraint Element: Revolute Joint
MPC184 Revolute Joint Element Description
The MPC184 revolute joint is a two-node element that has only one primary degree of freedom, the relative rotation about the revolute (or hinge) axis. This element imposes kinematic constraints such that the nodes forming the element have the same displacements. Additionally, only a relative rotation is allowed about the revolute axis, while the rotations about the other two directions are fixed.
MPC184 Revolute Joint Input Data
Set KEYOPT(1) = 6 to define a two-node revolute joint element.
Figure 184revo.1: MPC184 Revolute Joint Geometry shows the geometry and node locations for this element. Two nodes (I and J) define the element. The two nodes are expected to have identical spatial coordinates initially.
If KEYOPT(4) = 0, then element is an x-axis revolute joint with the local e1 axis as the revolute axis.
If KEYOPT(4) = 1, then element is a z-axis revolute joint with the local e3 axis as the revolute axis.
A local Cartesian coordinate system must be specified at the first node, I, of the element. The specification of the second local coordinate system at node J is optional. If the local coordinate system is not specified at node J, then the local coordinate system at node J is assumed to be the same as that at node I.
Either the local e1 or local e3 direction may be specified as the axis of rotation at the nodes. The specification of the other two local directions is not critical, but it will be used to determine the relative rotation between the two nodes during the course of deformation. The orientation of local directions must follow the convention specified in Figure 184revo.1: MPC184 Revolute Joint Geometry. These local coordinate systems evolve with the rotations at the respective nodes (if any). Use the SECJOINT command to specify the identifiers of the local coordinate systems.
The constraints imposed in a revolute joint element with the local e1 axis as the revolute axis are described below. Similar constraint conditions are set up when the local e3 axis is the revolute axis.
Consider the two local coordinate systems (Cartesian) attached to node I and node J (see Figure 184revo.1: MPC184 Revolute Joint Geometry). At any given instant of time, the constraints imposed in a revolute joint are as described below.
Displacement constraints:
uI = uJ
Where, uI is the displacement vector at node I and uJ is the displacement vector at node J.
Rotation constraints:
If the revolute axes
and
are not aligned at
the start of the analysis, then the angle between the two is held
fixed at the starting value.
The relative position of the local coordinate system at node I with respect to node J is characterized by the first Cardan (or Bryant) angle given by:
The change in the relative angular position between the two local coordinate system is given by:
Where, ϕ0 is the initial angular offset (the first Cardan (or Bryant ) angle measured in the reference configuration) between the two coordinate systems and m is an integer accounting for multiple rotations about the revolute axis.
The constitutive calculations use the following definition of the joint rotation:
Where
is the reference
angle, angle1, specified on the SECDATA command.
If this value is not specified, then ϕ0 is used in place of
.
Other input data that are common to all joint elements (material behavior, stops and limits, locks, etc.) are described in "Joint Input Data" in the MPC184 element description.
MPC184 Revolute Joint Input Summary
This input summary applies to the revolute joint element option of MPC184: KEYOPT(1) = 6.
- Nodes
I, J
Note: For a grounded joint element, specify either node I or node J in the element definition and leave the other node (the grounded node) blank.
- Degrees of Freedom
UX, UY, UZ, ROTX, ROTY, ROTZ
- Real Constants
None
- Material Properties
Use the JOIN label on the TB command to define stiffness, damping, and Coulomb friction behavior. (See MPC184 Joint in the Material Reference for detailed information on defining joint materials.)
- Surface Loads
None
- Body Loads
- Temperatures --
T(I), T(J)
- Element Loads
- Rotations --
ROTX (KEYOPT(4) = 0) ROTZ (KEYOPT(4) = 1) - Angular velocities --
OMGX (KEYOPT(4) = 0) OMGZ (KEYOPT(4) = 1) - Angular accelerations --
DMGX (KEYOPT(4) = 0) DMGZ (KEYOPT(4) = 1) - Moments --
MX (KEYOPT(4) = 0) MZ (KEYOPT(4) = 1)
- Special Features
Large deflection Linear perturbation - KEYOPT(1)
Element behavior:
- 6 --
Revolute joint element
- KEYOPT(4)
Element configuration:
- 0 --
x-axis revolute joint with local 1 direction as the revolute axis.
- 1 --
z-axis revolute joint with local 3 direction as the revolute axis.
MPC184 Revolute Joint Output Data
The solution output associated with the element is in two forms:
Nodal displacements included in the overall nodal solution
Additional element output as shown in Table 184revo.1: MPC184 Revolute Joint Element Output Definitions and Table 184revo.2: MPC184 Revolute Joint Element - NMISC Output.
These tables use the following notation:
A colon (:) in the Name column indicates the item can be accessed by the Component Name method [ETABLE, ESOL]. The O column indicates the availability of the items in the file Jobname.OUT. The R column indicates the availability of the items in the results file.
In either the O or R columns, Y indicates that the item is always available, a number refers to a table footnote that describes when the item is conditionally available, and a - indicates that the item is not available.
Table 184revo.1: MPC184 Revolute Joint Element Output Definitions
| Name | Definition | O | R |
|---|---|---|---|
| x-axis Revolute Joint (KEYOPT(4) = 0) | |||
| EL | Element Number | - | Y |
| NODES | Element node numbers (I, J) | - | Y |
| FX | Constraint Force in X direction | - | Y |
| FY | Constraint Force in Y direction | - | Y |
| FZ | Constraint Force in Z direction | - | Y |
| MY | Constraint Moment in Y direction | - | Y |
| MZ | Constraint Moment in Z direction | - | Y |
| CSTOP4 | Constraint moment if stop is specified on DOF 4 | - | Y |
| CLOCK4 | Constraint moment if lock is specified on DOF 4 | - | Y |
| CSST4 | Constraint stop status[1] | - | Y |
| CLST4 | Constraint lock status[2] | - | Y |
| JRP4 | Joint relative position | - | Y |
| JCD4 | Joint constitutive rotation | - | Y |
| JEF4 | Joint elastic moment | - | Y |
| JDF4 | Joint damping moment | - | Y |
| JFF4 | Joint friction moment | - | Y |
| JRU4 | Joint relative rotation | - | Y |
| JRV4 | Joint relative velocity | - | Y |
| JRA4 | Joint relative acceleration | - | Y |
| JTEMP | Average temperature in the element[3] | - | Y |
| JFST4 | Stick/slip status when friction is specified[4] | - | Y |
| JFNF4 | Normal moment in friction calculations | - | Y |
| z-axis Revolute Joint (KEYOPT(4) = 1) | |||
| EL | Element Number | - | Y |
| NODES | Element node numbers (I, J) | - | Y |
| FX | Constraint Force in X direction | - | Y |
| FY | Constraint Force in Y direction | - | Y |
| FZ | Constraint Force in Z direction | - | Y |
| MX | Constraint Moment in X direction | - | Y |
| MY | Constraint Moment in Y direction | - | Y |
| CSTOP6 | Constraint moment if stop is specified on DOF 6 | - | Y |
| CLOCK6 | Constraint moment if lock is specified on DOF 6 | - | Y |
| CSST6 | Constraint stop status[1] | - | Y |
| CLST6 | Constraint lock status[2] | - | Y |
| JRP6 | Joint relative position | - | Y |
| JCD6 | Joint constitutive rotation | - | Y |
| JEF6 | Joint elastic moment | - | Y |
| JDF6 | Joint damping moment | - | Y |
| JFF6 | Joint friction moment | - | Y |
| JRU6 | Joint relative rotation | - | Y |
| JRV6 | Joint relative velocity | - | Y |
| JRA6 | Joint relative acceleration | - | Y |
| JTEMP | Average temperature in the element[3] | - | Y |
| JFST6 | Slip/stick status when friction is specified[4] | - | Y |
| JFNF6 | Normal moment in friction calculations | - | Y |
0 = stop not active, or deactivated 1 = stopped at minimum value 2 = stopped at maximum value 0 = lock not active 1 = locked at minimum value 2 = locked at maximum value Average temperature in the element when temperatures are applied on the nodes of the element using the BF command, or when temperature are applied on the element using the BFE command.
Stick/slip status when friction is active:
0 = friction is not activated 1 = sticking 2 = slipping or sliding
The following table shows additional non-summable miscellaneous (NMISC) output available for all forms of the revolute joint element.
Note: This output is intended for use in the ANSYS Workbench program to track the evolution of local coordinate systems specified at the nodes of joint elements.
Table 184revo.2: MPC184 Revolute Joint Element - NMISC Output
| Name | Definition | O | R |
|---|---|---|---|
| The following output is available for all revolute joint elements (KEYOPT(4) = 0 and 1) | |||
| E1X-I, E1Y-I, E1Z-I | X, Y, Z components of the evolved e1 axis at node I | - | Y |
| E2X-I, E2Y-I, E2Z-I | X, Y, Z components of the evolved e2 axis at node I | - | Y |
| E3X-I, E3Y-I, E3Z-I | X, Y, Z components of the evolved e3 axis at node I | - | Y |
| E1X-J, E1Y-J, E1Z-J | X, Y, Z components of the evolved e1 axis at node J | - | Y |
| E2X-J, E2Y-J, E2Z-J | X, Y, Z components of the evolved e2 axis at node J | - | Y |
| E3X-J, E3Y-J, E3Z-J | X, Y, Z components of the evolved e3 axis at node J | - | Y |
| JFX, JFY, JFZ | Constraint forces expressed in the evolved coordinate system specified at node I | - | Y |
| JMX, JMY, JMZ | Constraint moments expressed in the evolved coordinate system specified at node I | - | Y |
Table 184revo.3: MPC184 Revolute Joint Item and Sequence Numbers - SMISC Items and Table 184revo.4: MPC184 Revolute Joint Item and Sequence Numbers - NMISC Items list output available via the ETABLE command using the Sequence Number method. See The General Postprocessor (POST1) in the Basic Analysis Guide and The Item and Sequence Number Table for further information. The table uses the following notation:
- Name
output quantity as defined in the Element Output Definitions table.
- Item
predetermined Item label for ETABLE command
- E
sequence number for single-valued or constant element data
Table 184revo.3: MPC184 Revolute Joint Item and Sequence Numbers - SMISC Items
| Output Quantity Name | ETABLE and ESOL Command Input | |
|---|---|---|
| Item | E | |
| x-axis Revolute Joint (KEYOPT(4) = 0) | ||
| FX | SMISC | 1 |
| FY | SMISC | 2 |
| FZ | SMISC | 3 |
| MY | SMISC | 5 |
| MZ | SMISC | 6 |
| CSTOP4 | SMISC | 10 |
| CLOCK4 | SMISC | 16 |
| CSST4 | SMISC | 22 |
| CLST4 | SMISC | 28 |
| JRP4 | SMISC | 34 |
| JCD4 | SMISC | 40 |
| JEF4 | SMISC | 46 |
| JDF4 | SMISC | 52 |
| JFF4 | SMISC | 58 |
| JRU4 | SMISC | 64 |
| JRV4 | SMISC | 70 |
| JRA4 | SMISC | 76 |
| JTEMP | SMISC | 79 |
| JFST4 | SMISC | 80 |
| JFNF4 | SMISC | 84 |
| z-axis Revolute Joint (KEYOPT(4) = 1) | ||
| FX | SMISC | 1 |
| FY | SMISC | 2 |
| FZ | SMISC | 3 |
| MX | SMISC | 4 |
| MY | SMISC | 5 |
| CSTOP6 | SMISC | 12 |
| CLOCK6 | SMISC | 18 |
| CSST6 | SMISC | 24 |
| CLST6 | SMISC | 30 |
| JRP6 | SMISC | 36 |
| JCD6 | SMISC | 42 |
| JEF6 | SMISC | 48 |
| JDF6 | SMISC | 54 |
| JFF6 | SMISC | 60 |
| JRU6 | SMISC | 66 |
| JRV6 | SMISC | 72 |
| JRA6 | SMISC | 78 |
| JTEMP | SMISC | 79 |
| JFST6 | SMISC | 82 |
| JFNF6 | SMISC | 86 |
Table 184revo.4: MPC184 Revolute Joint Item and Sequence Numbers - NMISC Items
| Output Quantity Name | ETABLE and ESOL Command Input | |
|---|---|---|
| Item | E | |
| The following output is available for all revolute joint elements (KEYOPT(4) = 0 and 1) | ||
| E1X-I | NMISC | 1 |
| E1Y-I | NMISC | 2 |
| E1Z-I | NMISC | 3 |
| E2X-I | NMISC | 4 |
| E2Y-I | NMISC | 5 |
| E2Z-I | NMISC | 6 |
| E3X-I | NMISC | 7 |
| E3Y-I | NMISC | 8 |
| E3Z-I | NMISC | 9 |
| E1X-J | NMISC | 10 |
| E1Y-J | NMISC | 11 |
| E1Z-J | NMISC | 12 |
| E2X-J | NMISC | 13 |
| E2Y-J | NMISC | 14 |
| E2Z-J | NMISC | 15 |
| E3X-J | NMISC | 16 |
| E3Y-J | NMISC | 17 |
| E3Z-J | NMISC | 18 |
| JFX | NMISC | 19 |
| JFY | NMISC | 20 |
| JFZ | NMISC | 21 |
| JMX | NMISC | 22 |
| JMY | NMISC | 23 |
| JMZ | NMISC | 24 |
MPC184 Revolute Joint Assumptions and Restrictions
The nodes I and J must be coincident.
The local coordinate systems at the nodes must be specified such that the revolute axis is well defined. Otherwise, it is possible that the rotational motion might not be what is expected.
Boundary conditions cannot be applied on the nodes forming the revolute joint.
Rotational degrees of freedom are activated at the nodes forming the element. When these elements are used in conjunction with solid elements, the rotational degrees of freedom must be suitably constrained. Since boundary conditions cannot be applied to the nodes of the Revolute Joint, a beam or shell element with very weak stiffness may be used with the underlying solid elements at the nodes forming the joint element to avoid any rigid body modes.
If both stops and locks are specified, then lock specification takes precedence. That is, if the degree of freedom is locked at a given value, then it will remain locked for the rest of the analysis.
In a nonlinear analysis, the component of relative motion (rotation around the revolute axis) is accumulated over all the substeps. It is essential that the substep size be restricted such that this rotation in a given substep is less than π for the values to be accumulated correctly.
The element currently does not support birth or death options.
The equation solver (EQSLV) must be the sparse solver or the PCG solver. The command PCGOPT,,,,,,,ON is also required in order to use the PCG solver.
The element coordinate system (/PSYMB,ESYS) is not relevant.