Constant Velocity Joint
Joint with two rotational DoFs between shafts constrained to spin with equal velocity
Library
Joints
Description
This block represents a joint with two rotational degrees of freedom constrained to maintain a constant angular velocity about the base and follower Z axes. The base and follower frame origins remain coincident throughout simulation.
The joint applies three rotation transformations between the base and follower frames in the sequence azimuth → bend angle → -azimuth. Each transformation takes place relative to the intermediate frame resulting from any prior transformations. For example, the bend angle transformation takes place relative to the intermediate frame resulting from the azimuth transformation.
Joint Degrees of Freedom
A set of optional state targets guide assembly for the joint primitive. Targets include position and velocity. A priority level sets the relative importance of the state targets. If two targets are incompatible, the priority level determines which of the targets to satisfy.
Optional sensing ports output the joint primitive motion through physical signals. Motion variables that you can sense include joint position, velocity, and acceleration. Selecting a variable in the Sensing menu exposes the physical signal port for that variable.
Parameters
Constant Velocity Primitive: State Targets
- Specify Position Target
Desired joint primitive position at the start of simulation. This is the relative angular position of the follower frame relative to the base frame. Selecting this option exposes priority and value fields.
- Specify Velocity Target
Desired joint velocity at the start of simulation. This is the relative angular velocity of the follower frame relative to the base frame. Selecting this option exposes priority and value fields.
- Priority
Select state target priority. This is the importance level assigned to the state target. If all state targets cannot be simultaneously satisfied, the priority level determines which targets to satisfy first and how closely to satisfy them. This option applies to both position and velocity state targets.
Priority Level Description High (desired)Satisfy state target precisely Low (approximate)Satisfy state target approximately Note
During assembly, high-priority targets behave as exact guides. Low-priority targets behave as rough guides.
- Value
Joint primitive angles to specify. Angles include bend and azimuth angles.
Value: Bend AngleAngle between the base and follower frame Z axes. The block applies this angle about the rotated Y axis resulting from the azimuth transformation. At zero bend angle, the follower frame Z axis is coincident with the base frame Z axis.
Value: AzimuthAngle about the base frame Z axis prior to bending. At zero azimuth, the base and follower Z axes are in the XZ plane of the base frame.
Constant Velocity Primitive: Sensing
Select the variables to sense in the constant velocity joint primitive. Selecting a variable exposes a physical signal port that outputs the measured quantity as a function of time. Each quantity is measured for the follower frame with respect to the base frame. It is resolved in the base frame.
| Variable | Description |
|---|---|
Bend Angle: Position | Angle between the base and follower frame Z axes |
Bend Angle: Velocity | First time derivative of the bend angle. |
Bend Angle: Acceleration | Second time derivative of the bend angle. |
Azimuth: Position | Angle about the base frame Z axis prior to bending. |
Azimuth: Velocity | First time derivative of the azimuth angle. |
Azimuth: Acceleration | Second time derivative of the azimuth angle. |
Mode Configuration
Specify the mode of the joint. The joint mode can be normal or disengaged throughout the simulation, or you can provide an input signal to change the mode during the simulation.
- Mode
Select one of the following options to specify the mode of the joint. The default setting is
Normal.Method Description NormalThe joint behaves normally throughout the simulation. DisengagedThe joint is disengaged throughout the simulation. Provided by InputThis option exposes the mode port that you can connect to an input signal to change the joint mode during the simulation. The joint mode is normal when the input signal is 0and disengaged when the input signal is-1. The joint mode can be changed many times during the simulation.
Composite Force/Torque Sensing
Select the composite forces and torques to sense. Their measurements encompass all joint primitives and are specific to none. They come in two kinds: constraint and total.
Constraint measurements give the resistance against motion on the locked axes of the joint. In prismatic joints, for instance, which forbid translation on the xy plane, that resistance balances all perturbations in the x and y directions. Total measurements give the sum over all forces and torques due to actuation inputs, internal springs and dampers, joint position limits, and the kinematic constraints that limit the degrees of freedom of the joint.
- Direction
Vector to sense from the action-reaction pair between the base and follower frames. The pair arises from Newton's third law of motion which, for a joint block, requires that a force or torque on the follower frame accompany an equal and opposite force or torque on the base frame. Indicate whether to sense that exerted by the base frame on the follower frame or that exerted by the follower frame on the base frame.
- Resolution Frame
Frame on which to resolve the vector components of a measurement. Frames with different orientations give different vector components for the same measurement. Indicate whether to get those components from the axes of the base frame or from the axes of the follower frame. The choice matters only in joints with rotational degrees of freedom.
- Constraint Force
Dynamic variable to measure. Constraint forces counter translation on the locked axes of the joint while allowing it on the free axes of its primitives. Select to output the constraint force vector through port fc.
- Constraint Torque
Dynamic variable to measure. Constraint torques counter rotation on the locked axes of the joint while allowing it on the free axes of its primitives. Select to output the constraint torque vector through port tc.
- Total Force
Dynamic variable to measure. The total force is a sum across all joint primitives over all sources—actuation inputs, internal springs and dampers, joint position limits, and kinematic constraints. Select to output the total force vector through port ft.
- Total Torque
Dynamic variable to measure. The total torque is a sum across all joint primitives over all sources—actuation inputs, internal springs and dampers, joint position limits, and kinematic constraints. Select to output the total torque vector through port tt.
Ports
This block has two frame ports. It also has optional physical signal ports for sensing dynamical variables such as forces, torques, and motion. You expose an optional port by selecting the sensing check box corresponding to that port.
Frame Ports
B — Base frame
F — Follower frame
Sensing Ports
The constant velocity joint primitive provides the following sensing ports:
qb — Bend angle
wb — First time-derivative of the bend angle
bb — Second time-derivative of the bend angle
qa — Azimuth angle
wa — First time-derivative of the azimuth angle
ba — Second time-derivative of the azimuth angle
The following sensing ports provide the composite forces and torques acting on the joint:
fc — Constraint force
tc — Constraint torque
ft — Total force
tt — Total torque
Mode Port
Mode configuration provides the following port:
mode — Value of the mode of the joint. If the input is equal to
0, the joint behaves normally. If the input is equal to-1, the joint behaves as disengaged.