Documentation

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.

C/C++ Code Generation

This block supports code generation for real-time simulation tasks. Certain blocks and block settings may be more suitable for simulation on a real-time device. For suggestions on how to improve real-time simulation performance, use the Simulink® Performance Advisor (Simulink). Suggestions include ways to reduce model complexity where helpful and to decrease numerical stiffness.

Select Analysis > Performance Tools > Performance Advisor in the Simulink menu bar to open the Performance Advisor. Set the Activity parameter to Execute real-time application to view suggestions specific to real-time simulation performance. Expand the Real-Time node in the tree view pane to select performance checks specific to Simscape™ products.

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 LevelDescription
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 Angle

Angle 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: Azimuth

Angle 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.

VariableDescription
Bend Angle: PositionAngle between the base and follower frame Z axes
Bend Angle: VelocityFirst time derivative of the bend angle.
Bend Angle: AccelerationSecond time derivative of the bend angle.
Azimuth: PositionAngle about the base frame Z axis prior to bending.
Azimuth: VelocityFirst time derivative of the azimuth angle.
Azimuth: AccelerationSecond time derivative of the azimuth angle.

Composite Force/Torque Sensing

Select the composite, or joint-wide, forces and torques to sense. These are forces and torques that act not at individual joint primitives but at the whole joint. Options include constraint and total forces and torques.

During simulation, the block computes the selected composite forces and torques acting between the base and follower port frames. It outputs these variables using physical signal output ports. Check the port labels to identify the output variables at different ports.

Direction

Forces and torques acting at joints do so in pairs. Newton’s third law of motion requires that every action be accompanied by an equal and opposite reaction. If the base frame of a joint exerts a force or torque on the follower frame, then the follower frame must exert an equal and opposite force or torque on the base frame.

Select whether to sense the composite forces and torques exerted by the base frame on the follower frame or vice versa. The force and torque vector components are positive if they point along the positive X, Y, and Z axes of the selected resolution frame.

Resolution Frame

You can resolve a vector quantity into Cartesian components in different frames. If the resolution frames have different orientations, then the measured components are themselves different—even though the vector quantity remains the same.

Select the frame in which to resolve the sensed force and torque variables. Possible resolution frames include Base and Follower. The block outputs the Cartesian components of the sensed force and torque vectors as observed in this frame.

Constraint Force

Joint blocks with fewer than three translational degrees of freedom forbid motion along one or more axes. For example, the Gimbal Joint block forbids translation along all axes. To prevent translation along an axis, a joint block applies a constraint force between its base and follower port frames. Constraint forces are orthogonal to joint translation axes and therefore do no work.

Select the check box to compute and output the 3-D constraint force vector [fcx, fcy, fcz] acting at the joint. Only constraint force components that are orthogonal to the joint translational degrees of freedom have nonzero values. Selecting this option causes the block to expose physical signal port fc.

Constraint Torque

Joint blocks with fewer than three rotational degrees of freedom forbid motion about one or more axes. For example, the Cartesian Joint block forbids rotation about all axes. To prevent rotation about an axis, a joint block applies a constraint torque between its base and follower port frames. Constraint torques are orthogonal to joint rotation axes and therefore do no work.

Select the check box to compute and output the 3-D constraint torque vector [tcx, tcy, tcz] acting at the joint. Only constraint torque components that are orthogonal to the joint rotational degrees of freedom have nonzero values. Selecting this option causes the block to expose physical signal port tc.

Total Force

A joint block generally applies various forces between its port frames:

  • Actuation forces that drive prismatic joint primitives.

  • Internal spring and damper forces that resist motion at prismatic joint primitives.

  • Constraint forces that forbid motion in directions orthogonal to prismatic joint primitives.

The net sum of the different force components equals the total force acting between the joint port frames. Select the check box to compute and output the 3-D total force vector [ftx, fty, ftz]. Selecting this option causes the block to expose physical signal port ft.

Total Torque

A joint block generally applies various torques between its port frames:

  • Actuation torques that drive revolute or spherical joint primitives.

  • Internal spring and damper torques that resist motion at revolute or spherical joint primitives.

  • Constraint torques that forbid motion in directions orthogonal to the revolute or spherical joint primitive axes.

The net sum of the different torque components equals the total torque acting at a joint. Select the check box to compute and output the 3-D total torque vector [ttx, tty, ttz]. Selecting this option causes the block to expose physical signal 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

Introduced in R2015a

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