Joint with coupled rotational and translational degrees of freedom

Joints

## Description

This block represents a joint with one rotational degree of freedom coupled with one translational degree of freedom. The coupling between the two degrees of freedom ensures that whenever the joint frames rotate relative to each other, they also translate by a commensurate amount and vice-versa. The joint lead determines the translation distance associated with a unit rotation angle while the joint direction determines whether a positive angle results in a positive or negative translation.

During assembly and simulation, the joint aligns the Z axes of its port frames. The common Z axis functions as the rotation and translation axis. Whenever the joint frames rotate, they do so about the common Z axis, and whenever the joint frames translate, they do so along the common Z axis. You can orient the motion axis in a different direction by applying rotation transforms to the joint frames through Rigid Transform blocks.

Joint Degrees of Freedom

A set of optional state targets guide assembly for the joint primitive. Targets include position and velocity. You can specify these based on the relative rotation or translation between the joint frames. 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.

Each joint primitive has a set of optional sensing ports. These ports provide physical signal outputs that measure joint primitive motion. Variables that you can sense include those describing translational motion, rotational motion, and constraint forces and torques.

## Parameters

Direction

Handedness of motion between the joint frames. Motion is right-handed if a positive rotation leads to a positive translation and left-handed if a positive rotation leads to a negative translation. The default setting is `Right-Hand`.

Translation distance between the joint frames due to a unit rotation angle. The larger the lead, the longer the frames must translate before completing a full revolution. The default value is `1.0` mm/rev.

### Lead Screw Primitive: State Targets

Specify the lead screw primitive state targets and their priority levels. A state target is the desired value for one of the joint state variables—position or velocity. The priority level is the relative importance of a state target. It determines how precisely the target must be satisfied.

Specify Position Target

Desired joint primitive position at the start of simulation. This is the relative position, rotational or translational, 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 velocity, rotational or translational, 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.

Based On

Motion type that the state target is based on. Options include `Rotation` and `Translation`. The default setting is `Translation`.

Value

Desired value of the position or velocity state target. The default value is `0`.

Select the variables to sense in the lead screw 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
`Rotation`: Position

Rotation angle of the follower frame relative to the base frame about the common Z axis. Selecting the check box exposes a physical signal port labeled q.

`Rotation`: Velocity

Rotational velocity of the follower frame relative to the base frame about the common Z axis. Selecting the check box exposes a physical signal port labeled w.

`Rotation`: Acceleration

Rotational acceleration of the follower frame relative to the base frame about the common Z axis. Selecting the check box exposes a physical signal port labeled b.

`Translation`: Position

Offset distance of the follower frame relative to the base frame along the common Z axis. Selecting the check box exposes a physical signal port labeled p.

`Translation`: Velocity

Translational velocity of the follower frame relative to the base frame along the common Z axis. Selecting the check box exposes a physical signal port labeled v.

`Translation`: Acceleration

Translational acceleration of the follower frame relative to the base frame along the common Z axis. Selecting the check box exposes a physical signal port labeled a.

### 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`.

MethodDescription
`Normal`The joint behaves normally throughout the simulation.
`Disengaged`The joint is disengaged throughout the simulation.
`Provided by Input`This 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 `0` and 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 lead screw joint primitive provides the following sensing ports:

• q — Angular position

• w — Angular velocity

• b — Angular acceleration

• p — Linear position

• v — Linear velocity

• a — Linear acceleration

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.

## Version History

Introduced in R2015a