# Pin Slot Joint

Joint with one prismatic and one revolute primitives possessing mutually orthogonal motion axes

Joints

## Description

This block represents a joint with one translational and one rotational degrees of freedom. One prismatic primitive provides the translational degree of freedom. One revolute primitive provides the rotational degree of freedom. Prismatic and revolute axes are mutually orthogonal.

Joint Degrees of Freedom

The joint block represents motion between the base and follower frames as a sequence of time-varying transformations. Each joint primitive applies one transformation in this sequence. The transformation translates or rotates the follower frame with respect to the joint primitive base frame. For all but the first joint primitive, the base frame coincides with the follower frame of the previous joint primitive in the sequence.

At each time step during the simulation, the joint block applies the sequence of time-varying frame transformations in this order:

1. Translation:

• Along the X axis of the X Prismatic Primitive (Px) base frame.

2. Rotation:

• About the Z axis of the Z Revolute Primitive (Rz) base frame. This frame is coincident with the X Prismatic Primitive (Px) follower frame.

The figure shows the sequence in which the joint transformations occur at a given simulation time step. The resulting frame of each transformation serves as the base frame for the following transformation.

Joint Transformation Sequence

A set of optional state targets guide assembly for each 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.

Internal mechanics parameters account for energy storage and dissipation at each joint primitive. Springs act as energy storage elements, resisting any attempt to displace the joint primitive from its equilibrium position. Joint dampers act as energy dissipation elements. Springs and dampers are strictly linear.

In all but lead screw and constant velocity primitives, joint limits serve to curb the range of motion between frames. A joint primitive can have a lower bound, an upper bound, both, or, in the default state, neither. To enforce the bounds, the joint adds to each a spring-damper. The stiffer the spring, the harder the stop, or bounce, if oscillations arise. The stronger the damper, the deeper the viscous losses that gradually lessen contact oscillations or, in overdamped primitives, keep them from forming altogether.

Each joint primitive has a set of optional actuation and sensing ports. Actuation ports accept physical signal inputs that drive the joint primitives. These inputs can be forces and torques or a desired joint trajectory. Sensing ports provide physical signal outputs that measure joint primitive motion as well as actuation forces and torques. Actuation modes and sensing types vary with joint primitive.

## Parameters

### Prismatic Primitive: State Targets

Specify the prismatic primitive state targets and their priority levels. A state target is the desired value for one of the joint state parameters—position and velocity. The priority level is the relative importance of a state target. It determines how precisely the target must be met. Use the Model Report tool in Mechanics Explorer to check the assembly status for each joint state target.

Specify Position Target

Select this option to specify the desired joint primitive position at time zero. This is the relative position, measured along the joint primitive axis, of the follower frame origin with respect to the base frame origin. The specified target is resolved in the base frame. Selecting this option exposes priority and value fields.

Specify Velocity Target

Select this option to specify the desired joint primitive velocity at time zero. This is the relative velocity, measured along the joint primitive axis, of the follower frame origin with respect to the base frame origin. It is resolved in 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

Enter the state target numerical value. The default is `0`. Select or enter a physical unit. The default is `m` for position and `m/s` for velocity.

### Prismatic Primitive: Internal Mechanics

Specify the prismatic primitive internal mechanics. Internal mechanics include linear spring forces, accounting for energy storage, and damping forces, accounting for energy dissipation. You can ignore internal mechanics by keeping spring stiffness and damping coefficient values at `0`.

Equilibrium Position

Enter the spring equilibrium position. This is the distance between base and follower frame origins at which the spring force is zero. The default value is `0`. Select or enter a physical unit. The default is `m`.

Spring Stiffness

Enter the linear spring constant. This is the force required to displace the joint primitive by a unit distance. The default is `0`. Select or enter a physical unit. The default is `N/m`.

Damping Coefficient

Enter the linear damping coefficient. This is the force required to maintain a constant joint primitive velocity between base and follower frames. The default is `0`. Select or enter a physical unit. The default is `N/(m/s)`.

### Prismatic Primitive: Limits

Limit the range of motion of the joint primitive. Joint limits use spring-dampers to resist travel past the bounds of the range. A joint primitive can have a lower bound, an upper bound, both, or, in the default state, neither. The stiffer the spring, the harder the stop, or bounce, if oscillations arise. The stronger the damper, the larger the viscous losses that gradually lessen contact oscillations or, in overdamped primitives, keep them from forming altogether.

Specify Lower Limit

Select to add a lower bound to the range of motion of the joint primitive.

Specify Upper Limit

Select to add an upper bound to the range of motion of the joint primitive.

Value

Location past which to resist joint travel. The location is the offset from base to follower, as measured in the base frame, at which contact begins. It is a distance along an axis in prismatic primitives, an angle about an axis in revolute primitives, and an angle between two axes in spherical primitives.

Spring Stiffness

Resistance of the contact spring to displacement past the joint limit. The spring is linear and its stiffness is constant. The larger the value, the harder the stop. The proportion of spring to damper forces determines whether the stop is underdamped and prone to oscillations on contact.

Damping Coefficient

Resistance of the contact damper to motion past the joint limit. The damper is linear and its coefficient is constant. The larger the value, the greater the viscous losses that gradually lessen contact oscillations, if any arise. The proportion of spring to damper forces determines whether the stop is underdamped and prone to oscillations on contact.

Transition Region

Region over which to raise the spring-damper force to its full value. The region is a distance along an axis in prismatic primitives, an angle about an axis in revolute primitives, and an angle between two axes in spherical primitives.

The smaller the region, the sharper the onset of contact and the smaller the time-step required of the solver. In the trade-off between simulation accuracy and simulation speed, reducing the transition region improves accuracy while expanding it improves speed.

### Prismatic Primitive: Actuation

Specify actuation options for the prismatic joint primitive. Actuation modes include and Motion. Selecting `Provided by Input` from the drop-down list for an actuation mode adds the corresponding physical signal port to the block. Use this port to specify the input signal. Actuation signals are resolved in the base frame.

Force

Select an actuation force setting. The default setting is `None`.

Actuation Force SettingDescription
`None`No actuation force.
`Provided by Input`Actuation force from physical signal input. The signal provides the force acting on the follower frame with respect to the base frame along the joint primitive axis. An equal and opposite force acts on the base frame.
`Automatically computed`Actuation force from automatic calculation. Simscape™ Multibody™ computes and applies the actuation force based on model dynamics.
Motion

Select an actuation motion setting. The default setting is ```Automatically Computed```.

Actuation Motion SettingDescription
`Provided by Input`Joint primitive motion from physical signal input. The signal provides the desired trajectory of the follower frame with respect to the base frame along the joint primitive axis.
`Automatically computed`Joint primitive motion from automatic calculation. Simscape Multibody computes and applies the joint primitive motion based on model dynamics.

### Prismatic Primitive: Sensing

Select the variables to sense in the prismatic 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. You can use the measurement signals for analysis or as input in a control system.

Position

Select this option to sense the relative position of the follower frame origin with respect to the base frame origin along the joint primitive axis.

Velocity

Select this option to sense the relative velocity of the follower frame origin with respect to the base frame origin along the joint primitive axis.

Acceleration

Select this option to sense the relative acceleration of the follower frame origin with respect to the base frame origin along the joint primitive axis.

Actuator Force

Select this option to sense the actuation force acting on the follower frame with respect to the base frame along the joint primitive axis.

### Revolute Primitive: State Targets

Specify the revolute primitive state targets and their priority levels. A state target is the desired value for one of the joint state parameters—position and velocity. The priority level is the relative importance of a state target. It determines how precisely the target must be met. Use the Model Report tool in Mechanics Explorer to check the assembly status for each joint state target.

Specify Position Target

Select this option to specify the desired joint primitive position at time zero. This is the relative rotation angle, measured about the joint primitive axis, of the follower frame with respect to the base frame. The specified target is resolved in the base frame. Selecting this option exposes priority and value fields.

Specify Velocity Target

Select this option to specify the desired joint primitive velocity at time zero. This is the relative angular velocity, measured about the joint primitive axis, of the follower frame with respect to the base frame. It is resolved in 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

Enter the state target numerical value. The default is `0`. Select or enter a physical unit. The default is `deg` for position and `deg/s` for velocity.

### Revolute Primitive: Internal Mechanics

Specify the revolute primitive internal mechanics. Internal mechanics include linear spring torques, accounting for energy storage, and linear damping torques, accounting for energy dissipation. You can ignore internal mechanics by keeping spring stiffness and damping coefficient values at `0`.

Equilibrium Position

Enter the spring equilibrium position. This is the rotation angle between base and follower frames at which the spring torque is zero. The default value is `0`. Select or enter a physical unit. The default is `deg`.

Spring Stiffness

Enter the linear spring constant. This is the torque required to rotate the joint primitive by a unit angle. The default is `0`. Select or enter a physical unit. The default is `N*m/deg`.

Damping Coefficient

Enter the linear damping coefficient. This is the torque required to maintain a constant joint primitive angular velocity between base and follower frames. The default is `0`. Select or enter a physical unit. The default is `N*m/(deg/s)`.

### Revolute Primitive: Limits

Limit the range of motion of the joint primitive. Joint limits use spring-dampers to resist travel past the bounds of the range. A joint primitive can have a lower bound, an upper bound, both, or, in the default state, neither. The stiffer the spring, the harder the stop, or bounce, if oscillations arise. The stronger the damper, the larger the viscous losses that gradually lessen contact oscillations or, in overdamped primitives, keep them from forming altogether.

Specify Lower Limit

Select to add a lower bound to the range of motion of the joint primitive.

Specify Upper Limit

Select to add an upper bound to the range of motion of the joint primitive.

Value

Location past which to resist joint travel. The location is the offset from base to follower, as measured in the base frame, at which contact begins. It is a distance along an axis in prismatic primitives, an angle about an axis in revolute primitives, and an angle between two axes in spherical primitives.

Spring Stiffness

Resistance of the contact spring to displacement past the joint limit. The spring is linear and its stiffness is constant. The larger the value, the harder the stop. The proportion of spring to damper forces determines whether the stop is underdamped and prone to oscillations on contact.

Damping Coefficient

Resistance of the contact damper to motion past the joint limit. The damper is linear and its coefficient is constant. The larger the value, the greater the viscous losses that gradually lessen contact oscillations, if any arise. The proportion of spring to damper forces determines whether the stop is underdamped and prone to oscillations on contact.

Transition Region

Region over which to raise the spring-damper force to its full value. The region is a distance along an axis in prismatic primitives, an angle about an axis in revolute primitives, and an angle between two axes in spherical primitives.

The smaller the region, the sharper the onset of contact and the smaller the time-step required of the solver. In the trade-off between simulation accuracy and simulation speed, reducing the transition region improves accuracy while expanding it improves speed.

### Revolute Primitive: Actuation

Specify actuation options for the revolute joint primitive. Actuation modes include and Motion. Selecting `Provided by Input` from the drop-down list for an actuation mode adds the corresponding physical signal port to the block. Use this port to specify the input signal. Input signals are resolved in the base frame.

Torque

Select an actuation torque setting. The default setting is `None`.

Actuation Torque SettingDescription
`None`No actuation torque.
`Provided by Input`Actuation torque from physical signal input. The signal provides the torque acting on the follower frame with respect to the base frame about the joint primitive axis. An equal and opposite torque acts on the base frame.
`Automatically computed`Actuation torque from automatic calculation. Simscape Multibody computes and applies the actuation torque based on model dynamics.
Motion

Select an actuation motion setting. The default setting is ```Automatically Computed```.

Actuation Motion SettingDescription
`Provided by Input`Joint primitive motion from physical signal input. The signal provides the desired trajectory of the follower frame with respect to the base frame along the joint primitive axis.
`Automatically computed`Joint primitive motion from automatic calculation. Simscape Multibody computes and applies the joint primitive motion based on model dynamics.

### Revolute Primitive: Sensing

Select the variables to sense in the revolute 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. You can use the measurement signals for analysis or as input in a control system.

Position

Select this option to sense the relative rotation angle of the follower frame with respect to the base frame about the joint primitive axis.

Velocity

Select this option to sense the relative angular velocity of the follower frame with respect to the base frame about the joint primitive axis.

Acceleration

Select this option to sense the relative angular acceleration of the follower frame with respect to the base frame about the joint primitive axis.

Actuator Torque

Select this option to sense the actuation torque acting on the follower frame with respect to the base frame about the joint primitive axis.

### Mode Configuration

Specify the mode of the joint. A joint can behave normally or disengaged from the beginning of the simulation, or you can provide an input signal to change its mode during the simulation.

If you set the Mode parameter to `Provided by Input`, a new port mode will be visible.

Mode

Select a method to specify the mode of the joint. The default setting is `Normal`.

MethodDescription
`Normal`The joint behaves normally.
`Disengaged`The joint is disengaged from the beginning of the simulation.
`Provided by Input`Provide an input signal that can be either `0` or `-1` to keep the joint in normal state or in disengaged state, respectively.

### 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 specifying actuation inputs and 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

### Actuation Ports

The prismatic joint primitive provides the following actuation ports:

• fx — Actuation force acting on the X prismatic joint primitive

• px — Desired trajectory of the X prismatic joint primitive

The revolute joint primitive provides the following actuation ports:

• tz — Actuation torque acting on the Z revolute joint primitive

• qz — Desired rotation of the Z revolute joint primitive

### Sensing Ports

The prismatic joint primitive provides the following sensing ports:

• px — Position of the X prismatic joint primitive

• vx — Velocity of the X prismatic joint primitive

• ax — Acceleration of the X prismatic joint primitive

• fx — Actuation force acting on the X prismatic joint primitive

• fllx — Force due to contact with the lower limit of the X prismatic joint primitive

• fulx — Force due to contact with the upper limit of the X prismatic joint primitive

The revolute joint primitive provides the following sensing ports:

• qz — Angular position of the Z revolute joint primitive

• wz — Angular velocity of the Z revolute joint primitive

• bz — Angular acceleration of the Z revolute joint primitive

• tz — Actuation torque acting on the Z revolute joint primitive

• tllz — Torque due to contact with the lower limit of the Z revolute joint primitive

• tulz — Torque due to contact with the upper limit of the Z revolute joint primitive

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.