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Universal Joint

Joint with two revolute primitives

Library

Joints

  • Universal Joint block

Description

This block represents a joint with two rotational degrees of freedom. Two revolute primitives provide the two rotational degrees of freedom. The base and follower frame origins remain coincident during simulation.

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. Rotation:

    1. About the X axis of the X Revolute Primitive (Rx) base frame.

    2. About the Y axis of the Y Revolute Primitive (Ry) base frame. This frame is coincident with the X Revolute Primitive (Rx) 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

To specify the target of the initial state for a joint primitive, use the parameters under State Targets. The targets are specified in the base frame. You can also set the priority levels for the targets. If the joint is not able to satisfy all the state targets, the priority level determines which targets to satisfy first and how closely to satisfy them. For an example, see Guiding Assembly.

To model damping and spring behavior for a joint primitive, use the parameters under Internal Mechanics. Specify the Damping Coefficient parameter to model energy dissipation and the Spring Stiffness parameter to model energy storage. Joint springs attempt to displace the joint primitive from its equilibrium position. Joint dampers act as energy dissipation elements. The springs and dampers are strictly linear.

To specify the limits of a joint primitive, use the parameters under Limits. The lower and upper bounds define the width of the free region. The block applies a force to accelerate the joint position back to the free region when the position exceeds the bounds. The block uses a smoothed spring-damper method to compute the force. See the Description section of the Spatial Contact Force block for more information about the smoothed spring-damper method.

The Force, Torque, and Motion parameters in the Actuation section govern the motion of a joint primitive during simulation. For more information, see Specifying Joint Actuation Inputs. Additionally, the joint block has ports that output sensing data, such as position, velocity, acceleration, force, and torque that you can use to perform analytical tasks on a model. For more information, see Sensing and Force and Torque Sensing.

Parameters

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 Torque 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
NoneNo actuation torque.
Provided by InputActuation 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 computedActuation 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 InputJoint 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 computedJoint 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. 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
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 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 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 revolute joint primitives provide the following actuation ports:

  • tx, ty — Actuation torques acting on the X and Y revolute joint primitives

  • qx, qy — Desired rotations of the X and Y revolute joint primitives

Sensing Ports

The revolute joint primitives provide the following sensing ports:

  • qx, qy — Angular positions of the X and Y revolute joint primitives

  • wx, wy — Angular velocities of the X and Y revolute joint primitives

  • bx, by — Angular accelerations of the X and Y revolute joint primitives

  • tx, ty — Actuation torques acting on the X and Y revolute joint primitives

  • tllx, tlly — Torques due to contact with the lower limits of the X and Y revolute joint primitives

  • tulx, tuly — Torques due to contact with the upper limits of the X and Y revolute joint primitives

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 R2012a