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Library

Joints

Description

This block represents a joint with one translational degreeof freedom. One prismatic primitive provides the translational degreeof freedom. The base and follower frames remain parallel during simulation.

Joint Degrees of Freedom

The joint block represents motion between the base and followerframes as a single time-varying transformation. The Z prismatic primitive(Pz) applies this transformation, which causes the follower frameto translate with respect to the base frame along the common Z axis.

Joint Transformation

A set of optional state targets guide assembly for each jointprimitive. Targets include position and velocity. A priority levelsets the relative importance of the state targets. If two targetsare incompatible, the priority level determines which of the targetsto satisfy.

Internal mechanics parameters account for energy storage anddissipation at each joint primitive. Springs act as energy storageelements, resisting any attempt to displace the joint primitive fromits equilibrium position. Joint dampers act as energy dissipationelements. 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 sensingports. Actuation ports accept physical signal inputs that drive thejoint primitives. These inputs can be forces and torques or a desiredjoint trajectory. Sensing ports provide physical signal outputs thatmeasure 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 prioritylevels. A state target is the desired value for one of the joint stateparameters—position and velocity. The priority level is therelative importance of a state target. It determines how preciselythe target must be met. Use the Model Report tool in Mechanics Explorerto check the assembly status for each joint state target.

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

Select this option to specify the desired joint primitive velocityat time zero. This is the relative velocity, measured along the jointprimitive axis, of the follower frame origin with respect to the baseframe origin. It is resolved in the base frame. Selecting this optionexposes priority and value fields.

Select state target priority. This is the importance level assignedto the state target. If all state targets cannot be simultaneouslysatisfied, the priority level determines which targets to satisfyfirst and how closely to satisfy them. This option applies to bothposition and velocity state targets.

Note

During assembly, high-priority targets behave as exact guides.Low-priority targets behave as rough guides.

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

Prismatic Primitive: Internal Mechanics

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Specify the prismatic primitive internal mechanics. Internalmechanics include linear spring forces, accounting for energy storage,and damping forces, accounting for energy dissipation. You can ignoreinternal mechanics by keeping spring stiffness and damping coefficientvalues at 0.

Enter the spring equilibrium position. This is the distancebetween base and follower frame origins at which the spring forceis zero. The default value is 0. Select or entera physical unit. The default is m.

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

Enter the linear damping coefficient. This is the force requiredto maintain a constant joint primitive velocity between base and followerframes. The default is 0. Select or enter a physicalunit. 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.

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

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

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.

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.

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.

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-downlist for an actuation mode adds the corresponding physical signalport to the block. Use this port to specify the input signal. Actuationsignals are resolved in the base frame.

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

Select an actuation motion setting. The default setting is AutomaticallyComputed.

Prismatic Primitive: Sensing

Select the variables to sense in the prismatic joint primitive.Selecting a variable exposes a physical signal port that outputs themeasured quantity as a function of time. Each quantity is measuredfor the follower frame with respect to the base frame. It is resolvedin the base frame. You can use the measurement signals for analysisor as input in a control system.

Select this option to sense the relative position of the followerframe origin with respect to the base frame origin along the jointprimitive axis.

Select this option to sense the relative velocity of the followerframe origin with respect to the base frame origin along the jointprimitive axis.

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

Select this option to sense the actuation force acting on thefollower frame with respect to the base frame along the joint primitiveaxis.

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.

Select one of the following options to specify the mode of the joint. The default setting is Normal.

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.

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.

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.

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.

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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.

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.

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 physicalsignal ports for specifying actuation inputs and sensing dynamicalvariables such as forces, torques, and motion. You expose an optionalport by selecting the sensing check box corresponding to that port.

Actuation Ports

The prismatic joint primitive provides the following actuationports:

• f — Actuation force acting on the Z prismatic joint primitive

• p — Desired trajectory of the Z prismatic joint primitive

Sensing Ports

The prismatic joint primitive provides the following sensingports:

• p — Position of the Z prismatic joint primitive

• v — Velocity of the Z prismatic joint primitive

• a — Acceleration of the Z prismatic joint primitive

• f — Actuation force acting on the Z prismatic joint primitive

• fll — Force due to contact with the lower limit of the Z prismatic joint primitive

• ful — Force due to contact with the upper limit of the Z prismatic joint primitive

The following sensing ports provide the composite forces andtorques 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.

Extended Capabilities

See Also

Revolute Joint Spherical Joint