SimMechanics

Joint Stiction Actuator

Apply classical friction to a joint primitive

Library

Sensors & Actuators

Description

The Joint Stiction Actuator block applies stiction (classical friction) to a prismatic or revolute joint primitive. The stiction is regulated by an idealized model whose parameters you specify. (See Stiction Theory following.) The Joint Stiction Actuator applies stiction to the joint primitive as a relative force/torque between the joint's connected Bodies. The bodies can experience additional forces independent of the joint.

The inports are Simulink signals. The output is a Connector Port. You cannot connect a Joint Stiction Actuator to a Spherical block or spherical primitive. Restrictions on simultaneous actuators and sensors:

• You cannot actuate a joint primitive simultaneously with a Joint Stiction Actuator and a Joint Actuator. But with the Joint Stiction Actuator inport External Actuation, you can apply to the joint primitive an external (nonfrictional) force/torque actuation signal equivalent to applying a Joint Actuator.
• You can simultaneously actuate a joint primitive with a Joint Stiction Actuator and a Joint Initial Condition Actuator.
• You can also simultaneously actuate a joint primitive with a Joint Stiction Actuator and measure the force/torque along/around the joint primitive with a Joint Sensor.

Dialog Box and Parameters

The dialog box has one active area, Stiction actuation.

Connected to primitive

In the pull-down menu, choose the joint primitive within the Joint which you want to actuate with the Joint Stiction Actuator. A primitive Joint block has only one joint primitive.

You cannot connect a Joint Stiction Actuator to a spherical primitive.

If the Joint Stiction Actuator is not connected to a Joint block, this menu shows only Unknown.

External force units

In the pull-down menu, choose units for the external nonfrictional force/torque F_ext. The default is N (Newtons) if connected to a prismatic primitive and N-m (Newton-meters) if connected to a revolute primitive.

Kinetic friction units

In the pull-down menu, choose units for the kinetic friction force/torque F_K. The default is N (Newtons) if connected to a prismatic primitive and N-m (Newton-meters) if connected to a revolute primitive.

Locking velocity threshold (MKS-SI units)

Enter the positive relative velocity of the joint primitive below which the joint locks by static friction. Above that velocity, the joint is unlocked. The units must be MKS: for a prismatic primitive, meters/second; for a revolute primitive, radians/second.

Summary of Joint Stiction Actuator inport signals

All the Simulink inports are 1-component signals. Here is an example of a prismatic joint connected between two bodies and actuated with stiction:

Joint Stiction Actuator Simulink Inport Signals

Summary of Joint Stiction Actuator Input Signals

Simulink inport	Friction Model Symbol	Description
External actuation	Fext	External nonfrictional force/torque
Kinetic Friction	FK	Kinetic friction
Forward Stiction Limit	FSf < 0	Static friction lower limit
Static Friction	Ftest	Static test friction
Reverse Stiction Limit	FSr > 0	Static friction upper limit

Units

You specify units in the dialog box only for the external nonfrictional and kinetic friction forces/torques, F_ext and F_K. These two friction signals are used to integrate the physical motion of the joint and have physical significance in the model context. So units are necessary for F_ext and F_K.

The other three signals are compared only to one another in the locking condition F_S^f < F_test < F_S^r. These friction signals are not used to integrate motion and thus do not have units set in the dialog box. But they must have the same implicit units for comparison.

Caution    The threshold velocity vth must be set greater than the Absolute tolerance in the Simulation Parameters dialog box to avoid a meaningless threshold value. Never set Absolute tolerance to auto if stiction actuators are present in a model. A recommended setting is to make vth at least 10 times the Simulation Parameters absolute tolerance. See Choosing Simulation Options for a discussion of setting simulation parameters.

Example

The mech_dpen_sticky model in the Demos library has two revolute joints actuated with stiction. See Joint Stiction Actuator Example: Mixed Static and Kinetic Friction in the Modeling Mechanical Systems chapter.

Stiction Theory

Kinematics

v and a are the velocity and acceleration along/around a joint primitive axis. These quantities are relative between the two bodies at the joint ends and signed to indicate forward or reverse. The joint directionality is set by the base (B)-follower (F) Body sequence of Bodies attached to the joint primitive being actuated.

Continuous Motion

A joint subject to stiction, if unlocked, moves in continuous motion. During this motion, you can apply two forces/torques at the joint primitive:

• a kinetic friction force/torque F_K:
• F_K < 0 retards forward motion
• F_K > 0 retards reverse motion
• an external, non-frictional force/torque F_ext

Discrete Modes: Locked, Wait, Unlocked

Besides its continuous motion state, a joint actuated by stiction has multiple discrete modes. The Joint Stiction Actuator switches a joint primitive between locked and unlocked modes via event detection. In one mode, the joint locks rigidly; in the other, it moves with the kinetic friction and external, nonfrictional forces/torques F_K and F_ext applied.

You specify the switching event by a two-condition threshold, constructed from four user-specified inputs. (See the following Discrete Joint Stiction Modes and Transition Thresholds figure).

• Joint unlocking threshold velocity v_th > 0 via the block dialog box.
• Static friction limits F_S^f< 0 and F_S^r > 0 for forward and reverse motion, and a static test friction F_test, all three specified via Simulink signals. The static test friction F_test and forward/reverse limits F_S^f and F_S^r can be functions of machine state and/or time.

The static test and kinetic frictions F_test and F_K and the threshold velocity v_th can be discontinuous, but should be physically sensible.

Locked Mode

In this mode, v and a of the joint are zero. The static computed force/torque F_S at the joint is internally computed to maintain this mode: F_ext + F_S + F_F - F_B = 0. The forces/torques F_B, F_F are the forces/torques on the base and follower Bodies apart from those forces/torques acting at the joint.

The mode remains locked as long as F_S^f < F_test < F_S^r.

In most realistic friction models, you would set F_test equal to the computed F_S.

Wait Mode

If the static test friction F_test leaves the static friction range [F_S^f, F_S^r], the joint has passed the first threshold condition for unlocking, and the simulation enters Wait Mode.

A search begins for a mode of this joint consistent with the modes of all other joints. During the search, the net force/torque at the joint primitive F = F_ext + F_K is computed, where F_K is the kinetic friction. If a < 0, the search returns to the Locked Mode. Once consistent modes for all joints are found, the simulation restarts, integrating a to obtain v. When exceeds v_th, the second threshold condition, the joint unlocks.

This mode prevents infinite cycling between Locked and Unlocked Modes, although it can noticeably slow down the simulation. The mode search uses an algebraic loop, which displays warnings at the MATLAB command line.

Unlocked Mode

In the Unlocked Mode, the joint primitive moves, actuated by the sum of the external, non-frictional force/torque F_ext and the kinetic friction F_K. The joint returns to the Locked Mode if Simulink detects v crossing zero.

Discrete Joint Stiction Modes and Transition Thresholds

See Also

Joint Actuator, Joint Initial Condition Actuator, Joint Sensor, Prismatic, Revolute

See Creating Joints.

In Simulink, see the Signal Routing Library and the Sources Library, and Zero Crossing Detection.

Joint Sensor

Linear Driver