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Joint Initial Velocity: Cylindrical

Joint Initial Velocity: Cylindrical

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Joint Initial Velocity: Cylindrical

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Model Element

Description

The JointInitialvel_Cyl element defines the initial velocity for a cylindrical joint element.  It allows you to specify the initial velocities for both the translational and the rotational degree of freedom.

Format

<JointInitialvel_Cyl

      joint_id  = "integer"

      trans_iv  = "real"

      rot_iv    = "real">

</JointInitialvel_Cyl>

Attributes

joint_id

The ID of the cylindrical joint whose initial velocity is being specified.

trans_iv

The initial translation velocity of the cylindrical joint.  The value specified is the translational velocity of the I marker of the joint relative to the J marker of the joint.  The unit is model length units per model time unit.

A positive value implies a velocity along the z-axis of theJ Reference_Marker. A negative value implies a velocity along the negative z-axis.

rot_iv

The initial rotational velocity of the cylindrical joint.  The value specified is the rotational velocity of the I marker of the joint relative to the J marker of the joint.  The unit is radians per model time unit.

A positive value implies the angular velocity of Reference_Marker I as measured by Reference_Marker J in its coordinate system is in the counterclockwise direction.

Comments
1.Besides joints, there are two other ways to specify initial velocity in MotionSolve models:  One is using the Motion_Joint or Motion_Marker element, and the other is using the Body_Flexible, Body_Rigid, or Body_Point element.
2.If there is a conflict among initial conditions specified using these various elements, the following precedence rule is applied: Motion elements override the joint elements which in turn override the body elements.
3.The number of initial conditions should not exceed the total number of degrees of freedom in the model.
•Thus, a system with one degree of freedom should have only one velocity initial condition.  The constraints apply consistent velocities to the rest of the states in the model.
•A system with zero degrees of freedom should have no velocity initial conditions.

Example

Consider James Watt’s flyball governor as shown schematically in the image below.  The yellow circles depict hinges, the two red spheres depict the flyballs, and the blue body depicts the sleeve. JIVC_ExFig1

James Watt's flyball governor

In his book, Out of Control, Kevin Kelly describes the flyball governor:

"Two leaden balls, each at the end of a stiff pendulum, swing from a pole.  As the pole rotates, the balls spin out levitating higher the faster the system spins.  Linkages scissored from the twirling pendulums slide up a sleeve on the pole, levering a valve which controls the speed of rotation by adjusting the steam."

The connection between the sleeve and the governor shaft may be modeled using a cylindrical joint element.

Assume that at the start of the simulation:

•The governor arms (and hence the sleeve) are spinning with angular velocity 3.147 radians per second.
•The sleeve is sliding upward on the shaft with velocity 4.5 mm/sec.

The initial velocity of the entire system may be specified simply by specifying the initial velocity of the cylindrical joint between the sleeve and the shaft, with id 1, as follows:

<JointInitialvel_Cyl

joint_id  = "1"

trans_iv  = "4.5"

rot_iv    = "3.147">

 </JointInitialvel_Cyl>

See Also:

Body_Rigid

JointInitialVel_Rev

JointInitialVel_Trans

Motion_Joint

Motion_Marker

Model Statements

Command Statements

Functions

Notation and Syntax

The following MDL Model statements:

*SetJointIC() - asymmetric joint pair

*SetJointIC() - single joint

*SetJointIC() - symmetric joint pair