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Multibody systems simulation software 97
It is also possible to define initial conditions associated with a joint such as
a revolute, translational or cylindrical. These are defined to be translational
or rotational according to the characteristics of the associated joint. An
example is shown below for a cylindrical joint that is defined to have an initial
translational velocity of zero but a starting displacement of 100 mm. At
this stage it is important to note that the ordering and direction of the z-axes
of the markers are important. For the example below this would in physical
terms define a 100 mm translation of the I marker 0703 relative to the J
marker 0403 in the direction defined by the positive z-axis of both markers:
JOINT/03,I0703,J0403,CYL,ICTRAN0,100
The initial condition is enforced at the start of analysis but released once
the simulation commences, in other words after time equals zero. For translational,
revolute and cylindrical joints it is also possible to constrain the
movement of the joint during the simulation using a motion statement of
the type shown below:
MOTION/04,JOINT04,ROT,FUNCTION360D*TIME
For the joint referenced it is necessary to define a functional equation, normally
only dependent on time, that controls the movement of the I marker
relative to the J marker at the associated joint. In the example shown here
the function is defining a rotation of 360 degrees, or one revolution, for
every second of time taken and as positive when rotating about the z-axes
of the markers. It will be seen later that the functional equation can be
extended to encompass more complex formulations using a library of offthe-shelf
mathematical functions and expressions of the type associated
with engineering or scientific programming software. Newcomers to multibody
systems analysis often find the concept of a defined motion being a
constraint difficult to grasp as the modelling element involves movement.
The motion statement here constrains the associated degree of freedom at
the joint. The movement defined by the function is enforced and cannot be
altered by, for example, changes to the mass properties of the bodies or the
introduction of external forces. It should also be noted that where a motion
is applied to a joint it would be inconsistent to specify initial conditions for
the degree of freedom associated with the motion at the joint.
Another constraint element that will be used in this text is referred to as a
coupler and is used to constrain, or couple, the movement of two or three
joints by applying scale factors. The main application of a coupler in this text
is to represent the mechanical behaviour of a steering box and so define the
ratio between the rotation of the steering column and the rack. A more
detailed description of the modelling issues for this is given later in Chapter 6.
An example of a coupler statement is given below:
COUPLER/0305,JOINTS03,04,TYPET:R,SCALES22D,-5
Care is needed with the syntax and ordering of this statement as can be seen
when we develop the algebraic equation that it represents. The coupler defined
here relates the translational motion at joint 03 with the rotational motion
at joint 04. The scale factors provided define the relationship as
22D q4 5 q3 0 or 22D q6 5 q3 (3.43)
In this case q3 is the translational motion at joint 03 and q4 is the rotational
motion at joint 04. So for every 22 degrees of rotation at joint 04 there is a