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LinkNumber
| A multibody dynamics system contains
degrees of freedom. Each degree of freedom is assigned a
link number starting at 1. The
LinkNumber connector on each
multibody dynamics component contains in its first
element the number of upstream
links in the chain between the base body and the current
component. |
|
The rest of the
elements of the LinkNumber connector contain the actual
link numbers of the upstream
links. The LinkNumber normally has a dimension of 20,
which supports up to 19 links in any particular chain. |
60 Length Vectors
| The multibody components in SimCreator
calculate the internal forces and
accelerations acting on the system due to
gravity, external forces, and velocity
with the joint accelerations set to zero and
store this in the first three elements
of the 60 length vectors in the order X, Y, and
Z.
For each degree of freedom
in the chain between the base body |
|
and the current body they calculate the
internal
forces and acceleration acting on the system due to a
unit (1.0) acceleration of
that degree of freedom. The corresponding element in the
LinkNumber connector defines
the appropriate link in the system. The results of these
calculations are stored in the
60 Length Vectors as follows. |
Linear
[0] - X Acceleration or Internal Force
due to gravity, external forces and velocity
[1] - Y Acceleration or Internal Force due to gravity,
external forces and velocity
[2] - Z Acceleration or Internal Force due to gravity,
external forces and velocity
[3] - X Acceleration or Internal Force due to a unit
acceleration in link number LinkNumber[1]
[4] - Y Acceleration or Internal Force due to a unit
acceleration in link number LinkNumber[1]
[5] - Z Acceleration or Internal Force due to a unit
acceleration in link number LinkNumber[1]
[…]
[57] - X Acceleration or Internal Force due to a unit
acceleration in link number LinkNumber[19]
[58] - Y Acceleration or Internal Force due to a unit
acceleration in link number LinkNumber[19]
[59] - Z Acceleration or Internal Force due to a unit
acceleration in link number LinkNumber[19]
Angular
[0] - Roll Acceleration or Internal
Force due to gravity, external forces and velocity
[1] - Pitch Acceleration or Internal Force due to
gravity, external forces and velocity
[2] - Yaw Acceleration or Internal Force due to gravity,
external forces and velocity
[3] - Roll Acceleration or Internal Force due to a unit
acceleration in link number LinkNumber[1]
[4] - Pitch Acceleration or Internal Force due to a unit
acceleration in link number LinkNumber[1]
[5] - Yaw Acceleration or Internal Force due to a unit
acceleration in link number LinkNumber[1]
[…]
[57] - Roll Acceleration or Internal Force due to a unit
acceleration in link number LinkNumber[19]
[58] - Pitch Acceleration or Internal Force due to a
unit acceleration in link number LinkNumber[19]
[59] - Yaw Acceleration or Internal Force due to a unit
acceleration in link number LinkNumber[19]
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In this way a multibody model can have
up to 19 links in any particular chain. Since a mass
matrix is symmetric the accelerations and
internal forces are only calculated up to the
current link number of the joint.
It is important to note that the
acceleration and forces stored in |
|
the 60 Length
Vectors
are not the actual accelerations and internal
forces but actually the perturbation in force
due to a unit perturbation in acceleration.
Therefore the accelerations should not be
used directly for anything other than multibody
dynamics calculations. In addition
external forces must be a function of position
and velocity and not a function of
acceleration. |
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