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Warning about redundant constraint equations.
This article applies to ADAMS/Chassis, ADAMS/View, ADAMS/Solver, ADAMS/Car, ADAMS/Driveline, ADAMS/Pre, ADAMS/Motorsports, ADAMS/Aircraft, ADAMS/Rail, ADAMS/Engine (no specific release) on all platforms.
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Question
What does it mean when I get a warning that certain constraints are redundant
or unnecessarily remove certain DOF?
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Answer
Constraints in ADAMS remove degrees of freedom (DOF) from the system by adding
algebraic constraint equations to the governing system of DAEs (Differential
and Algebraic equations). The different constraints in the ADAMS constraints
library remove different types and number of DOF. Joints can remove anywhere
from 1 to 6 DOF, depending on their type. For instance:
Fixed joints remove 6 DOF: 3 translational & 3 rotational;
Revolute joints remove 5 DOF: 3 translational & 2 rotational;
Spherical joint remove 3 DOF: 3 translational & 0 rotational;
Translational joints remove 5 DOF: 2 translational & 3 rotational;
InLine joints remove 2 DOF: 2 translational & 0 rotational;
etc., etc.
(For more information on the type and number of DOF removed, or conversely
allowed, by each joint in ADAMS, see the section on Constraints in the Using
ADAMS/View manual.)
Mathematically, however, ADAMS represents similar constrained DOF with similar
algebraic equations. Six algebraic equations used by ADAMS to represent DOF
constrained by joints are as follows:
Xi-Xj = 0 (eq. 1)
Yi-Yj = 0 (eq. 2)
Zi-Zj = 0 (eq. 3)
Zi.Xj = 0 (eq. 4)
Zi.Yj = 0 (eq. 5)
Xi.Yj = 0 (eq. 6)
Eq. 1-3 constrain translational DOF while eq. 4-6 constrain rotational DOF.
The English translation of these mathematical equations is as follows where,
of the 2 parts connected by the joint, the I marker is on the first part and
the J marker is on the second part:
1) Xi-Xj = 0 means that the global X coordinate of the I marker must always
remain identical to the X coordinate of the J marker.
2) Yi-Yj = 0 means that the global Y coordinate of the I marker must always
remain identical to the Y coordinate of the J marker.
3) Zi-Zj = 0 means that the global Z coordinate of the I marker must always
remain identical to the Z coordinate of the J marker.
4) Zi.Xj = 0 means that the Z axis of the I marker must always remain
perpendicular to the X axis of the J marker (which means no rotation about the
common Y axis).
5) Zi.Yj = 0 means that the Z axis of the I marker must always remain
perpendicular to the Y axis of the J marker (which means no rotation about the
common X axis).
6) Xi.Yj = 0 means that the X axis of the I marker must always remain
perpendicular to the Y axis of the J marker (which means no rotation about the
common Z axis).
(The . notation in equations 4-6 signifies a dot product operation. Recall
that when the dot product of two vectors = 0, the vectors are perpendicular.)
Each Fixed joint in your model uses 6 equations (eq. 1-6) while a Spherical
uses 3 equations (eq. 1-3), a Revolute uses 5 equations (eq. 1-5), a
Translational uses a different 5 equations (eq. 1,2,4-6), an InLine uses 2
equations (eq. 1-2), etc.
Notice how each of these five joints uses equations #1 & 2? Any such
duplication of constrained DOF can lead to overconstraining your system, or
introduce what are known as redundant constraint equations.
ADAMS outputs warning messages to try to help you understand which equations
are redundant and therefore which DOF are unnecessarily removed.
____________________________
Example 1) If, in your model, Joint_7 is a Revolute joint and ADAMS gives you
the 2 warning messages that:
WARNING:
Joint_7 unnecessarily removes Rotation Between Zi and Xj
Joint_7 unnecessarily removes Rotation Between Zi and Yj
then you have 2 redundant constraint equations. To get rid of them, you could
change Joint_7 from a Revolute to a Spherical joint. These messages indicate
that the rotational constraint eqs. 4 & 5 introduced by the Revolute joint are
not needed. Therefore you could safely replace it with a Spherical joint that
does not use these equations).
____________________________
Example 2) If, in your model, Joint_29 is a Translational joint and ADAMS
gives you the 3 warning messages that:
WARNING:
Joint_29 unnecessarily removes Rotation Between Zi and Xj
Joint_29 unnecessarily removes Rotation Between Zi and Yj
Joint_29 unnecessarily removes Rotation Between Xi and Yj
then you could change Joint_29 from a Translational to an InLine joint.
____________________________
Example 3) If you build a fourbar mechanism with 4 revolute joints you will
receive something similar to the following warning messages:
Joint_1 unnecessarily removes Rotation Between Zi and Xj
Joint_1 unnecessarily removes Rotation Between Zi and Yj
Joint_3 unnecessarily removes Rotation Between Zi and Xj
These messages indicate that Revolute Joint_1 could safely be changed to a
Spherical joint and Revolute Joint_4 could be changed to a Universal or Hooke
joint. Doing so would get rid of your redundant constraint warnings and could
possibly improve the performance of your solution. Alternatively, by changing
just one of the Revolute joints to an InLine joint you would also remove your
redundancies. There is almost always more than one way to remove redundant
constraints. The best way to proceed is to select your joint types to make
them match the way your physical system can move. .
Remember that ADAMS will not be able to calculate joint reaction forces in any
directions associated with redundant constraint equations since it
automatically removes these equations when it performs a simulation. So you
might also want to select your joint types based on where you want to measure
joint reaction forces. |
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发表于 2004-7-28 22:10:17
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