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paor815

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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