Multibody Dynamics and 60 Length Vectors


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]

 

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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Realtime Technologies Inc. (RTI) specializes in real time multibody vehicle dynamics, and graphical simulation and modeling.  We offer simulation software applications, consulting, custom engineering, software, and hardware development.  Realtime Technologies’ customer base includes international, government and private entities.  RTI was founded in 1998.