Linear Spring

A linear spring in 3 degrees of freedom.

Collaboration diagram for Linear Spring:

This is a SimObject representing a linear spring in three degrees of freedom. The tension in the spring is found from the following relations:

\begin{eqnarray*} \vec{f^A} &=& T \frac{\vec{l}}{L} \\ \vec{f^B} &=& -\vec{f^A} \\ T &=& k(L_0-L) \\ \vec{l} &=& p^B-p^A \\ L &=& ||\vec{l}|| \end{eqnarray*}

,

where

• \(T\) is the spring tension
• \(k\) is the spring stiffness
• \(L_0\) is the unstretched length of the spring
• \(L\) is the current length of the spring
• \(\vec{f^A}\) is the force from the spring on the end point A
• \(\vec{f^B}\) is the force from the spring on the end point B
• \(\vec{p^A}\) is the position of the end point A
• \(\vec{p^B}\) is the position of the end point B
• \(\vec{l}\) is the vector from the end A to the end B.

This spring also takes compression forces.

Author

Karl-Johan Reite

Date

01.01.2006 KJR: Initial version.

Example configuration excerpt

<Lib
  LibName       = "fhsim_base"
  SimObject     = "Cable/LinearSpring"
  Name          = "M"
  Stiffness     = "10"
  RelaxedLength = "10"
/>
...
<Connection
  M.PosA="0,0,0"
  M.PosB="0,0,5"
/>

Input Ports

Name	Width	Description
PosA	3	The position of end A.
PosB	3	The position of end B.

Output Ports

Name	Width	Description
ForceA	3	The spring force from end A.
ForceB	3	The spring force from end B.
PosA	3	The position of end A.
PosB	3	The position of end B.

Configuration parameters

Name	Width	Description
Stiffness	1	The stiffness of the spring.
RelaxedLength	1	The length of the spring when its tension is zero.

Initial conditions

This SimObject contains no initial conditions.

Full example file

<Contents>
  <OBJECTS>
 
  <Lib
    LibName="base"
    SimObject="Cable/LinearSpring"
    Name="M"
    Stiffness="10"
    RelaxedLength="10"
  />
 
  </OBJECTS>
 
  <INTERCONNECTIONS>
    <Connection
       M.PosA="0,0,0"
       M.PosB="0,0,5"
    />
  </INTERCONNECTIONS>
 
  <INITIALIZATION>
    <InitialCondition
    />
  </INITIALIZATION>
 
  <INTEGRATION>
    <Engine
    IntegratorMethod="2"
    NumCores="1"
    TOutput="0, 1, 30"
    LogStates ="1"
    stepsize ="0"
    HMax="0.002"
    HMin="0.00000001"
    AbsTol="1e-3" RelTol="1e-3"
    UseRSSNormInsteadOfInfNorm="0"
    FileOutput="objects:all"
    />
  </INTEGRATION>
</Contents>

This SimObject is referred to as Cable/LinearSpring