ModelicaAdditions.MultiBody.Sensors

Information

This package contains sensor elements

Main Author:

Martin Otter
Deutsches Zentrum für Luft und Raumfahrt e.V. (DLR)
Institut für Robotik und Mechatronik
Postfach 1116
D-82230 Wessling
Germany
email: Martin.Otter@dlr.de

Release Notes:

• April 5, 2000 by Martin Otter:
  Realized.

Copyright (C) 2000, DLR.

The Modelica package is free software; it can be redistributed and/or modified under the terms of the Modelica license, see the license conditions and the accompanying disclaimer in the documentation of package Modelica in file "Modelica/package.mo".

ModelicaAdditions.MultiBody.Sensors.Sensor

Information

A sensor element determines the relative kinematic quantities
between frame_a and frame_b (= variables of superclass 
Interact). It does not exert forces or torques.
The following relative variables can be determined:

  S_rel : Rotation matrix relating frame_a and frame_b, i.e. if
         hb is vector h resoved in frame_b and ha is vector h resolved
         in frame_a, hb = S_rel*ha.
  r_rela: Vector from the origin of frame_a to the origin of frame_b,
         resolved in frame_a.
  v_rela: (Translational) velocity of frame_b with respect to frame_a,
         resolved in frame_a: v_rela = der(r_rela)
  w_rela: Angular velocity of frame_b with respect to frame_a,
         resolved in frame_a: v_rela = vec( der(S_rel)'*S_rel )
  a_rela: (Translational) acceleration of frame_b with respect to
         frame_a, resolved in frame_a: a_rela = der( v_rela )
  z_rela: Angular acceleration of frame_b with respect to frame_a, 
         resolved in frame_a: z_rela = der( w_rela )

If needed, all of the above quantities can also easily be resolved in
frame_b, according to  Xrelb = S_rel*Xrela . However note, that
 v_relb  is NOT  der(r_relb)  (v_relb=S_rel*v_rela; r_relb=S_rel*r_rela).

Modelica definition

model Sensor "General sensor element" 
  extends MultiBody.Interfaces.Interact2;
equation 
  fa = zeros(3);
  fb = zeros(3);
  ta = zeros(3);
  tb = zeros(3);
end Sensor;

ModelicaAdditions.MultiBody.Sensors.LineSensor

Information

The distance as well as the first and second derivative of the 
distance between the cut-frames A and B are determined.

Terminal variables:
  s    : The distance between the origin of frame_a and the
         origin of frame_b in [m].
  sd   : The first derivative of s in [m/s].
  sdd  : The second derivative of s in [m/s^2].
  na(3): Unit vector on the line from the origin of frame_a to
         the origin of frame_b, resolved in frame_a.

Parameters:
  sEps: When  sd  and  sdd  are calculated, a division by zero takes
        place, if the distance becomes zero. Therefore, for this
        calculation the modified distance  smod = max(s, sEps)  is used.

Parameters

Name	Default	Description
sEps	1.E-6	prevent zero-division if rel. distance s=0 [m]

Modelica definition

model LineSensor "Measures kinematic data along a line" 
  extends MultiBody.Interfaces.Interact2;
  parameter Real sEps=1.E-6 
    "prevent zero-division if rel. distance s=0 [m]";
  SIunits.Acceleration sdd;
  Real na[3];
  SIunits.Position smod;
  
  SIunits.Position s;
  SIunits.Velocity sd;
  Modelica.Blocks.Interfaces.OutPort outPort_s(final n=1);
  Modelica.Blocks.Interfaces.OutPort outPort_sd(final n=1);
equation 
  
  fa = zeros(3);
  fb = zeros(3);
  ta = zeros(3);
  tb = zeros(3);
  
  s = outPort_s.signal[1];
  sd = outPort_sd.signal[1];
  
  /*calculate variables along line*/
  s = sqrt(r_rela*r_rela);
  
  smod = max([s, sEps]);
  na = r_rela/smod;
  sd = na*v_rela;
  sdd = na*a_rela + (v_rela*v_rela - sd*sd)/smod;
end LineSensor;