.PlanarMechanics.Sensors.Distance .PlanarMechanics.Sensors.DistanceThe distance between the origins of
frame_a and of frame_b are determined and
provided at the output signal connector distance. This
distance is always positive. Derivatives of this
signal can be easily obtained by connecting the block Modelica.Blocks.Continuous.Der
to distance (this block performs analytic
differentiation of the input signal using the
der(…) operator).
In the following figure the animation of the sensor is shown.
The light blue coordinate system is frame_a, the dark
blue coordinate system is frame_b, and the yellow
arrow is the animated sensor.
If the distance is smaller then the parameter
s_small (in the "Advanced" menu), it is approximated
such that its derivative is finite for zero distance. Without such
an approximation, the derivative would be infinite and
a division by zero would occur. The approximation is performed
in the following way: If
distance > ssmall, it is
computed as sqrt(r*r) where r
is the position vector from the origin of frame_a to
the origin of frame_b. If the distance becomes smaller
then ssmall, the "sqrt()" function is
approximated by a second order polynomial, such that the
function value and its first derivative are identical for sqrt()
and the polynomial at ssmall. Furthermore,
the polynomial passes through zero. The effect is, that the
distance function is continuous and differentiable everywhere. The
derivative at zero distance is
3/(2*ssmall).
Developed 2010 at the DLR Institute of System
Dynamics and Control