.ModelicaAdditions.MultiBody.CutJoints.Prismatic

Information

A prismatic joint is a joint with 1 translational degree of freedom.
An instance of this class is used as cut joint to break a kinematic
loop of a multibody system. Note, that a Prismatic joint cannot
be used in a planar (2D) loop, since here e.g. the constraint force
orthogonal to the plane of the loop is not unique if only rigid
bodies are within the loop. For a unique solution, additional
assumptions have to be made, e.g., that this force is zero.
These additional assumptions are stated in class  PrismaticCut2D .
Therefore use this class, if a prismatic joint has to be used as
cut joint in a planar loop.

  Parameters:
    n: Axis of translation with respect to the inertial frame in the
       home position.  n  must not necessarily be a unit vector.

Based on  n , two vectors  npy  and  npz  are constructed which
are perpendicular to  n  (e.g., if n=[1 0 0] then npy=[0 1 0]
and npz=[0 0 1]). The 5 constraint equations on position level state,
that the distance between the origins of frame_a and frame_b, projected
onto npx and npy, is zero and that the three essential elements of
the relative direction cosine matrix relating frame_a and frame_b
are zero as well.
The following constraint forces (= Lagrange multipliers) are used:

  fc(2): Constraint forces in the direction of npy, npz in [N]
         (fa = [npy, npz]*fc).
  tc(3): Constraint torques in the direction of ta in [Nm].