Joint with 3 constraints that define that the origin of
frame_a and the origin of frame_b coincide. By default this joint
defines only the 3 constraints without any potential states.
If parameter enforceStates is set to true
in the "Advanced" menu, three states are introduced.
Depending on parameter useQuaternions these are either
quaternions and the relative angular velocity or 3 angles
and the angle derivatves. In the latter case the orientation
of frame_b is computed by rotating frame_a along the axes defined
in parameter vector "sequence_angleStates" (default = {1,2,3}, i.e.,
the Cardan angle sequence) around the angles used as states.
For example, the default is to rotate the x-axis of frame_a
around angles[1], the new y-axis around angles[2] and the new z-axis
around angles[3], arriving at frame_b. If angles are used
as states there is the slight disadvantage that
a singular configuration is present leading to a divison by zero.
If this joint is used in a chain structure, a Modelica translator
has to select orientation coordinates of a body as states, if the
default setting is used. It is usually better to use relative coordinates
in the spherical joint as states, and therefore in this situation
parameter enforceStates might be set to true.
If this joint is used in a loop structure, the default
setting results in a cut-joint that
breaks the loop in independent kinematic pieces, hold together
by the constraints of this joint. As a result, a Modelica translator
will first try to select 3 generalized coordinates in the joints of
the remaining parts of the loop and their first derivative as states
and if this is not possible, e.g., because there are only spherical
joints in the loop, will select coordinates from a body of the loop
as states.
In the following figure the animation of a spherical
joint is shown. The light blue coordinate system is
frame_a and the dark blue coordinate system is
frame_b of the joint.
(here: angles_start = {45, 45, 45}o).
CONNECTORS
