JointUPS

Description

This component consists of a universal joint at frame_a, a spherical joint at frame_b and a prismatic joint along the line connecting the origin of frame_a and the origin of frame_b, see the default animation in the following figure (the axes vectors are not part of the default animation):

This joint aggregation has no mass and no inertia and introduces neither constraints nor potential state variables. It is especially useful to build up more complicated force elements where the mass and/or inertia of the force element shall be taken into account.

The universal joint is defined in the following way:

• The rotation axis of revolute joint 1 is along parameter vector n1_a which is fixed in frame_a.
• The rotation axis of revolute joint 2 is perpendicular to axis 1 and to the line connecting the universal and the spherical joint.

The definition of axis 2 of the universal joint is performed according to the most often occurring case. In a future release, axis 2 might be explicitly definable via a parameter. However, the treatment is much more complicated and the number of operations is considerably higher, if axis 2 is not orthogonal to axis 1 and to the connecting rod.

Note, there is a singularity when axis 1 and the connecting line are parallel to each other. Therefore, if possible n1_a should be selected in such a way that it is perpendicular to nAxis_ia in the initial configuration (i.e., the distance to the singularity is as large as possible).

An additional frame_ia is present. It is fixed on the line connecting the universal and the spherical joint at the origin of frame_a. The placement of frame_ia on this line is implicitly defined by the universal joint (frame_a and frame_ia coincide when the angles of the two revolute joints of the universal joint are zero) and by parameter vector nAxis_ia, an axis vector directed along the line from the origin of frame_a to the spherical joint, resolved in frame_ia.

An additional frame_ib is present. It is fixed in the line connecting the prismatic and the spherical joint at the origin of frame_b. It is always parallel to frame_ia.

Note, this joint aggregation can be used in cases where in reality a rod with spherical joints at each end are present. Such a system has an additional degree of freedom to rotate the rod along its axis. In practice this rotation is usually of no interest and is mathematically removed by replacing one of the spherical joints by a universal joint.

The easiest way to define the parameters of this joint is by moving the MultiBody system in a reference configuration where all frames of all components are parallel to each other (alternatively, at least frame_a, frame_ia and frame_ib of the JointUSP joint should be parallel to each other when defining an instance of this component).