.Modelica.Mechanics.MultiBody.Joints.Spherical

Information

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 derivatives. 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 division 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).