With Prescribed Motion you can control the relative motion in a joint, either by prescribing the displacement or the velocity. This is useful when the degrees of freedom in the joint are not free but are a known function of time. This is common in the field of robotics, for example.
The Translational Prescribed Motion and
Rotational Prescribed Motion versions of this feature are discussed in this section.
where up is the prescribed relative displacement. If reaction force computation has been requested by selecting
Evaluate reaction forces, then a weak constraint is used instead. An extra degree of freedom,
RF, is added for the reaction force. The contribution to the virtual work is
If a unidirectional constraint is used (by selecting Apply reaction only on joint variables), then the form of the virtual work is changed to
where vp is the prescribed relative velocity and
up is the velocity integration variable which then is used in the constraint. In case of a stationary study, the relative displacement in the joint is constrained to zero.
In the case of a Planar Joint, the relative displacements or velocities are prescribed along two axes oriented in a plane perpendicular to the joint axis. The first axis is specified by the user, while the second axis is in the same plane, and orthogonal to the first axis. The relative displacement along prescribed motion axis and along its orthogonal direction can be written as:
where ep is the normalized prescribed motion axis.
The theory for rotational prescribed motion is similar to that of Translational Prescribed Motion. The difference is that the rotation or angular velocity is prescribed instead of displacement or translational velocity.
For the Ball Joint and
Slot Joint features, relative motion is possible in all three directions. You prescribe the motion using a rotation axis and the magnitude of rotation or angular velocity about this axis.
The following constraint is added to Ball Joint and
Slot Joint features to prescribe the relative rotation in a joint:
where ϕp is the magnitude of the prescribed relative rotation, and
ep is the axis of relative rotation.
where Ωp is the prescribed relative angular velocity, and
ϕp is the angular velocity integration variable.
