The rotating motion constraint is used to define a rigid body rotation of the assigned entities. The user can define the rotation axis, the base point and the rotation angle. Each component can be defined as a formula or table value.
If Raθ denotes the rotation matrix of a general rotation about the axis with an angle of θ, then the displacement u⃗ of a point X⃗ is calculated as:
u⃗ =Raθ⋅(X⃗ −P⃗ 0)+P⃗ −X⃗
where P⃗ denotes the axis base point and P⃗ 0 it’s position at time t=0.0.
This point is the base point for the rotation axis. A possible movement of the base point with respect to the initial position at time t=0.0 during the rotation process is taken into account.
The rotation axis is defined by its three components in the global coordinate system.
If a component of the rotation axis is given as formula or table value the user has to make sure that the length of the axis vector is always positive.
The rotation angle is defined in a mathematical positive sense around the rotation axis.
If a continuous, transient rotation is required the rotation angle has to be given either as a formula or table value.
In the example below a unit cube was rotated with 60 rpm around the z-Axis with a base point moving in positive z-direction with 1m/s. The bottom face was assigned and the corresponding settings were:
- Base Point (0,0,t)
- Rotation axis (0,0,1)
- Rotation angle 2∗pi∗t
Rotation of the unit cube around the z-Axis with additional translation of the base point