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Rotating motion

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 \(\mathbf{R}_{\theta}^{a}\) denotes the rotation matrix of a general rotation about the axis \(a\) with an angle of \(\theta\), then the displacement \(\vec{u}\) of a point \(\vec{X}\) is calculated as:

\[\vec{u} = \mathbf{R}_{\theta}^{a} \cdot (\vec{X}- \vec{P}_0) + \vec{P} -\vec{X},\]

where \(\vec{P}\) denotes the axis base point and \(\vec{P}_0\) it’s position at time t=0.0.

Base Point

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.

Rotation Axis

The rotation axis is defined by its three components in the global coordinate system.

Important

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.

Rotation Angle

The rotation angle is defined in a mathematical positive sense around the rotation axis.

Important

If a continous, transient rotation is required the rotation angle has to be given either as a formula or table value.

Example

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 \(2*pi*t\)
Unit Cube Rotation

Rotation of the unit cube around the z-Axis with additional translation of the base point