  Parallel robots (PRs) are closed-chain manipulators with diverse applications
due to their accuracy and high payload. However, there are configurations
within the workspace named Type II singularities where the PRs lose control of
the end-effector movements. Type II singularities are a problem for
applications where complete control of the end-effector is essential.
Trajectory planning produces accurate movements of a PR by avoiding Type II
singularities. Generally, singularity avoidance is achieved by optimising a
geometrical path with a velocity profile considering singular configurations as
obstacles. This research presents an algorithm that avoids Type II
singularities by modifying the trajectory of a subset of the actuators. The
subset of actuators represents the limbs responsible for a Type II singularity,
and they are identified by the angle between two Output Twist Screws. The
proposed avoidance algorithm does not require optimisation procedures, which
reduces the computational cost for offline trajectory planning and makes it
suitable for online trajectory planning. The avoidance algorithm is implemented
in offline trajectory planning for a pick and place planar PR and a spatial
knee rehabilitation PR
