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

Rehabilitation tasks demand robust and accurate trajectory-tracking performance, mainly achieved with parallel robots. In this field, limiting the value of the force exerted on the patient is crucial, especially when an injured limb is involved. In human-robot interaction studies, the admittance controller modifies the location of the robot according to the user efforts driving the end-effector to an arbitrary location within the workspace. However, a parallel robot has singularities within the workspace, making implementing a conventional admittance controller unsafe. Thus, this study proposes an admittance controller that overcomes the limitations of singular configurations by using a real-time singularity avoidance algorithm. The singularity avoidance algorithm modifies the original trajectory based on the actual location of the parallel robot. The complemented admittance controller is applied to a 4 degrees of freedom parallel robot for knee rehabilitation. In this case, the actual location is measured by a 3D tracking system because the location calculated by the forward kinematics is inaccurate in the vicinity of a singularity. The experimental results verify the effectiveness of the proposed admittance controller for safe knee rehabilitation exercises

Moreover, PRs have other advantages over their serial counterparts, such as lower weight, higher working speed with high precision, and lower power consumption [1,2]. These advantages, mainly due to the closed kinematic chain architecture, are key aspects that have increased the interest in studying their use in the academic, industrial, and robotics service fields over the last three decades. However, the PR architecture reduces not only the size of the robot workspace but also its kinematic performance, owing to the possible presence of singularities within the workspace. Initially, Gosselin and Angeles [3] studied the singularities of a PR using Jacobian matrices obtained from constraint equations, and classified them into i) inverse kinematic or Type I singularity, where the robot loses at least one degree of freedom (DOF), and ii) Forward Kinematic or Type II singularity, where the PR gains at least one DOF. In particular, Type II singularities could be critical because the mobile platform at the singularity is unable to bear the external forces despite having all the actuators locked (losing control of the PR motion).

A novel kinematically redundant (6+3)-DoF parallel robot is presented in this paper. Three identical 3-DoF RU/2-RUS legs are attached to a configurable platform through spherical joints. With the selected leg mechanism, the motors are mounted at the base, reducing the reflected inertia. The robot is intended to be actuated with direct-drive motors in order to perform intuitive physical human-robot interaction. The design of the leg mechanism maximizes the workspace in which the end-effector of the leg can have a 2g acceleration in all directions. All singularities of the leg mechanism are identified under a simplifying assumption. A CAD model of the (6+3)-DoF robot is presented in order to illustrate the preliminary design of the robot.