Highlights• A cable-suspended robot is presented with a spatial purely translational motion.• Several special architectures are identified with distinctive and useful features.• The singularity-free/reachable/interference-free workspaces are analytically found.• The theoretical findings are validated by experimental tests.• The robot can perform dynamic trajectories outside the static equilibrium workspace.

Cable-suspended robots may move beyond their static workspace by keeping all cables under tension, thanks to end-effector inertia forces. This may be used to extend the robot capabilities, by choosing suitable dynamical trajectories. In this paper, we consider three-dimensional (3D) elliptical trajectories of a point-mass end effector suspended by three cables from a base of generic geometry. Elliptical trajectories are the most general type of spatial sinusoidal motions. We find a range of admissible frequencies for which said trajectories are feasible; we also show that there is a special frequency, which allows the robot to have arbitrarily large oscillations. The feasibility of these trajectories is verified via algebraic conditions that can be quickly verified, thus being compatible with real-time applications. By generalizing previous studies, we also study the possibility to change the frequency of oscillation: this allows the velocity at which a given ellipse is tracked to be varied, thus providing more latitude in the trajectory definition. We finally study transition trajectories to move the robot from an initial state of rest (within the static workspace) to the elliptical trajectory (and vice versa) or to connect two identical ellipses having different centers.

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In this paper, we analyze a spatial 3-DoF cabledriven robot with a finite-size end-effector. The robot has 6 cables that define 3 parallelograms, each composed by two cables: thus, the robot cannot rotate, but only perform translational motions. Also, since the two cables in a parallelogram are always kept at the same length, they can be actuated by the same motor, thereby meaning that the 3-DoF cablesuspended robot requires only 3 actuators. The kinematic and dynamic behaviour of such robots was studied in previous works. The property of purely-translational motion depends on a precise control of the extension of the cables. Therefore, in this paper we study how the platform pose changes as some errors of known maximum magnitude are introduced in the cable lengths. Finally, the results from both numerical simulations and tests are presented. The orientation of the platform is shown to be robust to cable extension errors.