Trajectory planning for the static to dynamic transition of point-mass cable-suspended parallel mechanisms

• Published in: Mechanism and machine theory Vol. 113; pp. 158 - 178
• Main Authors: Dion-Gauvin, Pascal, Gosselin, Clément
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-07-2017
• Subjects: Cable-suspended parallel mechanisms; Dynamic trajectory planning; Point-to-point motion; Dynamic trajectory planning; Cable-suspended parallel mechanisms; Point-to-point motion
• ISSN: 0094-114X; 1873-3999
• DOI: 10.1016/j.mechmachtheory.2017.03.003

•Formulation of the ideal kinematic states of a 2- and 3-dof cable-suspended mechanism.•A proof that any point below the cable spools can be reached.•A proof of the time optimality of the horizontal trajectory for 2-dof mechanisms.•Conditions for time optimality of horizontal trajectories for 3-dof mechanisms.•A lower bound for the minimum feasible number of horizontal oscillations exists.
This paper presents a trajectory formulation that connects an initial point at rest to a final point to be reached with zero velocity but nonzero acceleration for planar two-dof and spatial three-dof cable-suspended mechanisms with point-mass end-effectors. The trajectory is designed to reach the first of a sequence of target points that can be located outside of the static workspace of the mechanisms. The proposed motion consists of oscillations of progressively increasing amplitude centred at the initial point, whereby an upper bound for the minimum feasible number of oscillations is determined by ensuring positive tension in all cables throughout the trajectory. It is shown that this number of oscillations can be found for any trajectory that is entirely located below the spools. The paper provides novel insight into the dynamics of the three-dof mechanism, and highlights the similarities and differences between the planar and spatial motions. Simulation results of example trajectories are included in order to illustrate the approach, along with a video demonstration of an experimental validation performed using a three-dof prototype.