Dynamic trajectory planning of a 3-DOF under-constrained cable-driven parallel robot

In this paper, the trajectory planning of a spatial 3-dof under-constrained cable driven parallel robot is studied. We propose a geometrical approach to plan trajectories that extend beyond the static equilibrium workspace (SEW) of the mechanism. First, conditions for cable tensions to be positive along a straight line path are given geometrically. Then, a point-to-point trajectory which satisfies the cable tension constraints is designed in s-s¨ plane, where s denotes the path coordinate. The parameter of the trajectory can be selected by making a trade-off between the safety of cable tensions and the duration of the trajectory. To avoid failing to connect prescribed points, a new workspace is defined such that any target points in the workspace can be reached in sequence. Periodic trajectories including oscillations along a straight line and uniform circular motion in a horizontal plane are designed in a similar way. According to the geometric properties of the cable tension constraints, the range of the periodic trajectory parameters can be readily determined. The proposed approach yields analytical results and can ensure positive and continuous tensions in cables.