Equilibrium configuration analysis and equilibrium-based trajectory generation method for under-constrained cable-driven parallel robot

Under-constrained cable-driven parallel robots (UCCDPRs) manipulate the end-effector (EE) by employing fewer number of cables than the degree of freedom of the EE, which causes unwanted swaying motions and oscillations. These unwanted vibrations can be suppressed by using the regenerated EE trajectory through the input-shaper. However, in the case of the UCCDPR systems, generating the feasible EE trajectory and deriving the natural frequency for designing the input-shaper are not straightforward since finding the stable equilibrium configuration is challenging. This paper proposes a novel methodology to find the stable equilibrium configuration of the general UCCDPRs in the assigned EE position. With the proposed method, the EE trajectory can be reproduced as a vibration suppression trajectory through an input shaper designed based on the analysis of the natural frequencies, as well as generating feasible EE trajectories based on the equilibrium configuration. Also, even if the orientation trajectory is not given and only the position trajectory is given, the cable length to follow the given position trajectory of the EE can be obtained based on the equilibrium configuration corresponding to the given position trajectory. Computer simulations and hardware experiments were conducted to verify the effectiveness and performance of the proposed method.