Empirical Quasi-Static and Inverse Kinematics of Cable-Driven Parallel Manipulators Including Presence of Sagging

Cable-driven parallel manipulators (CDPMs) have been of great interest to researchers in recent years because they have many advantages compared to the traditional parallel robot. However, in many studies they lack the cable’s elasticity that leads to flexible cables just being considered as extendable rigid links. Furthermore, an external force acts on the extremities of cable and the self-weight is relevant to the length of it. Experimentally, a small change in length produces a huge change in tension act on the entire cable. By this property, the adjusting length of cable is often added to the traditional inverse kinematic solution in order to reduce the tension force exerted on the cable. This means that the load on the actuator is also reduced. Because of the relationship between tension that acts on the cable and its length, the kinematic problem itself does not make sense without concerning the static or dynamic problems. There is often interest in planning forces for actuators and the length of cables based on a given quasi-static trajectory of the moving platform. The mentioned problem is combined with the quasi-static problem with the inverse kinematic problem of CDPM. In this study, we introduce a novel procedure to produce the quasi-static model and inverse kinematic model for CDPM with the presence of sagging by using both an analytic approach and empirical approach. The produced model is time-efficient and is generalized for spatial CDPM. To illustrate the performance of the proposed model, the numerical and experimental approaches are employed to determine particular solutions in the feasible solutions set produced by our model in order to control the two redundant actuators’ CDPM tracking on a certain desired trajectory. Its results are clearly described in the experimental section.