Cable wrapping phenomenon in cable-driven parallel manipulator

Abstract

Mechanical interference between the rigid link of a cable driven parallel manipulator (CDPM) and its actuating cables as it moves about its workspace is a phenomenon that is not commonly studied. Allowing such interference to happen would cause the actuating cables to wrap around the rigid links of the manipulator. This operational space is generally ignored and excluded from the consideration due to the complexity of the analysis required to incorporate it into the systems modelling and control architecture. However, it can be observed that the accommodation of such wrapping phenomenon allows the manipulator to remain operational and it significantly extends the usable workspace of the manipulator. Since a cable can only be pulled but not pushed, an actuating cable of a CDPM must remain taut during its operation. Hence, the cable configuration is the shortest possible path between its two attachment points on the rigid link and on the fixed frame, respectively. In the conventional model of a CDPM, this path is generally assumed to be a straight line. This assumption holds when there is no mechanical interference between the rigid link and the actuating cable of a CDPM. However, when such an interference occurs, the cable would wrap around the rigid link. It is also possible that the wrapping goes further than 360 degrees such that the cable is no longer a straight line but a geodesic with revolutions. The direction of the cable force exerted on the rigid link therefore is no longer the vector between the two ends of the cables but is the same as the tangent at the point where the cable leaves the surface of the rigid link. In order to find this tangent, it is necessary to know the contact point where the cable leaves the surface of the rigid link. To this end, the cable configuration will need to be solved such that the contact point can be determined. An algorithm is developed to obtain the parametric expressions of the cable configuration by using the existing result of geodesic with the assurance of continuity along the cable. With the consideration of the features of the wrapping phenomenon, some other parameters are introduced in the expression of the cable configuration such as the wrapping direction and the number of revolutions. Once the cable configuration with the wrapping segment is found, the cable wrapping phenomenon can be included in the modelling of a CDPM. A CDPM formed by a circular disk and a CDPM formed by a cylindrical rigid link articulated with a ball-and-socket joint will be used as two examples across this thesis. Both of them are actuated by four cables with 3 degrees of freedom. The inverse kinematics of two mechanisms are solved based on the new model. That is, given the desired trajectory of a CDPM, the corresponding changes of lengths and configurations of the cables can be obtained. As a demonstration, a brief investigation on the forward kinematics of a CDPM that allows cable wrapping is performed. Given the measurement of the cable lengths and the properties of the CDPM, the pose of the end-effector in the task space of a CDPM is solved by numerically. The proposed model is compared with the conventional models which either stops at the interference or ignores the interference. The comparison is initially performed by solving the inverse dynamics of the CDPMs with respect to the three models. It is found that the model accuracy has been improved to a great extent with the incorporation of the cable wrapping phenomenon. At the same time, the wrapping cables are able to produce additional torque on the rigid link. Thus a more compact design in the mechanism of a CDPM can be achieved. In addition, wrench closure workspace analysis is also performed on different models. It is shown that the proposed model which takes cable wrapping into consideration provides the largest workspace compared to the other those that do not consider. Finally, a complete framework on modelling the cable-driven parallel manipulator which allows cable wrapping has been built. The study in this thesis not only improves the accuracy in the modelling of a CDPM but also expands the room for the design of a CDPM with the application of the cable wrapping phenomenon.