On The Mechanics And Stability For The Cable-driven Parallel Manipulators

The cable-driven parallel manipulators with redundant actuations, which are simple, light-weight structure, low energy consumption, easy to control, low moment inertia and high speed motion, higher accuracy and so on, play important roles in the family of parallel manipulators, therefore having abroad applications and valuable exploitations. Indeed, the unilateral constraints of the flexible drive cables makes the cable-driven parallel manipulators possess some distinctive features that the parallel ones with rigid handles do not. However, a major challenge in the theory study of the cable-driven parallel manipulators comes from the fact that, the flexible cables lead to the challenge of the stability.Due to the flexible property of the drive cables, the stability of the cable-driven parallel manipulators is the impotant part of the reseach on the cable-driven parallel manipulators, which has a critical influence on the overall performances. Based on the stability of conventional parallel manipulators, combining with the peculiarities of the cable-driven parallel manipulators, the critical parts influencing the stability of the cable-driven parallel manipulators are proposed, and moreover, the calculating method of the stability evaluating the stability of the cable-driven parallel manipulators are proposed in order to break the development bottleneck of the cable-driven parallel manipulators. To the authors’knowledge, there are two primary factors influencing the stability of the cable-driven parallel manipulators, and they are respectively the positions and the constraints. Both the present position and the constraint have an important influence on the stability of the cable-driven parallel manipulators, thus they are taken into consideration when evaluating the stability of the cable-driven parallel manipulators.The reseach on the cable-driven parallel manipulators is based on the key project of Natural Science Foundation of China. And moreover, the analysis of the kinematics, the distributions of the cable tensions in the workspace, the analysis of the stability for the cable-driven parallel manipulators and the stability workspace designed with the stability performance index are studied in this paper, furthermore, the research results can found theoretical and technical basis for the performance improvement and engineering application of cable-driven parallel manipulators. Indeed, the camera robot with high speed is one of the cable-driven parallel manipulators, which has some advantages over the conventional ways of the taking photographs. However, the high speed and flexible cables of the camera robot have an important influence on the stability of it, so the method evaluating the stability of the camera robot is needed to measure the overall performances.This paper deals with four issues, and they are respectively as follows:① the stability of the cable-driven parallel manipulators is discussed combining the positions and the constraints; ② based on the kinematics model of the cable-driven parallel manipulators, the position factors that have an important influence on the stability of the cable-driven parallel manipulators are proposed, and moreover, the distributions of the position factors are considered; ③ based on the optimization model of the cable tensions for the cable-driven parallel manipulators, the force factors that have an important influence on the stability of the cable-driven parallel manipulators are proposed, and moreover, the distributions of the force factors are considered; ④ the determining method of the workspace that possesses a specified stability for the cable-driven parallel manipulators is presented. The main contents can be described as follows:1. The position factors influencing the stability of the cable-driven parallel manipulators are discussed, and moreover, the distributions of the position factors are considered. Considering the catenary the large-span cables having, the influence mechanism of the dimensions and the weight of the cable-driven parallel manipulators for the shape of the catenary the large-span cables possessing is analysed. First of all, the analysis of the kinematics for the cable-driven parallel manipulators with the catenary and massless straight line models are discussed, in which two position factors having the significant effects on the stability for the cable-driven parallel manipulators are proposed respectively. And moreover, the kinematics and the two position factors of the cable-driven parallel manipulators with the two models are compared, therefore providing a systematic basis of reference for the stability of the movement for the cable-driven parallel manipulators.2. The force factors influencing the stability of the cable-driven parallel manipulators are discussed and the minimum cable tensions the current position having are defined. Furthermore, the distributions of the minimum cable tensions and the force factors with the catenary and massless straight line models are depicted based on the optimization algorithm solving the determining of the cable tensions with the proper optimal objective function. Considering the catenary the large-span cable-driven parallel manipulators having, the cable tensions optimization model is set up, and moreover, the iterated algorithm, that employs the length and the tensions of the cables with the straight line model as the initial values of them, is proposed to solve the cable tensions for the large-span cable-driven parallel manipulators. Comparing the cable tensions and two force factors with the two models leads to the necessity of taking the cable sags into consideration for the large-span manipulators.3. The stability performance index is described using the weighted method based on the two position factors and the two force factors. Apart from the above mentioned, the approach considers the flexible of the cables and integrates the key factors influencing the stability of the cable-driven parallel manipulators. Furthermore, the approach using the interval (0,1] to evaluate the stability of the cable-driven parallel manipulators is different from the traditional one and is capable of obtaining the workspace with the specified stability. Particular emphasis was placed on the primary factors influencing the stability of the cable-driven parallel manipulators, and they are studied in detail and worked out, therefore proposing the method with the crucial factors evaluating the stability of the cable-driven parallel manipulators. Moreover, comparing the stability with the two models concludes that it is necessary to regard the cables as the catenary for the large-span manipulators in order to evaluate the stability of the cable-driven parallel manipulators accurately.4. The stability workspaces combining the stability performance index and the definition of the workspaces for completely restrained and redundant restrained cable-driven parallel manipulators are investigated, and moreover, the existence conditions of the stability workspaces of the two types of the robots above are given and proved, in addition to, a solution strategy is proposed to determine the workspaces of the two types of cable-driven parallel manipulators above. Apart from the above mentioned, a new workspace, the Specified Minimum Cable Tension Workspace (SMCTW), is introduced, within which all the minimum tensions exceed a specified value, therefore meeting the specified tension requirement. Furthermore, the distributions of the minimum cable tensions in the workspace are depicted. At last, a robustness workspace with the external wrench compared with the stability workspaces is selected to demonstrate the effectiveness of the stability performance index above for the cable-driven parallel manipulators.