Accuracy analysis of a multi closed loop deployable mechanism
The multi closed loop deployable mechanism generates distortion which is caused by the deviation of each rod after being assembled as a result of manufacturing error, which leads to the degradation of the antenna performance or excess of the given envelope. The multi closed loop deployable mechanisms consist of many closed loops and have complicated topology structure and loop constraints coupling. The positioning accuracy analysis of such mechanism is more difficult than the open chain mechanisms or the single loop mechanisms. In order to solve this problem, first, based on the minimum of elastic deformation energy, the distortion analysis model is constructed. Second, the sensitivity of the mechanism distortion to the individual rod deviation is investigated by examining the Lagrange multipliers. By means of this model, the allowable tolerance of multi closed loop deployable mechanism is discussed and calculated. Last but not least, the above method and model are applied to the four closed loop deployable mechanism to solve the problems of its distortion, sensitivity, and tolerance in both fully deployed and folded configurations. It is demonstrated in this paper that the model and method proposed are well accommodated to the accuracy analysis of such mechanisms. The achievement of the research will help reduce the difficulties of the assembling and manufacturing of the multi closed loop deployable mechanisms.