Mathematic formulation for the generation of combined paths for mounting parts in assembly

Today, the assembly process is the least automated phase of production for mechanical products. The percentage of the automated assembly line operations of automobiles fluctuates between 10 and 20% according to manufacturers. The use of industrial robots in the assembly lines played a decisive role in the development of their activity despite the high cost. Indeed, this strategy is a key element that increases productivity. The use of robots in assembly tasks requires the trajectory determination of parts to be assembled from the design phase of the product. This problem is difficult if the part may interfere with other elements and requires combined trajectories to avoid the interference. Therefore, the simulation of part assembling trajectories from the design phase is an interesting and topical research issue. The main objective of this paper is to develop a new approach to generate multidirectional combined trajectories of parts. A mathematical formulation of the proposed approach is firstly proposed, being based on both the position matrix concept and the bounding box method. A didactic example is used to illustrate the different stages of the proposed approach. To highlight the computer implementation of the proposed method, an industrial case study is presented. This example was chosen to illustrate the effectiveness of the proposed approach such as the gain of assembly time, the reduction of costs by robotization of the work, and the programming assistance of these robots.