A mathematical modelling approach for the process of part orientation in batch assembly automation

The use of steps as active devices to automatically feed and correctly orient parts has received increased attention in recent years. The work reported so far on determination of the best step sizes for the cases of single-part and multiple-part types has focused either on experimental evaluation or analytical computation. We present mathematical models for describing the process of correctly orienting parts when steps are used as active devices in batch assembly automation. Two different cases – single and multiple-part types – have been considered. Each case is analysed as a single-step active device and as a two-step active device. For the single-part case, the objective function focuses on maximizing the efficiency, evaluated as the probability of correctly orienting the part. For multiple-part types, the focus is on minimizing the cycle time. This is in line with the current trend in just-in-time manufacturing which requires producing a quantity known as the ‘minimum part set’. A series of example problems are solved to illustrate each case. The results obtained further demonstrate how the model can be conveniently used by practitioners in industry to determine the best step sizes to use in part-feeder mechanisms.