The Component Placement Process in Surface Mount Technology Based on Coordinate Calculation Equations

Accurate component placement in Surface Mount Technology (SMT) is essential for assembly yield and long-term product reliability. In practice, placement accuracy is often degraded by fixture offsets, vibration, and feeder/nozzle variability, while many optimization approaches remain predominantly offline and therefore cannot directly compensate for runtime deviations. This paper proposes a generalized coordinate calculation framework based on linear transformation principles, implemented in a PLC-controlled three-axis pick-and-place prototype. Using a small set of reference parameters, the proposed method generates consistent coordinates for passive components, ICs, and feeders and supports fast recalculation when the PCB reference origin changes. Experimental validation was conducted on 62 PCB assemblies, achieving a placement success rate of 91.94% (57/62). For all successful boards, the placement deviation remained within the predefined tolerance window (±0.2 mm), and observed failures were attributable to hardware issues (feeder misfeed and vacuum loss) rather than the coordinate model. The research contribution of this paper is a practical, real-time adaptable alternative for coordinate programming in SMT pick-and-place systems, with future work focusing on vision-assisted referencing, hardware reliability improvements, and benchmarking against offline optimization methods on larger PCB layouts.