This paper presents S-RGM \(^{*}\) , a sampling-based approach utilizing a geometric model specifically adapted for path planning in unmanned aerial manipulators designed for pick-and-place applications. As the demand for autonomous aerial systems grows in sectors such as inspection, delivery, and maintenance, efficient trajectory planning for manipulators mounted on unmanned aerial vehicles (UAVs) becomes crucial. The proposed approach leverages a geometric model to enhance the accuracy and reliability of path planning, addressing key challenges related to obstacle avoidance, accessibility, and precise object manipulation. Through simulations, S-RGM \(^{*}\) demonstrates superior performance compared to traditional methods in navigating complex environments and achieving precise manipulator positioning for pick-and-place tasks. This work represents a significant advancement in enhancing the autonomy and operational scope of unmanned aerial manipulators, paving the way for more versatile and efficient aerial robotic systems.