Design optimization and validation of a permanent-magnet array for gravity compensation in long-stroke linear motion

Conventional gravity compensation methods, such as spring- or counterweight-based approaches, often introduce additional friction and/or inertia and require auxiliary force transmission components. Although magnet-based designs mitigate these drawbacks through non-contact magnetic forces, their effectiveness in long-stroke linear motion remains limited. This paper presents a permanent-magnet array for passive gravity compensation in linear motion, enabling payload balancing over a vertical motion range several times the side length of the employed cubic magnet. The design process optimizes the positions and orientations of magnets anchored to the frame, which interact with a magnet attached to the payload to generate the necessary counteracting force. Two illustrative examples demonstrate the proposed design. The first achieves over 92 % gravity reduction for a payload weighing 20 times the magnet's weight, with a travel range six times the magnet's height. The second example enhances balancing capacity by incorporating additional magnets on the payload. One of these designs was experimentally validated. Finally, the study explores optimal magnet distribution patterns, the ideal magnet-to-travel-range ratio, methods to amplify balancing capacity, and the scalability of the proposed concept.