Objective To enhance the motion smoothness and reliability of cam-linkage combined mechanisms under high-speed operating conditions and to investigate a cam profile design method based on Fourier series.Methods This study derives the motion law expression of a cam-linkage combined mechanism through the Fourier series expansion theory and analyzes the influence of initial parameters on motion characteristics. Taking the lifting mechanism of packaging machinery as an example, the study employs MATLAB for cam profile curve design based on Fourier series and validates the basic dimensions and motion and dynamic performance of the cam.Results When the Fourier series expansion order k is 15, motion accuracy and acceleration fluctuations can be effectively balanced. The designed cam profile curve is continuous and impact-free with a maximum pressure angle of 41.39° and a minimum curvature radius of 5.42 mm. Both the velocity and acceleration curves meet the requirements for high-speed operation.Conclusion The method simplifies the design process by applying Fourier series expansion with a single motion law, eliminating the complexity of segmented calculations. It significantly improves the stability and dynamic performance of cam-linkage mechanisms under high-speed conditions.