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Six-link transmission mechanism optimization design was proposed with the multi-objective demand of path, velocity and acceleration. A brief uniform mathematical description of the slide motion path was established using Fourier series theory. Then the formulas of the slide velocity and acceleration were obtained. According to the constraint conditions of mechanism engineering design, taking the minimum deviation error of slide kinematics data and the minimum mechanism height as the optimization object, the optimization model of transmission mechanism design was established. It was performed by the composite optimization algorithms based on penalty function and complex algorithm. The validity and effectiveness of the proposed method were verified by a practical instance.