An Improved Fourier-Based Method for Path Generation of Planar Four-Bar Linkages without Prescribed Timing

Four-bar linkages are critical fundamental elements of many mechanical systems, and their design synthesis is often mathematically complicated with iterative numerical solutions. Analytical methods based on Fourier coefficients can circumvent these difficulties but have issues with time parameters assignment for path generation without prescribed time in previous studies. In this paper, an improved Fourier-based point-to-point combination method is presented, which generates more points by Fourier approximation and assigns the time parameters to the given points while allowing discarding solutions with order defects. This method relies on the Fourier coefficients, improving the accuracy of synthesis solutions, and simplifying the computational procedure. Time parameters are assigned directly to the given points, which avoids the complex calculations to find intersection points in the given path, eliminates combinations that would lead to solutions with order defects, and simplifies the assessment process of synthesis results. The parameters obtained by the point-to-point combination method can be used as the parameters of the input dyad, skipping the first set of design equations for faster calculation. Several examples are presented to demonstrate the advantages of the proposed synthesis method, which is easy-understanding, computationally efficient, and yields more accurate solutions than available synthesis methods.