A novel analytical method for function generation synthesis of planar four-bar linkages

• A novel analytical synthesis method is proposed for function generation synthesis.
• The new design equations are performed to simplify the function generation problem.
• A general formula for calculation of the design parameters is derived.
• The proposed method is simpler and more applicable compared with other methods.

In this paper, a novel analytical approach is presented to solve function generation synthesis problems for planar four-bar linkages with no limitations on the number of precision points. Firstly, the output rotation-angle function is formulated according to the Fourier series components of the input angle, and is substituted into a vector loop equation. Then, the relationship between the design parameters of the linkage and the Fourier coefficients of the output function is obtained. On the basis of this, the new design equations are established. Finally, a cubic polynomial equation is obtained by dialytic elimination. Three non-trivial solutions for the new design equations are ultimately obtained analytically. Three examples are provided to verify the effectiveness of the proposed technique. As a result, a general formula is derived for calculation of the design parameters of a planar four-bar linkage using the Fourier coefficients of the prescribed function.