Synthesis of function generating spherical four bar mechanism for the six independent parameters

This study deals with the function generation synthesis of spherical four bar mechanism for six independent construction parameters φ₀, ψ₀, α₁, α₂, α₃, and α₄ by giving six or more design points with respect to the methods that are used in synthesis procedure. Quaternion algebra is used to derive the objective function of spherical four bar mechanism by following some rotational sequences. Three different methods as interpolation approximation, least squares approximation and Chebyshev approximation are used during synthesis procedure. During the consecutive trials in Chebyshev approximation, a new approach is taken to renew the design points φ_i by plotting the graph of the objective functions derivative and taking the roots of it as new design points with two boundary points. Separate examples are given for each section and the results are tabulated. Discussions about the study and comparisons between the used methods are given at the end of the study.