Synthesize a four-bar mechanism to generate a function \(y=\sin x\) for \(0^{\circ} \leq x \leq 90^{\circ}\). The range of the output crank may be chosen as \(60^{\circ}\) while that of input crank be \(120^{\circ}\). Assume three precision points which are to be from Chebyshev's spacing. Length of fixed link \(=52.5 \mathrm{~mm}\), \(\phi_{1}=105^{\circ}\) and \(\psi_{1}=66^{\circ}\).