Kinematic synthesis problems are important in mechanism and machine science. This thesis focuses on function synthesis. The synthesis of different mechanisms with 1 and 2 degrees-of-freedom (dof) are issued by using least squares and Chebyshev approximations. There are various studies with these approaches in the literature. However, there are not many studies of function synthesis of 2-dof mechanisms in the literature. The aim is to study function synthesis of 2-loop and 2 dof mechanisms. 2-dof planar 5R mechanism, 1-dof Bennet 6R mechanisms, 2-dof 7R double-spherical mechanism and finally 7R planar 2-dof mechanism are worked out for function synthesis. It is shown that the function synthesis problems can be solved analytically and semi analytically. The formulations are applied using MS Excel and the results were verified using Solidworks software. It is seen that the numerical results give reliable results and construction parameters are successfully determined.