A four-bar linkage system is shown below. The first link, a, is an input link (crank) of length 1m. The second link, b, is a coupler link of length 2m. The third link, c, is an output link of length 3m. The fourth link, d, is the fixed link (ground) of length 4m.

The angular position of the output link (θ₄) of a four-bar linkage corresponding to the angular position of the input link (θ₂) can be computed using Freudenstein’s equation:



Using the Newton-Raphson method to determine the value of θ₄ when θ₂ = 40ᵒ. With an initial guess of x_i = 100ᵒ and precision of 0.0001.

The derivative of the Freudenstein equation is