This paper presents a method that permits the calculus of the dimensions of the component links of a quadrilateral mechanism that ensures the optimisation of the variation on a cinematic cycle of the connection forces in the joints of the mechanism when some functional constraints are imposed. The connection forces are obtained in an analytical form, depending on the driving crank angle, the angular speed of the driving crank, the dimensions, linear masses and mass moments of inertia of the component links and the value of the technological moment that works on the rocker of the quadrilateral mechanism. For this purpose, a simulation program has been developed using Maple program that has powerful symbolic computation functions. The dimensions of the component links of the quadrilateral mechanism that ensure the optimum values of the connection forces in the joints of the mechanism have been determined using the Sequential Quadratic Programming approach with which operates the optimisation function NLPSolve from Maple program. The calculus has been developed by imposing two functional constraints: the total rotating angle of the rocker during a cinematic cycle and the value of the crank angle corresponding to one of the two extreme positions of the rocker.