In this paper, a new method for the numerical solution of the finite displacement problem in spatial mechanisms with revolute (R), cylindrical (C), spherical (S), and prismatic (P) pairs is presented. It is based on the use of special points’ coordinates as Lagrangian coordinates of the mechanism. The kinematic constraint equations are imposed as constant distances, areas, and volumes of segments, triangles, and tetrahedrons determined by those points. The system of nonlinear equations is solved via the Gauss-Newton variation of the Least Squares Method. Finally, three examples are presented in which the good convergence properties of the method can be seen.

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