Abstract: The paper studies the application of variation principle in the field of 3D assembly geometric constraint solution,and an algorithm based on kinematics variation principle is presented.By applying the relative coordinate method,the algorithm transforms the parametric space from the Cartesian coordinate space to the relative coordinate space.In the case of open chain constraint system, 3D assembly geometric constraints can be satisfied by sequential choice of the relative coordinates.For the closed chain constraint system,by cutting constraints,the algorithm converts the closed chain to a generalized open chain and a system of equations of cutting constraints.In addition,the Jacobin matrix formulation of equations of cutting constraints can be analytically obtained kinematics variation principle.In the end,the presented algorithm is validated by an example of 3D geometric closed chain constraint system.