Abstract: In order to avoid the iterative solution of complex nonlinear equations derived from 3D assembly geometric constraint closed-loops,a projection transformation approach is proposed to solve the planar geometric constraint closed-loop problem in 3D assembly design.Firstly,the equivalence analysis algorithm is adopted to eliminate pseudo geometric constraint closed-loops and the block finding algorithm of undirected graph is utilized to decompose geometric constraint graph.Then,the subgraphs of the geometric constraint closed-loops are converted to kinematic joint graphs using screw theory,and the characteristic parameters of the kinematic joints are analyzed to determine whether the geometric constraint closed-loops can be projected to the 2D plane.At last,the 3D geometric constraint closed-loops that can be projected to the 2D plane is transformed into 2D geometric constraint system,which will be solved to obtain the solution of the 3D geometric constraint closed-loops.The proposed method can downsize the constraint equations and variables that have to be solved simultaneously and reduce the complexity of constraint equations,so it can improve the efficiency and robustness of an assembly constraint solver significantly.