Abstract: The finite element method (FEM) is widely used in structural strain, stress and dynamic analysis. But few developments are made in the field of rigid body kinematic analysis. The gradient vector, stiffness matrix and Hessian matrix are derived based on the principle of minimum potential energy for the new finite element, which represents the hinge joints constraints in spatial linkage. The two special geometries of the two joints axes, namely, parallelism and coplane, are investigated. And the formulas and method are also given. In the large deployable mechanism, there are many duplicate mechanisms with identical structure and closed-loop kinematic chains. This method based on FEM can be used to analyze the kinematics of the spatial closed-loops mechanisms without decomposing the kinematic chains. The kinematics of the three typical spatial closed-loop mechanisms are simulated by using this method. And the result shows that it’s simple and accurate to calculate the kinematics of the spatial closed-loop mechanisms with this element, so it has an excellent prospect for application in large deployable mechanisms.

Key words: Finite element, Hinge joints, Kinematics, Principle of minimum potential energy, Spacial closed-loop mechanism