A new ball joint actuator with three-degree-of-freedom is proposed to solve the problem of space motion. It can perform some specific work in a certain space with multiple degrees of freedom. At first, the kinematics and workspace of the actuator are analyzed. Then, the dynamics is analyzed using the LaGrange method. In this paper, a modeling approach from the serial robotic arm is utilized to derive a symmetric, positive definite inertia matrix. It facilitates easier access to the dynamical model. Finally, simulation analysis is performed to verify the effectiveness of the method.