The N-3 Revolute-Prismatic-Spherical (N-3RPS) manipulator is a kind of serial-parallel manipulator and has higher stiffness and accuracy compared with serial mechanisms, and a larger workspace compared with parallel mechanisms. The locking mechanism in each joint allows the manipulator to be controlled by only three wires. Modeling the dynamics of this manipulator presents an inherent complexity due to its closed-loop structure and kinematic constraints. In the first part of this paper, the inverse kinematics of the manipulator, which consists of position, velocity, and acceleration, is studied. In the second part, the inverse and forward dynamics of the manipulator is formulated based on the principle of virtual work and link Jacobian matrices. Finally, the numerical example is presented for some trajectories.