A three-dimensional (3D) model of a novel 5-DoF type parallel manipulator with a couple-constrained wrench is constructed and its couple-constrained wrench is analyzed. First, the formulas are derived for solving the displacement, velocity, acceleration of the moving platform and moving links, and a workspace is constructed. Second, the formulas are derived for solving the inertial wrenches of the moving links. Third, a dynamics equation is established by considering the inertial wrenches and friction, and the formulas are derived for solving the dynamically active forces and the dynamically couple-constrained wrench. Finally, a numerical example is given to demonstrate the analytic solution of the kinematics and the dynamics, and the analytical solutions are verified by utilizing a simulation mechanism.