SUMMARYA novel 3-leg 5-DoF parallel manipulator (PM) with a UPU-type composite active constrained leg is proposed and its kinematics and statics are analyzed systematically. First, the formulae are derived for solving the inverse/forward displacements, inverse/forward velocities, and active/constraint forces. Second, the formulae are derived for solving inverse/forward accelerations. Third, a simulation mechanism of this PM is created and its workspace is constructed and analyzed. Finally, the analytic results are verified by its simulation mechanism. The line from a i to o, e i = e.The line fromThe active leg and its length. l i , L i The side of m and B. P, S The prismatic joint and the spherical joint. R jThe revolute joints (j = 1, 2, 3, 4).The universal joint with R 1 and R 2. U BThe universal joint with R 3 and R 4. {m} Coordinate frame o-xyz fixed on m. {B} Coordinate frame O-XYZ fixed on B. v riThe input velocity of active leg. e, E The distances from a i to o and from A i to O. F, T The concentrated force and torque applied on m at o. F aiThe active forces applied on and along r i. T aThe active torque applied on R 1. T λThe active torque applied on R 4. F c , T c The constrained force and the constrained torque. T bThe bending moment exerted on r 2. Rotational matrix from {m} to {B}. J, HThe Jacobian matrix and Hessian matrix.