This paper presents a new method for solving the inverse kinematics of robot manipulators. The method defines incremental units in joint and Cartesian spaces, which represent the position resolutions in each space. Based on these units, the incremental computation of the DDA integrator is used to solve the direct kinematics. The repetitive calculation of the inverse Jacobian matrix is replaced by a simple look-up table. By using an iterative procedure with convergence rules, the inverse kinematics algorithm is established. A 3 DOF robot is considered as the combination of two types of a 2 DOF robot. Simulation and experiment are performed to test the algorithm.