This paper presents a new approach for solving the inverse kinematics of a 4R manipulator in a spatial plane. The conventional D-H algorithm method involves complex matrix transformations. The proposed method reduces computational complexity by using several geometric relationships and constraints. It defines a linear relationship between the output radius and a diagonal distance to avoid singular regions. The radius and diagonal distance are used to calculate angular parameters and solve for the inverse kinematics without complex computations. This approach makes for a faster response time of electronic systems controlling the manipulator.