In space-constrained environments where real-time performance is crucial, such as a harvesting robot in the greenhouses, analytical inverse kinematics methods are essential for robotic motion planning. However, these analytical methods are influenced by the robotic arm's structure and often lack universality compared to numerical optimization techniques. Therefore, it is necessary to conduct kinematic analysis specific to the target robotic arm to address these limitations. This paper presents an arm-angle-based inverse kinematics method for redundant robotic arms and demonstrates an improved PB-PSO algorithm for optimizing joint resolution in harvesting robots. The optimization objectives include minimizing joint motion and keeping the joints away from their limits. This method calculates optimal joint positions based on the harvesting position and initial posture. A comparison with numerical methods validates the effectiveness of this approach, achieves faster speeds, completing the optimal solution output in only 31.4 ms and 38.7 ms, with a smaller joint motion variation.