Redundant serial robots possess the advantages of a large workspace and good dynamic characteristics, and have been widely used in human-robot collaboration. Due to the characteristics of unstructured scenes and diversified tasks in human-robot collaboration, it is necessary to control the end stiffness of robots to ensure interaction safety. However, common stiffness planning algorithms suffer from low power transmission efficiency and inefficient computation. Aiming to address these issues, a Cartesian stiffness planner was proposed based on motion/force transmission performance. The algorithm employed a sequential least squares optimization technique to compute the robot’s workspace trajectory. Local transmission indices were introduced to enhance power transmission efficiency within the trajectory. The optimization objective was simplified through the use of a geometric shaping method based on stiffness ellipsoids. Furthermore, the optimization space dimensions were reduced by extending the arm angle description method, thereby improving the computational efficiency of the optimization algorithm and reducing computational resource consumption. The efficacy of the proposed trajectory planner, based on the geometric shaping method for robot Cartesian trajectories, was demonstrated through simulation verification conducted by using the Matlab-based Simulink platform. Experimental validation was performed on the Franka Panda redundant serial robot platform, confirming the feasibility of realizing the desired stiffness direction at the robot end by this planner.