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. To address these issues, this paper proposes a Cartesian stiffness planner based on motion/force transmission performance. The algorithm employs a sequential least squares optimization technique to compute the robot's workspace trajectory. Local transmission indices are introduced to enhance power transmission efficiency within the trajectory. The optimization objective is simplified through the use of a geometric shaping method based on stiffness ellipsoids. Furthermore, the optimization space dimensions are 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, is demonstrated through simulation verification conducted using the MATLAB-based Simulink platform. Experimental validation is 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.