## 1 Introduction
Advancements have also been made in control methodologies; [PERSON] et al. [18] proposed an optimal trajectory tracking control method using Particle Swarm Optimization (PSO) based on inverse kinematics in order to improve the precision of the 3-DOF surgical robot. The proposed controller exhibited faster convergence to the desired trajectory and reduced steady-state errors, indicating its potential efficacy in enhancing the accuracy and reliability of surgical robotsSeveral challenges of the 3-DOF robots for surgery imply singularity issues (presence of singularities within the robot's workspace can lead to control difficulties and reduced accuracy during the surgical procedure) and safety concerns (focused on developing secure robotic solutions for surgical procedures, emphasizing the identification and mitigation of safety issues from the early design stage) [19]. Efforts are underway to design parallel robots with large, singularity-free workspaces and the development of accurate dynamic models for effective control and performance [20]. This paper presented the optimization of a 3-DOF parallel robot for laparoscopic pancreatic surgery, integrated with a passive spherical mechanism to ensure a stable Remote Center of Motion (RCM) at the trocar. The novelty of this robotic structure is given by the fact that the robot employs a novel 3-DOF parallel mechanism combined with a passive spherical mechanism that specifically constrains the Remote Center of Motion (RCM). This hybrid approach ensures that instrument motions are precisely pivoted about the RCM--a critical requirement in minimally invasive surgery--while maintaining a compact and efficient structure. The scope of this research is the development and optimization of the parallel robotic system for laparoscopic pancreatic surgery utilizing a sophisticated optimization framework that integrates genetic algorithms and fuzzy logic. The study aimed to determine optimal configurations of critical robotic parameters. Initially, the focus lies on optimizing the Remote Center of Motion (RCM), essential for enhancing workspace accessibility and improving instrument maneuverability. Subsequent optimization steps include identifying optimal lengths for crucial robotic links, significantly impacting the surgical robot's performance. The study further validates the optimized robotic design through detailed simulation studies and graphical evaluations, demonstrating improvements in workspace and reachability. The scope also extends to practically integrating these optimized parameters into a functional robotic system within an operating room setting, including performing virtual simulations to test and validate robotic performance under realistic surgical conditions. The paper is structured as follows: Section 1 introduces the research context and objectives. Section 2 outlines the genetic algorithm-fuzzy logic optimization framework and robotic design methods. Section 3 details the results of the optimization and the mechanical design implementation. Section 4 discusses these findings comprehensively, while Section 5 concludes by summarizing the key insights and potential implications of this research.