INTRODUCTION: The advent of da Vinci surgical robot (Intuitive Surgical, California, USA) has allowed complex surgical procedures in urology, gynecology, cardiothoracic, and pediatric to be performed with better clinical outcomes. The end effectors of these robots exhibits enhanced dexterity with improved range of motion leading to better access and precise control during the surgery. Understanding the design and kinematics of these end effectors (imitating surgical instruments' tooltips) would assist in replication of their complex motion in a computer-generated environment. This would further support the development of computer-aided robotic surgical applications. The aim of this work is to develop a software framework comprising of the geometric three-dimensional models of the surgical robot tool-tips along with their kinematic analysis. METHODS: The geometric models of the surgical tooltips were designed based on the EndoWristTM instruments of the da Vinci surgical robot. Shapes of the link and inter-link distances of the EndoWristTM instrument were measured in detail. A three-dimensional virtual model was then recreated using CAD software (Solidworks, Dassault Systems, Massachusetts, USA). The kinematic analysis was performed considering trocar as the base-frame for actuation. The actuation mechanism of the tool composed of a prismatic joint (T1) followed by four revolute joints (Ri ; i = 1 to 4) in tandem (Figure 1). The relationship between the consequent joints was expressed in form of transformation matrices using Denavit-Hartenberg (D-H) convention. Equations corresponding to the forward and the inverse kinematics were then computed using D-H parameters and applying geometrical approach. The kinematics equations of the designed tooltips were implemented through a modular cross-platform software framework developed using C/C++. In the software, the graphical rendering was performed using openGL and a multi-threaded environment was implemented using Boost libraries. RESULTS AND DISCUSSION: Five geometric models simulating the articulated motion of the EndoWristTM instruments were designed (Figure 2). These models were selected based on the five basic interactions of the surgical tooltip with the anatomical structures, which included: Cauterization of the tissue, Stitching using needles, Applying clips on vascular structures, Cutting using scissors, and Grasping of the tissues. The developed software framework, which includes kinematics computation and graphical rendering of the designed components, was evaluated for applicability in two scenarios (Figure 3). The first scenario demonstrates the integration of the software with a patient-specific simulator for pre-operative surgical rehearsal and planning (Figure 3a). The second scenario shows the applicability of the software in generation of virtual overlays of the tooltips superimposed with the stereoscopic video stream and rendered on the surgeon's console of the surgical robot (Figure 3b). This would further assist in development of vision-based guidance for the tooltips. CONCLUSION: The geometrical modeling and kinematic analysis allowed the generation of the motion of the tooltips in a virtual space that could be used for both pre-operatively and intra-operatively, before and during the surgery, respectively. The resulting framework can also be used to simulate and test new tooltip designs.


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