## Abstract

Tele-operation has brought about a paradigm shift in the way minimally invasive surgeries are carried out. Several tele-operated robotic systems have been developed in the last three decades. In this research work, we present a practical approach for the complete design of a six degree-of-freedom (DoF) master–slave tele-operated robotic system with limited resources. This research work elaborates on the methodology followed by us for the complete system design, methods for simplifying the surgical tool design with decoupled DoF wrist utilizing stationary wire guides instead of pulleys, and method of reducing the number of balancing masses required for gravity compensation of master manipulator arms. We also demonstrate the avenues for utilizing compliant mechanism for several mechanisms of the system to reduce complexity and to mitigate the issue of biofouling. The concepts and design methodology described in this paper would serve as a starting point and design guideline for future designers of such systems in resource-constrained environments.

## Introduction

The use of a tele-operated surgical robot improves surgical outcome and reduces surgeons' fatigue. Such a system provides hand tremor compensation, scaling of motion, and improved dexterity compared to manual laparoscopic procedures. Mechanical tele-operation was pioneered by Goertz and his team for remote handling of radioactive elements [1,2]. With continued developments, mechanical tele-operation became electronically tethered for improved payload handling and bilateral servomanipulators that offered force feedback. There have been several tele-operation based robotic assisted laparoscopic surgical (RALS) systems developed in the last three decades. The Zeus® system, developed by Computer Motion, Inc., Goleta, CA originally developed for cardiac surgery, performed the first transcontinental RALS in 2001 [3].

The commercially successful daVinci® system from Intuitive Surgical, Inc., has performed over 1.2 million surgical procedures with an installation base of around 5764 systems worldwide to date [4]. Other commercial tele-operated systems include EnosTM surgical system from Titan Medical, Inc. [5], Versius® surgical robotic system from CMR Surgical [6], Senhance® Surgical System from TransEnterix Surgical, Inc. [7], Dexter® from Distalmotion SA [8], Revo‐i® robotic platform from Meere Company, Inc. [9], and avatera system from avateramedical® GmbH [10]. Notable tele-operated research platforms developed by various research universities are SRI Telepresence surgery system [11], RAMS system from NASA/JPL and MicroDexterity Systems, Inc. [12], Black Falcon from MIT [13], Telesurgical workstation from UC Berkeley and UCSF [14], Tele-endoscopic surgical system from University of Tokyo [15], DLR Mirosurge [16], RAVEN from University of Washington [17], and Sofie from TU Eindhoven [18]. All the systems, despite their differences in mechanical construction, have a four degree-of-freedom (DoF) slave arm that carries a 2DoF robotic laparoscopic tool [19] controlled by a master arm.

Many of the existing systems use complicated surgical tool designs with coupled wrist degree-of-freedom, a nonintuitive interface for master arm design, and complicated mechanical design. Commercially available systems are also costly, and their adoption and running costs for low-income countries are prohibitive. There is also an avenue for substituting multipart mechanisms of several subsystems of the robot with monolithic compliant mechanisms to simplify the mechanical design.

The key design goals of this paper are listed below

1. Design of a master arm with high stiffness that would inherently require a minimal number of balancing masses for gravity compensation

2. Gravity compensation of the slave arm assembly for safety

3. Designs for monolithic surgical tooltip based on compliant mechanisms to mitigate the issue of biofouling and reduce mechanical complexity

4. Design of a simple, compliant mechanism-based grasper for the master arm

5. Design of surgical tool wrist with decoupled DoF for simplified position control and reduced tether fraying

We have built the system with limited resources but capable of providing 6DoF tele-operation with good dexterity, reduced system complexity, and improved safety. We believe the design details described in the paper for each subsystem would provide future designers of such systems, a good reference point to start with and improve upon. Design guidelines for proper tether routing following “law of belting” for power transmission of subsystems, actuator placement to reduce the volume of the surgical tool, and modal analysis (MA) of the slave arm are described in detail in the paper. We first present the system architecture, specifications, followed by individual subsystem design and then present the modal analysis of the slave arm and system testing.

## Methods

System architecture. Figure 1(a) shows the system workflow diagram depicting the information flow from the surgeon console to the slave arms of the tele-operated system. Figure 1(b) shows a CAD of the complete tele-operated surgical robot. The tele-operated robotic system consists of two pair of master arms, a central controller, and two slave arms. The central controller carries out the forward kinematics for the master arm and the inverse kinematics for the slave arm. There is also a circular prismatic joint based camera arm to relay surgical site video to a monitor placed at the master arms. The master manipulators each have 6DoF input (excluding grasping DoF) and are electronically tethered to the slave arms via the controller, as shown in Fig. 1. Each slave arm carries a remote center of motion mechanism (RCM) capable of 3DoF (pitch, roll and translation) and a surgical tool capable of 3DoF (rotation, pitch and yaw) excluding grasping DoF.

System specifications. The key design specifications of the robot are listed in Table 1. The design specifications for the system are established based on the forces and range of motion of the surgical tool needed for general surgical procedures [14,2022]. The specifications in Table 1 are taken as design goals for the tele-operated robotic system, and the components such as actuators, power supply, and motor drivers are chosen to meet or exceed the required design specifications.

System safety and reducing complexity. Providing an intrinsically safe system is imperative for any robotic surgical system. Several safety factors were considered that are inherent in the current system design. The system has limited peak operational velocity (<0.1 m/s) to minimize impact forces. The system also should not move under the action of gravity when there is a failure of power. An actuator fault-tolerant system can be achieved by equipping the system with drive motors having a high reduction ratio. However, in surgical robotics application, a high reduction ratio is not preferred since it would make the system nonback drivable.

The drive actuator is selected such that a good compromise was reached by having a moderately back drivable (medium gear reduction) mechanism with gravity compensation [23]. This implies that the manipulator arms would start to “droop” downward [24] during power failure under the action of gravity, and this can be avoided by suitable gravity compensation of the system [13]. Therefore, the master arm manipulator and RCM mechanism of the slave arm are gravity compensated.

## Subsystem Design

Master arm design. The master arm of the surgical robot serves as an input device to the system. A desired feature of a master arm is mechanical transparency [1]. In other words, the user should not feel the inertia and resistance in moving the master arm. The master arm should be able to capture all 6DoF (3 position + 3 orientation) input from the user. There are several types of master arm designs prevalent in literature [2527]. The primary performance requirements for a master arm are good dexterity, static balancing, hand centered rotation [26] of the gimbal used to track hand orientation for intuitive feel, and minimal inertia. A serial chain of links will be generally used for tracking of the surgeon's hand position, and a gimbal assembly connected to this serial chain will be used for sensing the orientation in three-dimensional (3D) space. All the three axes of the gimbal are orthogonal and should have a common intersection point for simplified kinematics. The grasper should be placed at this common intersection point for hand centered rotation.

One of the key design challenges in designing a master arm is making a rigid arm without compromising the usable workspace. A serial arm would provide good workspace; however, the arm rigidity will be poor. On the contrary, use of parallel linkages would give rigid linkage assembly but may compromise the usable workspace. A series-parallel mechanism commonly found in palletizing robots is proposed as a design solution to address this issue [28]. This design combines the rigidity of a parallel manipulator while allowing the workspace of a serial manipulator. It will enable remote placement of balancing masses and drive actuators which reduces the reflected inertia. The CAD model of the master arm manipulator is shown in Fig. 2. A detailed kinematic analysis of this manipulator can be found in our earlier research work [29].

Master arm gravity compensation. Multiple methods of passive gravity compensation utilizing countermasses, springs, gear train, etc., can be referred from the literature [30]. A balancing scheme is proposed to provide passive gravity compensation for the master arm through the use of auxiliary balancing masses. A kinematic diagram of the master arm is shown in Fig. 3. The absolute orientation of link $l4$ does not change due to the kinematic constraint imposed by the parallel links which keep the orientation of link $l4$ constant within the workspace. Hence, the gimbal axis $α$ always remain perpendicular to the ground independent of $θ2$ and $θ3$.

Any rotation of gimbal angle $α$ will not alter the potential energy of the subsequent gimbal links, and therefore, balancing is not required for this joint. Similarly, no balancing is needed for rotation $γ$ if uniform mass distribution about that rotational axis is ensured. In such a situation, balancing is required only for the masses that rotate through the angle $β$ as far as the gimbal is concerned. The parallelogram linkage assembly requires only two balancing masses $M1$ and $M2$ for gravity compensation since any change in input angle $ψ$, i.e., the out of plane spatial rotation of the parallelogram linkage, does not change the potential energy of the manipulator. Therefore, this design requires only three balancing masses for passive gravity compensation as opposed to four needed for a conventional serial linkage based master arm design.

Gravity compensation is independently required for both the positional ($θ2$, $θ3$) and gimbal axis $β$ of the manipulator. Gimbal axis $β$ is easily counterbalanced with a countermass, as shown in Fig. 2. For counterbalancing the parallelogram linkage assembly, the mass $M1$ and $M2$ and their placement $L1$ and $L2$ need to be determined. The optimization problem can be stated as minimize ($F$), where the objective function $F$ is obtained from the potential energy $P$ of the master arm assembly and by integrating the change in potential energy for the input angles $θ2$ and $θ3$ as given in the following equation:
$F=∫θ3minθ3max∫θ2minθ2max((δPδθ2)2+(δPδθ3)2)δθ2δθ3$
(1)
The limits for the variables are taken based on physical constraints and the maximum allowable joint position and are as follows:
$10≤L1≤ 110 mm$
(2)
$10≤L2≤ 110 mm$
(3)
$0.1≤M1≤ 1 kg$
(4)
$0.1≤M2≤ 1 kg$
(5)
$θ2= 60–140 deg$
(6)
$θ3= 150–217 deg$
(7)

The limits for $θ2$ and $θ3$ were chosen to keep the manipulator away from singularity. Constrained nonlinear minimization algorithm was used for optimization, and the optimized values for the lengths $L1$ and $L2$ were found to be 109 mm. The values for the countermasses $M1$ and $M2$ were 0.99 kg and 0.69 kg, respectively.

Master arm grasper design. The role of master arm grasper is to measure the opening angle command given by a surgeon and relay it to the surgical tooltip carried by the slave manipulator. The design of master arm grasper is critical for the ease of use and the surgeon's comfort. The commercially available da Vinci surgical system makes use of a four-bar crank-slider mechanism for its master arm grasper. The crank of the four-bar mechanism serves as the grasper, and the slider is connected to a linear position sensing element. This mechanism enables the measurement of the opening angle of the grasper. Such a complex set of linkages can be replaced with a monolithic compliant mechanism, which also offers an avenue for weight reduction. Most of the commercially available robots and robotic trainers make use of a precision grip [27,31] over other types of grips for good control over the grasp DoF of the surgical grasper. Kota et al. [32] have shown that for surgical applications, compliant mechanisms are ideal candidates due to key advantages such as joint-free design, the absence of wear and debris, and lubrication-free operation. This section focuses on the design of a partially compliant grasper for the master arm.

A semicompliant grasper design is proposed for acquiring the grasping input from the surgeon, which allows backlash-free operation and offers better performance due to the utilization of flexures in its design. The proposed design for the grasper consists of two components, a monolithic pair of grasper and a follower.

A CAD model of the grasper is shown in Fig. 4. A small-length flexural pivot [33], as shown in Fig. 4, provides compliance for the grasper. The inner portion of each grasper has a circular profile. There is a wedge-shaped follower between the grasper. The follower converts the rotary motion of the grasper to linear motion which is read by a linear potentiometer. A plastic bearing liner (iglide® tribo-tape) was used to reduce contact friction. A large deflection finite element analysis (FEA) was performed to estimate the peak bending stresses on the flexure, caused by deflection of the grasper. The maximum bending stress, $σmax,$ for the grasper deflection (δθ = 4.5 deg) from its initial position was found to be 16 MPa. This value is far below the flexural strength (75 MPa) of Vero Clear [34] photopolymer. The grasper and the follower were made by rapid prototyping on an Objet™ polyjet printer. The follower is connected to a linear potentiometer (BI technologies) for sensing the position. Figure 5 shows the prototype of the proposed compliant grasper in open (neutral) and in fully closed position. The flexure recoils back to its neutral position when released because of stored strain energy. It thus negates the need for a separate spring for restoring the grasper to its initial position. The spring-loaded follower maintains contact with the circular portion of the grasper and also aides the grasper to return to its neutral position quickly.

Master arm prototype. The 6DoF prototype of the master arm with the proposed grasper integrated to it is shown in Fig. 6. The links of the master arms are made of hollow carbon fiber tubes of diameter 10 mm and the joints with miniature low friction bearings (FL675Z—Misumi® Group, Inc.). The master arm is also equipped with 3 Maxon™ RE-40 motors with integrated encoders for joint tracking. These three motors would potentially facilitate haptic feedback capability to the system; however, in the current implementation, these motors are not utilized. Preloaded capstan drives connect the motors to the parallelogram linkages for backlash-free operation. The gimbal joints are equipped with quadrature encoders (U.S. digital, E4T model). Countermasses for gravity compensation, based on calculation from the Master Arm Gravity Compensation section, are made of Tungsten carbide and are placed on the semicircular capstan drums. The grasper assembly is connected to the gimbal of the master arm, as shown. The Velcro straps of the grasper loop around the fingers and keep them in place without slipping. The grasper is found to have adequate out of plane stiffness that enables moving the entire master arm assembly within its workspace in all possible orientations and performs well for its intended use.

Surgical tooltip designs. The surgical tool functions as an extension of the surgeon's arm, and there is a need for articulating (yaw and pitch DoF) the wrist of the surgical tool to restore some of the lost DoF and limited dexterity imposed by the constraints of minimally invasive surgery. Another key design requirement of a robotic surgical instrument operating within a confined space is the swept volume. The swept volume should be as small as possible for effective use of space within the insufflated cavity of a patient.

To achieve these design goals, several concepts have been explored, and three designs are proposed. Two compliant mechanism based designs, namely, compliant surgical tooltip and “MagNex” surgical tooltip are presented to address the problem of biofouling. The third design uses a wrist with decoupled DoF. Merits of each design are investigated, and a final design is chosen to be deployed in the telesurgical robot.

Compliant surgical tooltip. This compliant tooltip can be disposed of after single use to mitigate the effects of biofouling. The entire tooltip is monolithic with an integrated grasper and uses joints constructed using a corner fileted contact aided flexures that provide increased buckling and torsional resistance. The contact aid is provided by circular guide arcs that serve an alternate load flow path and share the loads borne by the flexures of the tool wrist. Each flexural joint can bend up to 20 deg. The tooltip has 3DoF (pitch, yaw and grasp) and is realized by six compliant joints placed in an alternating fashion, orthogonal to each other as shown in Fig. 7. The tooltip is actuated by three pairs of tethers that run along the conduits in the tooltip, as shown in Fig. 7. The inset figure in Fig. 7 shows an individual contact aided flexure. Figure 8 shows a 3D printed prototype of the tooltip in completely bent (pitch DoF) position. Inset figure in Fig. 8 shows the grasping action of the integrated graspers. Further design details and analysis of this design can be found in our earlier publication [35].

MagNex tooltip. After every surgical procedure, biological material contaminates the surgical tool and its transmission elements. To mitigate this issue, a hermetically sealed tool which is operated by magnetic flux coupling is proposed. Sealing the tool shaft prevents the drive elements of the surgical tool coming into contact with biological material. A magnetic flux linkage communicates the motive power to drive the tooltip through the sealed barrier using permanent magnets. The pluggable tooltip can be disposed of after single use. Hence, the effects of biofouling are mitigated.

The compliant tooltip design presented in the Compliant Surgical Tooltip section has a large swept volume which limits its applications. Hence, a different approach is taken here to realize the tooltip with smaller swept volume, good torsion, and off-axis and compression strength. To address these design challenges, a hybrid flexure is obtained by combining a simple flexure and a serpentine flexure. This tooltip like the previous design has 3DoF. A prototype of the design is shown in Fig. 9. FEA analysis of the proposed design has confirmed that the hybrid serpentine flexure has twice the off-axis and compressive strength compared to a corner fileted flexure, without compromising the range of motion. A detailed description of the tooltip design, magnetic flux-based power transmission, and analysis of this design can be seen in our prior publication [36].

Surgical tooltip with decoupled wrist DoF. The two designs described in the Compliant Surgical Tooltip and MagNex Tooltip sections despite their advantages can only exert a limited force (∼0.3 N) for tissue manipulation. Therefore, to improve the usable force of the tooltip, an alternate design is proposed using conventional joints. The key design focus is to have reduced mechanical complexity, decoupling wrist DoF, and using the “Law of Belting (LoB)” for the design of tether driven power transmission. Many of the conventional surgical tool wrist design found in the literature have mechanically coupled wrist and do not follow LoB, which leads to complex control requirements, tether slippage and fraying. Designs with decoupled wrist found in the literature have complicated mechanical arrangements [37] and do not follow LoB [38].

In the proposed design, the mechanical decoupling between the pitch and yaw DoF of the wrist is achieved by routing the drive tethers through the plane of symmetry of the tool. To simplify the mechanical construction, stationary circular guide arcs are used to guide the tethers that drive the tool wrist. These guide arcs eliminate the conventional use of pulleys to route the tethers. These guide arcs guide the tethers connected to the graspers to enter/exit through the midplane of the pulleys, thus following the LoB. The tool wrist can pitch and yaw ±90 deg and roll ±180 deg with minimal swept volume. A metal 3D printed prototype of the proposed design is shown in Fig. 10(a). Figure 10(b) shows that the graspers' orientation does not change during pitch motion, demonstrating the decoupled wrist characteristic of the tooltip. The tooltip can exert sufficient gripping force (6 N) required for typical surgical procedures. A detailed description on proper tether routing to follow LoB, achieving decoupling of the wrist DoFs, and mathematical procedure for optimal placement of the circular guide arcs for minimal change in tether length during operation can be found in our earlier work [39].

Slave arm design. The slave arm reproduces the motion commands of the master arm. There are a pair of slave arms that are electronically tethered to the pair of master arms. Each slave arm consists of a 3DoF RCM mechanism that carries a 4DoF robotic laparoscopic surgical tool at its distal end. Each slave arm is mounted to a pedestal, as shown in Fig. 11. The RCM of each slave manipulator is connected to the pedestal by three passive joints with the roll DoF assembly in between them. The RCM mechanism carries the pitch DoF. The passive arm assembly is a planar 3R manipulator. It allows positioning the surgical tool at the proper incision point on the patient before the surgical procedure. All passive joints are equipped with holding brakes at every joint for locking them at any arbitrary angle. A counterweight made of Tungsten carbide is placed at the other side of the passive arm assembly to balance the entire passive arm assembly and the RCM mechanism. In RALS, the use of a surgical tool with a rigid stem necessitates the need for an RCM mechanism. The surgical tool is subject to a kinematic constraint such that it can only pivot about the insertion point in addition to the translatory in and out motion, as shown in Fig. 12.

We have utilized a parallelogram 1R1T planar mechanism which has one rotary (R) actuator for pivoting the tool about the RCM point and one prismatic (T) joint for in and out motion of the surgical tool [40]. Unlike RCM constraint achieved with redundant serial linkage [16,41], a passive RCM mechanism is actuator fault-tolerant since the mechanism can maintain the kinematic constraint without actuators.

The entire RCM mechanism is offset from the roll axis, as shown in Fig. 12 to make the surgical tool's axis coincident with the roll axis. The surgical tool is mounted on the side face of the RCM to facilitate the tool axis passing through the insertion point. This is vital to make all three axes (roll, pitch and translation) of the surgical tool to be coincident at the insertion (trocar) point to ensure minimum tissue rupture. An L-shaped base link enables offsetting the RCM mechanism from the roll axis, as shown in Fig. 12. The RCM mechanism is gravity compensated by the same procedure followed for gravity compensating the master arm. The very first link of the RCM mechanism offers an access point to add a countermass. The residual imbalance present in the RCM mechanism after balancing is countered by the back driving torque presented by the roll and pitch DoF motors (Maxon EC-max 30 with GP32 planetary gearbox). The integrated encoders present in the motors help track the position of the joints. Weight reduction was carried out to have a structure close to as fully stressed as possible. The linear motion of the surgical tool is facilitated by a linear drive mechanism shown in Fig. 13. The linear drive is tether driven to keep the inertia to a minimum, and the motor for the linear drive is placed behind the RCM mechanism. A slot was provided in the link that carries the balancing mass to vary the position of the mass. This is to make up for uncertainty in the final mass of the surgical tool caused due to additional items such as wires and printed circuit boards.

The RCM mechanism carries the pitch motor on the base link, and this affects the counterbalancing of the mechanism. Also, the entire RCM mechanism is offset from the roll axis, as described before.

Hence, the imbalance caused by the RCM offset and the pitch motor is corrected by a separate countermass attached to the base of the RCM mechanism, as shown in Fig. 13(a).

Tooltip selection and integration. Three different concepts for the surgical tooltip design were proposed in the earlier section. Table 2 presents the relative merits and shortcomings of these designs and is used to select a suitable tooltip design to be integrated into the tele-operated surgical robot. It can be seen from Table 2 that the only shortcoming of the conventional mechanism-based tool is its need for sterilization postsurgery. Other than that, this design has the lowest hand length offering and the smallest swept volume inside the operating field. The design also has the highest grasping force, large range of motion and the smallest diameter of the three designs. Hence, this design is implemented in the tele-operated surgical robot.

Surgical tool assembly. The selected surgical tool wrist is assembled into a fully functioning tool and is integrated into the RCM mechanism. As described before, the tether-based transmission is favored because of its compactness, ease of preloading for backlash-free operation and ability to be routed through complex pathways. Figure 14 shows a half section view of the complete tool and the tether routing from the drive box through the tool shaft to the tool wrist. The tool has a hollow shaft of diameter 12 mm and a wall thickness of 1 mm. The tool has four integrated motors placed at its distal end (Maxon™ EC-max16 with a GP16A planetary gear reduction). The drive motors are placed with their longitudinal axes parallel to the tool shaft and are stacked in two layers to minimize the volume of the drive box, as shown in Fig. 14. More details on the drive arrangement can be found in our earlier publication [39].

Central control unit. The central control unit houses the motor drivers (EPOS2 (24/5) from Maxon™) for six drive actuators (roll, pitch and translatory DoF) of the two slave arms, a field programmable gate array (FPGA) myRIO 1900 from National Instruments for the controller, and a switched-mode power supply unit (Quint PS 24/20 from M/s Phoenix Contact). The forward kinematics is programed using LabVIEW and ported to myRIO. The inverse kinematics is run on a Windows-based personal computer with LabVIEW systems engineering software.

The rest of the drive actuators (8 for both the surgical tools) is mounted directly over the surgical tools to reduce wiring complexity.

System control architecture. Unilateral tele-operation of the robotic surgical system is shown in Fig. 15. The FPGA controller reads digital inputs from the master arm joint encoders, performs forward kinematics, and sends the motion command through USB communication to a Windows-based personal computer. There is a real-time LabVIEW code that performs the inverse kinematics of the slave arm manipulator. The FPGA controller provides the position and orientation data input for the inverse kinematics. The joint angles for the slave arm are sent through USB communication to one of the motion controllers of the slave arm. The motion controllers communicate with each other by a daisy-chained CAN communication protocol. Various controls such as clutching/declutching the master and slave and scaling of movement can be done using a Graphical User Interface developed using LabVIEW.

Camera arm. A circular prismatic joint based RCM mechanism [40] functions as the camera arm. This arm was designed to carry an endoscopic camera to obtain images from the surgical site. The camera arm maintains the kinematic constraint at the point of insertion. The pitch and roll DoF of the camera are passive and can be manually adjusted to the desired orientation and locked in place. A motor powers the in and out linear motion of the camera about the insertion axis and is controlled by foot pedal located at the surgeon's console. The camera arm is counterbalanced for added safety, as shown in Fig. 16.

Complete system integration. A pair of master arms and slave arms are integrated to form the complete tele-robotic setup, and the finished prototype is shown in Fig. 17. Figure 17(a) shows an operator at the command of the master arm, and Fig. 17(b) shows a simple suturing procedure carried out on a silicone polymer specimen using the system. The fully assembled, tele-operated surgical robot is shown in Fig. 17(c). It can also be seen from Fig. 17(c) the placement of the camera arm in between the two slave arms.

Modal analysis. Since the surgical tool is cantilevered at the end of the slave arm, it is imperative to know the natural frequencies of the slave arm as the vibration of the slave arm would lead to objectionable movement of the tooltip. The natural frequencies of the slave arm are a function of the material, geometry, and its kinematic configuration. MA was carried out on the slave arm to identify the natural frequencies of the slave manipulator in various configurations. For practical purposes, it is enough to know the first three mode shapes of the slave arm for a given configuration. MA was carried out using standard commercial FEA software to obtain the Eigen frequencies of the slave arm and corresponding deflections. Since the slave arm has hundreds of components in its various subassemblies, a separate CAD model of the slave arm was made by lumped body approximation for the analysis. The effect of gravity was also included in the analysis. Contact between connecting elements (passive joints, bearings) in the slave arm assembly and stiffness between them were defined in the FEA model.

Since the positional accuracy of the surgical tooltip is most important in any surgical procedures, the mode shapes of the surgical tool are given prime importance in the analysis. The configurations for the modal analysis are chosen based on the dexterous workspace [20] for the RCM mechanism in typical surgical procedures. MA was carried out for different configurations of the RCM mechanism within the dexterous workspace. A representative image of the first mode shape ($ω1$ = 32.828 Hz) for one of the configurations (roll = 0 deg and pitch = 90 deg) is shown in Fig. 18. The legend in the figure shows the resultant amplitude of vibration in mm.

The minimum fundamental frequency at which the tooltip starts to vibrate is at $ω1$ = 29.5 Hz for a pitch and roll of 90 and 45 deg, respectively. The deflection of the tooltip was around 1 mm. All other frequencies at which the tooltip vibrates are well above 40 Hz for different configurations of the slave arm. The input movement command for manipulation of the slave arm for surgical tasks has a frequency content of less than 2 Hz [42]. In contrast, the tremor from surgeons' hand will be typically between 8 and 12 Hz region [43]. Therefore, the chances of exciting the natural frequency of the system are low, and vibration due to resonance was not observed during testing of the system.

Testing. The position tracking of the slave in 3D task space is a metric to assess the performance of the system. To evaluate the system performance such as master–slave position tracking, a circular like trajectory was drawn with the master arm, as shown in Fig. 19. The position tracking by the slave is also shown in Fig. 19. The motion of the tooltip in each of the individual Cartesian coordinates (x, y, and z) is shown in Figs. 20(a)20(c), respectively. The root-mean-square error in tracking between the master and slave for the x, y, and z axes was 0.0092 m, 0.0034 m, and 0.0034 m, respectively, for the circular input trajectory.

## Discussion

The key focus of this work is the design and development of a tele-operated robotic system that has mechanical systems with simplified kinematics and novel designs for the surgical tool wrist based on compliant and conventional mechanisms. It was demonstrated in a laboratory environment to address the prevalent problem of biofouling by using a model of a single-use surgical tooltip constructed by contact aided compliant flexure and novel hybrid serpentine flexure. The proposed magnetic flux coupling mode of power transmission for operating the surgical tooltip is first of its kind. It opens up new methods of conveying motive power to operate the instrument wrist. The tracking error between the master and slave can be attributed to the system being not calibrated and the use of nylon tethers (low stiffness) for the capstan drive of the master arm and the surgical tool due to component sourcing limitations. One of the key learnings we had from the system development is that proper planning of wire routing should have been done from the initial stages of development. We faced considerable challenges in electrical wiring of the entire system as this impacts both the system dynamics (increased joint stiffness imposed by wires) and the complexity of the system. Proper placement of motor drivers would go a long way in simplifying this issue. One of the key objectives of the paper was reducing the mechanical complexity of the system. Therefore, the cost of the system was also minimized.

## Conclusion

The work presented in this paper demonstrates the realization of a complete tele-operated surgical robot with the use of basic mechanisms available in the literature. The work also presents the development of a sophisticated system with limited resources. This opens up the gateway for development of low-cost systems with adequate functionality for developing economies in future. Experimental laboratory testing of the system demonstrates the potential and viability of the system for actual surgical procedures. Some key conclusions that can be arrived from this work are as follows

1. The proposed decoupled DoF wrist provides a surgical tool design with an easier control strategy. The guidelines and optimization methodology for tether routing presented in the work serve as design guidelines for the optimal design of tether driven minimally invasive robotic surgical instruments.

2. The proposed gravity compensation methodology for static balancing of a master manipulator and the RCM mechanism is simple but effective. The imbalance due to gravity for the master and slave arms was reduced by 80% and 85%, respectively.

3. The master arm manipulator design uses a fewer number of balancing masses and provides required workspace with good stiffness of the structure.

4. Use of compliant mechanisms for robotic surgical tool design greatly simplifies mechanical complexity and provide reliable and maintenance-free design.

5. New flexures with improved characteristics proposed in this work add to the database of flexures in literature. The concept of single-use compliant mechanism based surgical tooltip opens up a new approach of addressing the problem of biofouling that plagues minimally invasive surgical procedures.

The entire paper serves as a case study for establishing guidelines for the development of a full-fledged tele-operated surgical robot. The single-use compliant mechanism based surgical tooltip solves the problem of biofouling; however, it has limited force exertion capability to be useful in any surgical procedure. Further design iterations are needed to improve the force-carrying ability of the tool wrist design using a compliant mechanism-based approach. For the surgical tool design that uses magnetic flux linkage for power transmission, an alternate arrangement of placing magnets like Halbach array can be investigated to improve the force that can be transferred through the magnetic flux linkage. At least one of the closed-loop parallel linkages of the master arm manipulator can be replaced with synchronous transmission to simplify the mechanical construction with identical kinematics to the existing design. This would reduce the inertia of the master arm further and reduce the mechanical complexity of the master arm. Due to manufacturing and material availability constraints, nylon tethers were utilized for power transmission of the surgical tool and the master arm. The nylon tethers can be replaced by Dyneema® or high strength stainless steel rope for improved force characteristics of the surgical tool. Haptic feedback can be provided to the system with accurate identification of surgical tool dynamics even when the force sensor is placed outside the patient's body [44]. The system as such does not have redundancy for any of the subsystems, components, software, etc., which is critical for any surgical system and need to be addressed in future developments.

## Funding Data

• Department of Science and Technology, Government of India (IDP/MED/2010/28; Funder ID: 10.13039/501100001409).

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