Existing robotic surgical platforms face limitations which include the balance between the scale of the robot and its capa- bility in terms of range of motion, load capacity, and tool manip- ulation. These limitations can be overcome by taking advantage of ﬂuid power as an enabling technology with its inherent power density and controllability. As a proof-of-concept for this ap- proach, we are pursuing the design of a novel, dexterous robotic surgical tool targeted towards transgastric natural oriﬁce surgery. The design for this hydraulic surgical platform and the cor- responding analysis are presented to demonstrate the theoretical system performance in terms of tool positioning and input re- quirements. The design involves a combination of a novel 3D valve, hydraulic artiﬁcial muscles, and multi-segmented ﬂexible manipulator arms that ﬁt in the lumen of an endoscope. A dy- namic model of the system is created. Numerical simulations show that a hydraulic endoscopic surgical robot can produce the desired performance without using large external manipulators such as those employed by conventional surgical robots. They also provide insight into the component interactions and input response of the system. Future work will include manufacturing a prototype to validate the concept and the numerical models. NOMENCLATURE A0The oriﬁce area of the control valve inlet oriﬁce. AfThe curtain area at the controlled valve outlet. Address all correspondence to this author.bThe length of each strand within the braided sheath of an artiﬁcial muscle actuator. Cd0The discharge coefﬁcient of the control valve inlet oriﬁce. Cd f The discharge coefﬁcient of the valve outlet. DThe diameter of the artiﬁcial muscle actuator. DNThe ﬁxed diameter of the valve outlet. EElastic modulus of the manipulator backbone material. FaThe contractile force produced by the artiﬁcial muscle actu- ator. FbForce load at the distal end of the manipulator due to beam deformation. FLExternal force load applied at the distal end of the manipu- lator. FxTotal load in the transverse direction at the distal end of the manipulator. FzTotal load in the longitudinal direction at the distal end of the manipulator. gThe gap between the oriﬁce face and the ﬂapper within the control valve. gThe angle of each strand of the braided sheath measured rel- ative to the longitudinal axis of the actuator. ISecond moment of area of the manipulator backbone. IbMoment of inertia at the distal end of the manipulator. LThe length of the manipulator backbone. LaThe overall length of the artiﬁcial muscle actuator. MTotal moment at the distal end of the manipulator. mMass at the distal end of the manipulator. MbInternal moment of the beam.ASME 2012 5th Annual Dynamic Systems and Control Conference joint with the JSME 2012 11th Motion and Vibration Conference DSCC2012-MOVIC2012 1 Copyright © 2012 by ASMEDSCC2012-MOVIC2012-8685October 17-19, 2012, Fort Lauderdale, Florida, USA MLExternal moment load applied at the distal end of the ma- nipulator. nThe number of turns completed by one strand within the braided sheath of an artiﬁcial muscle actuator. PaThe internal pressure of the artiﬁcial muscle actuator mea- sured relative to the external pressure. PE Potential energy within the beam for any arbitrary beam shape. PsThe supply pressure provided to the control valve. QaFlow rate of ﬂuid entering or exiting the actuator. Q1Flow rate of ﬂuid entering the control valve. Q2Flow rate of ﬂuid passing through the controlled ﬂow re- striction and exiting the control valve. rRadius of the routing discs on the manipulator backbone. rDensity of the ﬂuid. sPosition coordinate along the manipulator backbone. Varies from 0 to L. qAngular orientation of the beam cross-section. VThe internal volume of the artiﬁcial muscle actuator. xBeam position in the transverse direction. zBeam position in the longitudinal direction. INTRODUCTION Robots have been used in surgery since approximately 1985 when Shao et al. used a robot designed for industrial applica- tions to perform a neurosurgical biopsy [1, 2]. Since that time, the ﬁeld of surgical robotics has undergone many changes as the procedures performed with the aid of robots have become less invasive and more complex. Current developments in sur- gical practice are leaning increasingly towards endoscopic tools and techniques [3]. For surgical robots to adapt to these devel- opments, it is necessary to overcome signiﬁcant challenges in terms of tool manipulability and precision. Most systems rely on a large external robot manipulating cable driven tools. Due to hydraulics’ advantages in power density and relative incom- pressibility [4], hydraulics may allow surgical robotics to be em- bedded endoscopically. Yet, the use of hydraulics in this ﬁeld has been under-explored due to difﬁculties associated with the inte- gration of hydraulic components into the distal end of the robotic manipulator due to size constraints [5]. For hydraulic actuation to be employed advantageously in an intuitive robotic minimally invasive surgical platform, some barriers need to be overcome: small size, realization of multi- ple degrees of freedom, and achieving the range of force and motions necessary to perform procedures effectively. To take advantage of the existing infrastructure of endoscopic devices, the new surgical tools must be constrained to an overall outer diameter of 5-6 mm based upon existing endoscopic tool chan- nel sizes. Fluid power components of this scale are not availablecommercially. Work is currently in progress exploring the use of hydraulic ﬂuid power at the meso-scale (mm to cm) for use in prosthetics [6] and at the micro-scale ( µm to mm) for which the research is ongoing in the ﬁeld known as microﬂuidics [7]. However, as pointed out by Love et al., there exists a gap be- tween conventional ﬂuidics and microﬂuidics that includes the type of high pressure-low ﬂow rate ﬂuid power components that would be necessary for the application of hydraulic power to the ﬁeld of surgical robotics [6]. In addition to the size constraints placed upon the surgical device, it is also necessary to consider the force requirements of typical procedures encountered in the operating room. Pre- liminary evaluations of these constraints based upon the mea- surement of force requirements for organ manipulation and su- turing tasks have revealed that a tool load capacity in the range of ﬁve Newtons is sufﬁcient for the majority of common usage cases [8]. Further, it is desirable that the robotic manipulator be able to achieve full retroﬂexion to enable the level of dexterity necessary for complex surgical procedures. The robotic surgical platform proposed here is being de- signed to meet these requirements while maintaining a smaller footprint than conventional surgical robots. By meeting these re- quirements through the use of hydraulics, it is possible to develop a more capable endoscopic surgical robot which can be pack- aged in a compact way. This technology would allow the robotic manipulator to exhibit greater freedom of motion, have better controllability, be more cost effective, and have superior ease of mobility. Hydraulic actuation typically displays greater stiffness and faster response time than the comparable electromechanical or pneumatic counterparts. When compared with a pneumatic approach, hydraulic power provides less susceptibility to leak- age and is a safer choice if leakage were to occur. Thus hy- draulic power can be safely operated at a higher pressure than a similar pneumatic system. Further, if a compatible hydraulic ﬂuid is selected, such as saline, leakage is not likely to result in contamination of the abdominal cavity. Lastly, the low costs of the components used in this design would permit the device to be one time use and thus loosen requirements for sterilization. Similar work in this area has explored the use of contin- uum manipulators ranging from pre-curved tubes or electrome- chanical, tendon-driven manipulators for surgical applications to pneumatic McKibben actuators for large-scale object manipula- tion [9–11]. One particularly interesting example is the combi- nation of pneumatic actuation with a precurved concentric tube manipulator for surgical treatment of epilepsy [12]. This work demonstrates the feasibility of a ﬂuid power approach; however, the robotic control unit is too large for internal abdominal ac- cess with an endoscope. Additionally, there is a long history of hyperredundant robots consisting of a multitude of rigid links providing similar yet distinct operating characteristics [13, 14].2 Copyright © 2012 by ASME Our proposed design builds from these similar solutions in order to provide improved performance and miniaturization for surgi- cal robotics. In particular, we propose a combination of a novel 3D valve, hydraulic (e.g. saline) actuated McKibben muscles, and ﬂexible manipulators to take advantage of the possible high power density and low compressibility of hydraulics. The remainder of this paper ﬁrst describes the proposed de- vice design including particular details of the arrangement of the device components and an overview of the novel control valve design. Next, analysis of each of the components is presented as well as a description of the theoretical behavior of the de- vice based upon this analysis. Finally, some conclusions are dis- cussed as well as a proposal for future work. PLATFORM DESIGN AND ANALYSIS The proposed surgical robotic platform consists of three ba- sic units: manipulators, actuators, and control valves. All com- ponents are designed to be located at the distal end of the endo- scope and contained within its working channel whose diameter is6mm. Figure 1 shows a simpliﬁed version with two manip- ulators. Each manipulator can be divided into multiple serially connected segments with a single ﬂexible backbone and is actu- ated by a set of tendons/cables, similar to other serpentine like robots [15–17]. The bending of each manipulator segment is controlled by a group of three tendons antagonistically operated by hydraulic artiﬁcial muscle actuators at the base of the plat- form. The tendons, which are arranged circumferentially, pass through intermediate discs and terminate at the end of the given segment. The tensions in the tendons control the bending of the segment in 2-degrees of freedom. Unlike cable driven sur- gical tools that are actuated via long cables by external motors or actuators, here, the tendons are kept relatively short since the muscle actuators in our design are small enough to be stacked serially and placed distally within the lumen of the endoscope. Hydraulic ﬂow/pressure to the muscle actuators are modulated by valves which are also contained within the endoscope behind the muscle actuators (Fig. 2). Thus the only connections re- quired externally are lines for the hydraulic supply (assumed to be a constant pressure supply) and return, and electronic signal wires. In the following sections, the individual system components are presented and modeled. They are then assembled into a sys- tem model. The model can be simulated to evaluate the design. For simplicity of presentation, in the rest of the paper, instead of the general three dimensional situation, we consider only the planar case in which each manipulator segment has one DOF of bending and requires only two tendons and actuators for each segment. A similar methodology can be easily extended to the 3D case. Figure 1. MODEL OF THE ROBOTIC SURGICAL TOOL DESIGN. Backbone Mechanics The use of a continuous backbone for cable driven robots has been well documented in the literature [10,14–17]. Here, the backbone of each manipulator segment is modeled as an Euler- Bernoulli beam which is cantilevered at the base. Assuming that the position and orientation of the distal end is given, we wish to determine the shape and the beam reaction force and moment acting on the end-effector at the distal end of the beam. We as- sume that the number of discs along the actuator tendons are sufﬁciently large so that each tendon can be considered to be par- allel to the beam at a distance r. This way, the tendons present loading on the beam only via the terminal disc but not via the intermediate discs. One method of modeling the deformation of a robot with a continuous backbone is to use an energy formulation [18]. The basis of this method is that of all the shapes that satisfy the end point conﬁguration, the continuous backbone with negligi- ble mass will assume the shape with the least potential energy. Knowing this shape for the speciﬁed location and orientation of the distal end of the beam, it is then possible to calculate the resulting load applied at the distal end of the beam. This in- verse kinematics model assumes planar bending and neglects the effects of the mass of the beam itself [15, 17]. Further, it is as- sumed that the beam stiffness is such that only bending occurs and the beam does not shear or stretch. Lets2[0;L]denote the distance along the beam of length L, andq(s)be the angular orientation at location s.q()is de- scribed by a smooth parameterized curve with sufﬁcient degrees of freedom. The potential energy stored within the beam can be expressed as PE(q(s)) =1 2ZL 0EIq0(s)2ds (1)3 Copyright © 2012 by ASME Figure 2. LINE DRAWING SHOWING HOW THE VALVE, ACTUATOR, AND TENDON COMPONENTS ARE CONNECTED. where Iis the second moment of area, Eis the elastic modu- lus, and Lis the length of the beam segment. The beam shape is speciﬁed as a n-degree polynomial parameterization of q(s). Assuming that the location and orientation of the distal end of the beam are speciﬁed as inputs such that xend,zend, andqendare known. As axial and transverse strain are neglected, x(s)and z(s)can be speciﬁed as functions of q(s)such that x(s) =Zs 0cos(q(s))ds;s2[0;L] (2) z(s) =Zs 0sin(q(s))ds;s2[0;L] (3) Beam shape is then given by the constrained optimization of the potential energy of the beam subject to boundary conditions at s=L, x(L) =xend;z(L) =zend;q(L) =qend (4) and at s=0 q(0) =0 (5) An example of the output from this model is shown in Fig. 3. Inputs to the model were 30 mm for both the tangential and longitudinal tip positions and an angle of 10for the tip orien- tation. Here, a high order polynomial is used to parameterize q(s). The optimization then produces a result that meets those end conditions and minimizes the strain energy in the beam. Once the potential energy of the beam has been minimized using an optimization algorithm, the beam shape is known and the end load can be calculated. This is done by approximating the internal moment of the beam as a function of q(s)as Mb(s) =EIq0(s) (6) Figure 3. EXAMPLE BACKBONE MODEL OUTPUT FOR ARBITRARY INPUT PARAMETERS. Then the moment load at the distal end of the beam is just Eq. (6) evaluated at s=L. By taking moments at two locations on the beam (e.g. s=0 and s=L=2), the resulting force (Fb;x;Fb;z) can be calculated as  Mb(0)Mb(L) Mb(s)Mb(L) = (z(L)z(0))x(L)x(0) (z(L)z(s))x(L)x(s) Fb;x Fb;z (7) Alternately, (Fb;x;Fb;z;Mb(L))can be computed from the La- grange multipliers corresponding to the constraints in Eqs.(4). Artiﬁcial Muscle Actuator Modeling Although hydraulic actuation offers high power density, me- chanical rigidity and high dynamic response, the force capability of a conventional linear hydraulic actuator is limited by the pis- ton area, F=PA. In view of the stringent diametric require- ment of the present application, we explore the use of hydraulic artiﬁcial muscles [19] which can be shown to have better peak4 Copyright © 2012 by ASME Figure 4. ARTIFICIAL MUSCLE ACTUATOR GEOMETRY (LEFT) AND MAGNIFIED VIEW OF THE BRAID GEOMETRY (RIGHT). force capability than conventional linear actuators for the same pressure and diameter. Artiﬁcial muscle actuators consist of a contained internal bladder, surrounded by a ﬂexible, braided outer sheath. It is the geometry of this outer sheath that transmits the radial expan- sion of the internal bladder due to applied pressure to contractile force along the longitudinal axis of the muscle actuator rather than elongation as in a traditional hydraulic actuator. The load capacity of the artiﬁcial muscle actuator is then a function of the geometry and orientation of the outer sheath and the pressure applied to the internal bladder. This makes it possible to achieve greater peak load capacity for the same cross sectional area [20]. Typically, artiﬁcial muscles are actuated pneumatically with compressed gas [11, 12, 21, 22]. In our approach, the artiﬁ- cial muscles are actuated hydraulically with a pressurized liq- uid. There are two important advantages: 1) a higher pressure can be applied so that force and power density can be further in- creased and the actuator diameter can be decreased; 2) liquid has a much lower compressibility and therefore better rigidity than compressed gas. As shown in Fig. 4, adapted from Chou and Hannaford, it is ﬁrst necessary to deﬁne the geometric parameters of the braided sheath [20]. These parameters include the length of the individ- ual braided strands, b, the number of turns each strand makes over the length of the actuator, n, and the angle between the strands and the longitudinal axis of the actuator, g(t). The overall length of the actuator, La(t), and the actuator diameter, D(t), can then be represented in terms of the constants, nandb, and as functions of the variable g(t), as seen in Eq. (8)and Eq. (9). La(t) =bcosg(t) (8) D(t) =bsing(t) np(9) Then, calculating the volume of a cylinder and substituting in the functions for LaandD, V(t) =pD(t)2La(t) 4=b3 4pn2sin2g(t)cosg(t): (10) The ﬁrst derivatives of La(t)andV(t)with respect to g(t)are calculated as dLa(t) dg(t)=bsing(t) (11) dV(t) dg(t)=b3sing(t) 2pn2(cos2g(t)1 2sin2g(t)) (12) From Eq. (11) and Eq. (12), the ﬁrst derivative of V(t)with respect to La(t)is given as dV(t) dLa(t)=dV(t)=dg(t) dLa(t)=dg(t)=b2 4pn2(3cos2g(t)1): (13) From the principle of virtual work we have: Fa(t)dLa(t) =Pa(t)dV(t) (14) and solving Eq. (14) for the force output with Eq. (8 and 13) results in Fa(t) =Pa(t)b2 4pn2 3La(t)2 b21 (15) =Pa(t)pD(t)2 43cos2(g(t))1 sin2(g(t)) (16) where Fais the contractile force and Pais the pressure differential across the bladder wall. Because the term within the brackets in5 Copyright © 2012 by ASME Eq. (16) can be greater than 1, the force capability of a artiﬁcial muscle can be greater than that of a hydraulic piston actuator for the same area and pressure. Notice, however, that this advantage comes with the price that the force/pressure relationship varies withg(t)or actuator length La(t). Because the actuator is connected to the terminal disc of the backbone via the tendon, the length of the actuator, La(t)can be determined by the change in the tendon length as the manipulator bends. The actuator length is given by: La(t) =La0rq(L) (17) where La0is the length of the actuator when the manipulator is straight (i.e. q(s) =0 for all s2[0;L]), and ris the radius of the routing disc. Reﬁnements to this basic model have been presented in the literature; however, given the actuator size and pressure used in this application, the basic model provides sufﬁcient accuracy to gain an understanding of the theoretical system performance [20–22]. This analysis suggests that it is possible to achieve the design requirement of ﬁve Newtons at the distal end of the manipulator using a relatively modest operating pressure of 700 kilopascals while staying within the size constraints of the endo- scope working channel. Control Valve In order to achieve precise manipulation, it is necessary to obtain a control valve that will provide a controllable ﬂuid ﬂow rate and pressure while occupying as little space as possible within the device. A review of the available commercial valves and common micro-ﬂuidic valve solutions was conducted and no existing valve design was found suitable for the present applica- tion due to the limitations of high supply pressure, proportional control, and method of activation. Therefore, development of a novel control valve (see model in Fig. 5) capable of manipulat- ing high pressure ﬂows on a small scale is in progress. The basic concept being employed is a ﬂapper-style valve which acts as a pressure divider to control the proportion of the supply pressure that is applied to the internal bladder of the actuator. For size comparison, a ﬁrst generation prototype of the valve is shown in Fig. 6. Each manipulator segment is driven by a hydraulic circuit of the form shown in Fig. 5. It consists essentially of three ﬂapper nozzle valves [23] controlled by one single tetrahedral valve plug that plays the role of the ﬂapper. The valve is normally open thus permitting ﬂow to bypass the actuator and dump to the return line. The tetrahedral shaped valve plug can move both in plane and out of plane. When the valve plug is activated in a particu- lar direction in the plane, the oriﬁces are activated differentially: Figure 5. HYDRAULIC CIRCUIT AND MODEL OF PHYSICAL REAL- IZATION OF VALVE DESIGN. the oriﬁce(s) that the plug gets closer to become more restrictive, and the corresponding actuator pressures increase; the oriﬁce(s) that the plug get further again become less restrictive, and the corresponding actuator pressures decrease. This in turn realizes a directional actuation of the manipulator to bend in the direction where the oriﬁces become more restrictive. Out of plane move- ment of the valve plug pressurizes or de-pressurizes the actuators simultaneously. This has the effect of increasing or decreasing the manipulator stiffness. This style of valve has the advantages of low complexity and insensitivity to contaminants in the ﬂuid [23]. However, since it is difﬁcult to achieve complete closure of the oriﬁce, the system must be able to accommodate some leakage. This presents little concern as the ﬂow rate required to inﬂate the actuators is sig- niﬁcantly smaller than the available ﬂow rate of the supply, ﬁve liters per hour based on actuator ﬁll time versus 55 liters per hour based on available ﬂow rate for endoscopic irrigation pumps, re- spectively [23,24]. The valve consists of a single supply pressure input which feeds three downstream oriﬁces. The central plug is manipulated electromagnetically by three independent control signals. The plug can be manipulated to block each downstream oriﬁce individually, in pairs of two, or all three depending on how the control signals are applied. When an oriﬁce is blocked, pressure increases at the feed point for the corresponding actua- tor. Conversely, when the oriﬁce is unblocked, ﬂow passes to the6 Copyright © 2012 by ASME Figure 6. PHOTOGRAPH OF FIRST GENERATION VALVE PROTO- TYPE. return line and pressure at the actuator feed point decreases. Fig- ure 7 shows one third of the ﬂow path when the variable oriﬁce is open (top) and when the oriﬁce is blocked (bottom). In the open position, ﬂow passes through the valve following the least resis- tance path and exits to the return line. When the variable oriﬁce is blocked, the path to the return line has a high ﬂow resistance and thus the ﬂuid ﬂow is directed into the actuator. In the steady-state condition when no ﬂow passes to the ac- tuator, the upstream and downstream ﬂow rates become equal and the equations simplify to Pa Ps=" 1+Cd fAf Cd0A02#1 (18) This relationship is shown in Fig. 8 [23]. This plot shows that there is large region of approximately linear response between 0.4 and 1.6 for the oriﬁce ratio. Further, it can be seen that the pressure response ﬂattens out an oriﬁce ratio of approximately 3.0, meaning that this is a reasonable upper limit placed on the size of the ﬂapper valve exit area relative to the upstream ﬂow restriction. The valve design is modeled as a ﬂapper style valve and thus the ﬂow through the upstream oriﬁce for each oriﬁce ( Q1) and the downstream valve oriﬁce ( Q2), shown in Fig. 5, is calculated in Eqs. (19) and (20). Q1=A0Cd02 r(PsPa)1 2 (19) Figure 7. MODEL OF CONTROL VALVE SHOWING PART OF THE FLOW PATH FOR BOTH OPEN (TOP) AND BLOCKED (BOTTOM) VARI- ABLE ORIFICE CONDITIONS. Q2=AfCd f2 rPa1 2 =pDNgCd f2 rPa1 2 (20) Here it is shown that the upstream ﬂow rate is consistent with the standard oriﬁce equation while the downstream ﬂow exiting the downstream oriﬁce is restricted by the ﬂapper. In this case the curtain area ( Af) rather than the nozzle area is used in the ﬂow rate calculation. The curtain area is equivalent to pDNg, where DNis the oriﬁce diameter and gis the gap between the oriﬁce and the ﬂapper. Further, the discharge coefﬁcient for the ﬂapper oriﬁce ( Cd f) is typically on the order of 0 :8Cd0[23]. Additionally, the ﬂow rate to or from the actuator must sat- isfy the difference between the upstream and downstream ﬂow rates as in Eq. (21). Qa=Q1Q2 (21) Thus, since Qais equal to ˙V(t)under the incompressibility as- sumption, actuator pressure, Pa(t), can be found by combining Eq. (19, 20, and 21) with Eq. (10).7 Copyright © 2012 by ASME Figure 8. PLOT OF PRESSURE RATIO VERSUS ORIFICE RATIO FOR A FLAPPER VALVE. System Modeling A model of the system was developed in MAT- LAB/SIMULINKR (The MathWorks Inc.) as a combination of the models described in the previous sections. The current model assumes planar bending and doesn’t take into account de- formation due to beam mass. It is assumed that an end-effector is placed at the distal end of the manipulator. A force and moment balance is applied to the end-effector mass, treated as a free body as shown in Fig. 9. Loads applied to the end mass originate from the actuators, the reaction load from the backbone, and from any external loading due to tissue manipulation or collision as shown in Eq. (22-24). The system components are coupled together through both hydraulic and geometric relationships. The control valve supplies pressure directly to the actuators. Each actuator is coupled to a tendon which in turn is routed along the manipulator backbone. Backbone shape directly determines relative length of each actuator. Thus, actuator length is combined with pressure from the control valve to calculate load applied to the distal end of the manipulator. åFx=m¨x=Fb;x+FL;x+Fa1;x+Fa2;x (22) åFz=m¨z=Fb;z+FL;z+Fa1;z+Fa2;z (23) åM=Ib¨q=Fa1rFa2rMbML (24) Figure 9. FREE BODY DIAGRAM FOR MASS AT DISTAL END OF THE MANIPULATOR. Figure 10. SIMPLIFIED BLOCK DIAGRAM OF SYSTEM MODEL. As shown in Fig. 10, translational and rotational inertial dy- namics form the basis of the model and allow for calculation of the location and orientation of the distal end of the manipula- tor due to applied control. From this model, it was possible to determine system response for a single segment manipulated in planar bending by a single actuator. The result is shown in Fig. 11, where actuator pressure denotes the pressure at the feed point to the activated actuator and tip orientation is the angular orien- tation of the distal tip of the manipulator. The tip orientation is zero when the manipulator is straight and has no deformation. The plot shows that under the ideal unloaded conditions, the tip orientation approached 180, corresponding to full retroﬂexion as speciﬁed in the design requirements, as the pressure at the ac- tuator feed point approaches 200 kilopascals. This shows that the desired beam deﬂection can be achieved with approximately 30 percent of the proposed supply pressure when no load is ap- plied to the manipulator. It was found that the dynamics of this model was limited by the ﬂow rate of the valve rather than the inertia of the manipulator due to low mass and low moment of inertia at the distal end, on the order of 10.2 milligrams and 16.2 mgmm2, respectively. The valve oriﬁces are on the order of 0.3 mm in diameter for both the upstream and downstream oriﬁces sized to achieve both sufﬁcient ﬂow rate and appropriate valve control. The entire motion of the manipulator was completed in8 Copyright © 2012 by ASME Figure 11. PLOT OF TOOL TIP ORIENTATION VERSUS ACTUATOR PRESSURE. Figure 12. PLOT OF PLANAR BEAM DEFLECTION FOR INCREAS- ING ACTUATOR PRESSURE WITH NO EXTERNAL LOAD. less than half of one second. This time was determined to be suf- ﬁcient for most applications, especially true when considering that most applications will not require full retroﬂexion. The range of motion for a single segment manipulator with no external loading is then deﬁned by the sweep between the undeformed conﬁguration and the fully deformed conﬁguration as shown in Fig. 12. This sweep range can be rotated around the longitudinal axis of the undeformed manipulator in order to project the workspace into the third dimension.CONCLUSIONS AND FUTURE WORK This paper provides a ﬁrst look at our current work on the development of a hydraulic platform for minimally invasive sur- gical procedures. The primary beneﬁt of this approach is that the control and actuation components are all located within the distal end of the endoscope while meeting requirements of com- mon surgical procedures. To achieve this, a novel design for a ﬂow control valve has been introduced. A basic approach to the modeling of each of the components of this surgical manipulator has been presented and assembled into a system model in order to assess the performance of the system as a unit. Future work will include the development of a more com- plete model which allows for three dimensional deformation. Further, a prototype of this design is being produced in order to validate the model and demonstrate the feasibility of ﬂuid power for driving a serpentine manipulator for minimally inva- sive surgery. Development of an appropriate control approach will be necessary to achieve precise positioning of the manip- ulator. While the present work uses transgastric natural oriﬁce surgery as a case study to deﬁne the design constraints, it is ex- pected that the device will be suitable for a variety of surgical ac- cess methodologies including laparoscopies, laparotomies, and single port access surgeries. ACKNOWLEDGEMENTS This work is supported by the University of Minnesota, In- stitute for Engineering in Medicine (IEM) Seed Grant program.