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# Current Directions in Biomedical Engineering

### Joint Journal of the German Society for Biomedical Engineering in VDE and the Austrian and Swiss Societies for Biomedical Engineering

Editor-in-Chief: Dössel, Olaf

Editorial Board: Augat, Peter / Buzug, Thorsten M. / Haueisen, Jens / Jockenhoevel, Stefan / Knaup-Gregori, Petra / Kraft, Marc / Lenarz, Thomas / Leonhardt, Steffen / Malberg, Hagen / Penzel, Thomas / Plank, Gernot / Radermacher, Klaus M. / Schkommodau, Erik / Stieglitz, Thomas / Urban, Gerald A.

Open Access
Online
ISSN
2364-5504
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Volume 1, Issue 1

# Design and control of a 3-DOF hydraulic driven surgical instrument

Timo Cuntz
/ Laura Comella
Published Online: 2015-09-12 | DOI: https://doi.org/10.1515/cdbme-2015-0036

## Abstract

Although the use of minimally invasive surgery techniques has steadily increased, the development of new tools for these procedures has stagnated. Indeed a new generation of surgical instruments, with tips that have multiple degrees of freedom, has been developed. However, they are facing so many technical problems that none have been able to establish themselves in the medical market. To overcome the problems these instruments are facing, a micro hydraulic power transmission system has been developed and been presented in [1]. With these driving units it was possible to design an instrument for minimally invasive surgery with a tip which is movable in 3 degrees of freedom (DOF) and that is light in weight, small in size and powerful in movements and gripping. This paper presents the mechanical setup (including dimensions and materials), describes the theoretical basis for the control with the inverse kinematic model, discusses the external drives setup and gives first performance data of this novel hydraulically actuated laparoscopic instrument with 3 degrees of freedom.

## 1 Introduction

Surgical techniques have seen major developments over the last two decades, with the role of laparoscopy having an increasingly relevant place in modern medicine. The reasons for its success are the advantages for the patients, such as reduced haemorrhaging and smaller incisions, which in turn reduce pain and shorten recovery time [2, 3]. However, the tools and instruments for laparoscopic surgery have not kept up with this progress. The equipment setup in this domain has remained largely unchanged since the days in which this surgical method was introduced.

Besides some exceptions, the instrumentation consists of rigid rod-like graspers and scissors. Nonetheless, minimally invasive procedures have continued to evolve and new operation modes have been developed such as Single Port and NOTES surgery. These procedures aim to reduce complications related to port placement, but they make high demands on the instrumentation setup [4]. Even though innovative and novel instruments have been developed, such as articulating and flexible shaft instruments, none of them have been successfully introduced in surgical procedures. Due to limited force transmission, impossibility of robust grasping [5] and complicated handling [6], these mechanical multi degree-of-freedom (DOF) instruments have never really found their application [7].

By integrating electromechanical drives into the instrument’s handle to actuate the tip’s DOFs, it was possible to overcome some of the disadvantages described above. Unfortunately, this created new problems due to the weight of the motors and hence this solution failed before it could become widespread. This is supported by the fact that one of these systems has already been withdrawn from the market.

Fraunhofer PAMB, instead, proposes in [1], a new approach: laparoscopic instruments powered by hydraulics. This technology has the advantage that the actuators have a higher force and power density than most of the others [9] and, because of their dimensions, they can be located directly on the tip. The instruments featuring this technology are both small and light as their drives (the pumps producing hydraulic pressure) can be located remotely. Moreover, sensors to measure actuator parameters do not contribute to the instrument’s weight, as they can be located anywhere in the hydraulic circuit. In this paper, details about the instrument technology will be given together with information about the control concept - namely the drive set up and instrument’s inverse kinematic equations.

## 2 Methods

To determine the specifications of a handheld surgical instrument with multiple degrees of freedom at the tip, requirement analyses have been conducted [9].

Together with the problems existing instruments are facing, this breakdown has shown that it is impossible to develop mechanically driven instruments that fit the specifications. The main reason being the combination of holding the instrument, moving and applying force on the instrument’s tip for multi degrees of freedom.

To solve this, mechanical decoupling of the movements and forces applied by the doctor to the user interface and the movements and forces working on the instrument’s tip is necessary. This decoupling necessitates builtin drives in the instrument [5]. Hence possible drive solutions have been explored. As result, actuation with micro hydraulic systems was the only solution to fulfil the requirements listed above.

Subsequently the usability of hydraulic systems for medical applications was verified. Therefore potential hydraulic fluids compatible with use in medical devices have been examined. Then the feasibility of sterilizing hydraulic systems filled with these fluids was investigated [1].

## 3.1 Mechanical setup with external drives

It was possible to develop a surgical instrument with 3 hydraulically actuated DOF shown in Figure 3. The instrument’s tip consists of three segments connected via two cylindrical joints which are o?set by 90 degrees about their longitudinal axis. The joints are connected in a serial chain and each joint is actuated by an internal mechanism consisting of two antagonistic linear hydraulic actuators.

In total, the movements of the tip are powered by 6 integrated micro hydraulic cylinders with a piston diameter of 2.45 mm. Being designed for a maximum working pressure of 200 bar, they can produce an actuator force of 94N each. Sealed with micro O-rings which are lubricated with medical white oil, their average internal friction can be kept below 2N, about 2% of the total actuator force. All the actuators and mechanical parts can be integrated in a cylindrical shape of 8 mm in diameter.

The instrument’s cylinders are powered by hydraulic syringe pumps: each cylinder of the instrument is connected with its own pump over a closed circuit. For filling and bleeding out the air, the circuit can be opened with valves. This hardware configuration has the advantage to be free from the non-linearity associated with the use of valves in hydraulic circuits. Moreover, since every syringe pump is directly connected to one of the instrument’s cylinders, equipping the syringe pump with sensors makes it possible to acquire information about the corresponding cylinder in the instrument. A position or a pressure sensor in every syringe pump makes a straightforward implementation of a closed loop control possible without increasing the instrument’s weight, as the sensors are not integral to the instrument, but located within the pump.

Figure 1

Picture of the 3 DOF instrument tip, actuated by 6 hydraulic cylinders 3.

## 3.2 Control concept and inverse kinematic model

The control concept can be summarized as follows: The control software receives the desired configuration of the tip as an input; this information is converted by the inverse kinematics module into actuator extensions and sent as a command to each syringe. The syringe pump displacement translates directly to an actuator extension with a known transmission ratio.

The first step for the implementation of this control system is the definition of the inverse kinematic equations. Given the mechanical design of the instrument, a relationship needs to be established between the actuator extensions, hence the joint rotations, and finally the tool tip position. The equations will be derived by applying inverse kinematic theory for both mechanisms: the serial chain and the internal mechanisms. The relationship between tool tip position and joint rotations can be established by applying to the serial chain the inverse serial kinematic method of Denavit-Hartenberg (DH). The relationship between the joint rotations and the actuator extensions can be determined by applying a geometrical method to the internal mechanism. The details of the derivations are described in the following paragraphs.

Figure 2

Image showing the instrument’s tip from two sides: a frontal face and a view of the instrument rotated by 90 degrees. The frame’s position and orientation, placed on the joints accordin to the Denavit-Hartemberg convention, are also defined.

Table 1

Denavit-Hartemberg Parameters, defined for finding the relationship between instrument tool tip position and joint rotation.

In order to find the relationship between tool tip position and joint rotations, reference frames of the mechanism’s joints were affixed according to the Denavit-Hartemberg convention [10], as shown in Fig. 2 and the DH parameters were defined as shown in Table 1 where:

• a is the distance between zi and zi+1 measured along xi;

• α is the angle from zi to zi+1 around xi;

• d is the distance between xi−1 and xi measured along zi;

• – is the angle from xi−1 to xi around zi;

Using these parameters it is then possible to define the homogeneous transformation matrix ${}_{30}T$.

$30T=10A×32A=cθ1cθ2cθ1sθ1sθ1−c×cθ2cθ1−b×cθ1asθ1cθ2−sθ2sθ1−cθ1−c×cθ2sθ1−b×sθ1sθ2cθ20−csθ20001$$10A=100a010000100001$(1)$21A=cos⁡θ10sin⁡θ1bcos⁡θ1sin⁡θ10−cos⁡θ1−bsin⁡θ101000001$(2)$32A=cos⁡θ20−sin⁡θ2ccos⁡θ2sin⁡θ20cos⁡θ2−csin⁡θ200100001$(3)

The last column of the matrix (1) represents the vector that links the tip reference frame and the origin. Its components are defined as: $px=−ccos⁡θ2cos⁡θ1−bcos⁡θ1−apy=−ccos⁡θ2sin⁡θ1−bsin⁡θ1pz=−csin⁡θ2$(4)

• – a is the distance between reference frame and joint 1;

• – b is the distance between joint 1 and joint 2;

• – c is the distance between joint 2 and the tip frame;

px; py and pz define the desired position in the reference coordinate system of one of the two pliers jaws; θ1 and θ2 are respectively the rotation angles of joints 1 and 2. The system equation 5 can be, with the help of Fig. 2, easily adapted for the second pliers jaw.

Hence from equation (4) it is possible to deduce the relationship between end-effector jaw position and joint rotations:

$θ1=arcsin⁡(−pyccos⁡θ2)$(5)$θ2=arcsin⁡(−pzccos⁡θ2+b)$(6)

With the relationship between tool tip position and joint rotation defined, a relationship can be established between the joint rotation and actuator extensions from the inverse kinematics of the internal mechanism. A schematic of this mechanism is shown in Fig. 3.

Figure 3

Schematic diagram showing the parallel kinematic mechanism.

Defined as: hp the x coordinate of the joint; La, Lb and, Lc the segment dimensions of the parallel kinematic; θb1 and θb2 the angle between the first and the second segment of the two branches of the mechanism; θc1 and θc2 the angle between the third segment of the two mechanism branches and a horizontal line; x1 and x2 the distance between piston and cylinder base.

A geometrical method is used to establish the following kinematic relationships:

$θb1=arcsin⁡[1Lb(Lccos⁡θc1−Ld)]$(7)$x1=hp−La−Lbsin⁡[arcsin⁡(LcLbcos⁡θc1−LdLb)]−Lcsin⁡θc1$(8)$θb2=arccos⁡[1Lb(Lccos⁡θc2−Ld)]$(9)$x2=hp−La−Lbsin⁡[arccos⁡(LcLbcos⁡θc2−LdLb)]+Lcsin⁡θc2$(10)$θc2+φ−θc1=π$(11)

The identities resulting from the serial and internal mechanisms are linked by the following geometrical relationship:

$θc1=Cθ+θ1$(12)

Where Cθ is a constant angle due to the parallel kinematic structure (Cθ is the value of θc1 when x1 = x2). (12) Defines that a rotation of the joint corresponds to an equal change of θc1 from its equilibrium position. It can be concluded that once the end-effector position (px; py and pz) is defined, θ1 and θ2 can be calculated from (5) and (6). Knowing θ1, the orientation of joint 1, it is possible to calculate θc1 from (12) and then θc2 from (11). At last θc1 and θc2 can be respectively substituted in (8) and (10), obtaining x1 and x2, the piston extensions.

## 4 Conclusion

A hydraulically actuated surgical instrument with a multiple DOF tip was designed. As these systems can be built as lightweight, powerful and small assemblies, they have the potential to overcome the majority of problems that similar mechanically or electrically powered instruments face.

As even small hydraulic cylinders with diameters of 2.5mm can produce forces up to 100N, it is possible to place the actuation of the tips DOF directly in the tip.

The hydraulic power can be transmitted through thin tubes, allowing the power units used to produce the hydraulic pressure to be placed beside the operating table. It is therefore possible to build powerful surgical instruments not exceeding the weight of those being actuated by hand.

Furthermore, a new control concept for a new hydraulically actuated instrument has been developed together with the mathematical description of its inverse kinematic. The pressure supply configuration, with 6 syringe pumps driving 6 hydraulic cylinders, has the advantages of a direct transmission of the pump displacement to the hydraulic actuator extension as well as enabling a straightforward implementation of closed-loop control.

• – Sensor integration in the instrument cylinders to enhance safety of closed loop control via redundancy.

• – Development of alternative pressure supply methods which can match the current system’s performance but improve the current solution in terms of size and cost.

## References

• [1]

T. Cuntz, G. James, et al., “Next generation surgical instruments powered by hydraulics,” Biomedical Engineering/Biomedizinische Technik, 2013.

• [2]

T. Carus, Operationsatlas Laparoskopische Chirurgie. Springer, 2010 Google Scholar

• [3]

P. Dasgupta, J. Fitzpatrick, et al., New Technologies in Urology. Springer, 2010, vol. 7 Google Scholar

• [4]

R. Autorino, R. J. Stein, et al., “Current status and future perspectives in laparoendoscopic single-site and natural orifice transluminal endoscopic urological surgery,” International journal of urology: official journal of the Japanese Urological Association, vol. 17, no. 5, pp. 410–31, May 2010. Google Scholar

• [5]

J. H. Kaouk, R. Autorino, et al., “Laparoendoscopic single-site surgery in urology: worldwide multi-institutional analysis of 1076 cases.,” Eur. Urol., vol. 60, no. 5, pp. 998–1005, Nov. 2011 Google Scholar

• [6]

F. Gaboardi, A. Gregori, et al. (2011). ‘LESS’radical prostatectomy: a pilot feasibility study with a personal original technique. BJU international, 107(3), 460-464. Google Scholar

• [7]

P. Dasgupta, J. Fitzpatrick, et al., “New Technologies in Urology”. Springer, 2010 Google Scholar

• [8]

M. De Volder, “Pneumatic and hydraulic micro actuators: a new approach for achieving high force and power densities at micro scale,” status: published, 2007.Google Scholar

• [9]

T. Cuntz, “Untersuchungen zur Eignung mikrohydraulischer Antriebe für die minimal invasive Chirurgie”, in press Google Scholar

• [10]

J. J. Craig, Introduction to Robotics, P. E. international Google Scholar

Published Online: 2015-09-12

Published in Print: 2015-09-01

#### Author’s Statement

Conflict of interest: Authors state no conflict of interest. Material and Methods: Informed consent: Informed consent has been obtained from all individuals included in this study. Ethical approval: The research related to human use has been complied with all the relevant national regulations, institutional policies and in accordance the tenets of the Helsinki Declaration, and has been approved by the authors’ institutional review board or equivalent committee.

Citation Information: Current Directions in Biomedical Engineering, Volume 1, Issue 1, Pages 140–144, ISSN (Online) 2364-5504,

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