Proceedings of the IASTED International Conference Modelling and Simulation (MS 2013) July 17 - 19 , 201 3 Banff, Canada

DYNAMICS STRESS ANALYSIS FOR A MINIMAL INVASIVE SCALPEL DESIGN *Yu-Tin Chao, *Ya-Lin Yu, *Jia-Yush Yen, *Che-Jung Hsu, *Michael Kam, †Ming Chih Ho ‡Yung-Yaw Chen, §Jiunn Fang, ‡Feng-Li Lian *Department of Mechanical Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei, 10617 Taiwan(R.O.C.) [email protected] ‡Department of Electrical Engineering National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei, 10617 Taiwan(R.O.C.) †Department of Surgery National Taiwan University Hospital and Collage of Medicine, No.7, Chung Shan South Road. , Zhongzheng Dist., Taipei City 10002, Taiwan(R.O.C.) §Department of Aerospace and Systems Engineering, Feng Chia University, No. 100, Wenhwa Rd., Seatwen, Taichung, 40724 Taiwan( R.O.C.) body in order to provide an enough space for operation; however, this technique generates not enough space and has a lot of restriction during operation. So far, doctors use long-hold tools which can operate MIS through a small hole; the operation space and degree-of-freedom still have a lot of restrictions which cannot manipulate intuitively. Although there are many kinds of MIS tools, they generally provide only single-direction rotation with limit degree range. There are many studies about the rotation joint mechanism [1] and flexible joint-chain which used shape memory alloy (SMA)[2-5]; however, these mechanisms in general, have less degree-of-freedom[6-9]. The main goal of this study was to design multi degree-of-freedom and high-stiffness mechanism tool under a finite-space surgery. A tissue incision generates a huge stress to the surgical tools; in order to rotate with high-stiffness, different design methods will determine whether the structure of MIS would fracture or not. This MIS has several characteristics, but the main drawbacks are high cost and long operation period; also, the cutting angle has to be adjusted during the operation. If the target surgical channels are not sliced properly during the operation, it is necessary to be sliced more channels. So far, there are three types of arm-robotic systems: Aesop, Zeus, and DaVinci. In 2003, DaVinci's parent company was merged with Zeus's, since then, it becomes the dominant company on the market. DaVinci can operate with 6 degree-of-freedom motion which is more advance than 4 degree-of-freedom laparoscope system; in addition, the robotic arms can execute dexterous motion without shaking [10-12]. A DaVinci surgical system costs about $ 100 to 160 million with annual maintenance cost about $ 100,000. It is mainly used in the cardiovascular and urology surgeries. Dr.Himpens completed the first mechanical-arm for laparoscopic cholecystectomy in 1997 [13,14]. Since then, robotic arms have been applied for other laparoscopic abdominal surgeries. However, robotic surgeries are not popular due to its high cost. Moreover, doctors are still

ABSTRACT In this article we bring up a new-type bendable mechanical arm based on four-bar linkage which is composed by several micro-mechanical parts and can be applied on minimally invasive surgery. The advantage of this new design is that the actuator and the mechanical arm can be designed separately, so that our mechanical arm will not interfere with the operation of actuator. Compare with the traditional bendable surgical designed instruments which are made by single structure, the designed instrument of this research which is based on four-bar linkage own better stiffness. Herein this study not only carry out the design of linkage model for minimally invasive surgery, but also analyze the kinematics of designed model. By building up the kinematic relationship between input and output, this study got the dynamic stress of the designed structure and prove that the designed structure have high stiffness , so this research propose a novel design of a high-stiffness bendable scalpel. KEY WORDS Minimal invasive surgery, Scalpel, Four-bar linkage

1. Introduction Minimally invasive sugary (MIS) becomes more common; namely, this type of surgery generates only a small wound on patient’s body. This operation has several advantages, including small wound dimension, and less recovery period .The main goal of this study is to design a high-stiffness-driven tool for minimally invasive surgery. It is necessary to understand the practical operation environment before designing the tool. In general, a basic MIS has several essential to satisfy; first, an endoscope combined with a lighting device and image capture system which can capture digital image and display on a monitor in order to provide image processing and records. Second, it is necessary to place an inflator into patient’s DOI: 10.2316/P.2013.802-028

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not used to changing their operation mode. Therefore, this study presented a type of mechanism which manipulators are able to change the angle of forward part of the tool during a surgery. Most bendable surgical tools consist of a single supporting structure. The tools utilize a tube to constrain the inner bending structure. While conducting an operation, the inner bending structure is pushed out by a manipulator and it will bend simutaneosly. Due to the bending design is made by single structure, it has less hardness. When the force feedback given from operation is not small enough, the mechanism is likely to generate undesired bending motion which enables the manipulator to conduct surgery smoothly. On the future development of surgical tools, the tools need to be fabricated into small dimension to increase stiffness which stabilizes the surgical process and minimize tools dimension to fit through a channel into a patient body. Therefore, the best solution is to separate an actuator from the bendable mechanism. There are few examples that the robotic-finger actuators and rotation joints are designed seperated. Most of the surgical tools are driven by wiring devices; therefore, the actuators could be placed outside of the surgery area; namely, two operation parts are held. It is an advantage that the tools design of the actuators and mechanism are independent. To design a rotated-mechanism, operators can use either a gear-rotated mechanism on each joint [15-17] or rotating mechanism driven by wiring device; in addition, there is also a new type of stackable four-bar-linkage design has been proposed [18-21]. This paper presented a novel linkage design which used only one actuator to complete operation. This design provided sufficient stiffness property that enabled the tools to operate smoothly without additional failure and angles variations when slicing tough tissues during a surgery. This study not only presented kinematic equations but also simulates the dynamic stress on the mechanism, proving this design has sufficient stiffness.

Figure 3. First dynamic model of designed structure.

Figure 4. second dynamic model of designed structure

2. Structure design and theorem This study presents a novel mechanism(see Figure 1). The main components are an actuator and a novel able-rotated mechanism; the able-rotated design is with small dimension(see Figure 2). This designed mechanism can be divided into two parts. The first (see Figure 3) is known as a slider crank mechanism which is regarded as an actuator that generates thrust. To manipulate a linkage mechanism, it is necessary to understand the kinematic of the mechanism first. Deriving the input-to-output relative equation, we know the angle variation caused by the input ust. In slider-crank mechanism, we set a target point( ) at the middle of the output bar ; the next step is to derive the clockwise and counterclockwise thr equations of coordinates. (1)

Figure 1. Bendable Scalpel structure

180 180

(2) (3) (4) (5) (6)

Figure 2. Dimensions of bendable designed structure (unit: inch)

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The equations (1), (2), and (3) clockwise; and the equations (4) (5) (6) are counterclockwise. It is worthwhile to notice that the angles of the former equations only appear and ; moreover, the angle of the other equations only appear . Taking derivative of all equations above, we can obtain the state space model of velocity (7)(8).

Then, derive a velocity state space model.

[

̇ ̇

[

[

][

180

]

̇ ]

̇

]

(19) ̇ ]

̇ ̇

][ ̇ ]

[

̇ ] The left side of the equations (7) and (8) are equivalent; therefore, combining (7) and (8), consequently, we obtain (9) which express the relation of the input and output variables. [

] [ ][ ̇ ]

̇ [ ̇ ] ̇

(9)

The (9) can be simplified as (10) ̇ [ ][ ] [ ][ ̇ ] (10) ̇ Finally (11), where [ ] [ ] [ ] ̇ [ ] [ ][ ̇ ] (11) ̇ At the left side of the equation, ̇ is the most important state variables among the three angular velocities because it can set as an input rotation of the four-bar linkage. ̇ [ ][ ̇ ] (12) Variables of the left and the right side of the equal sign in (12) is represented as outputs and inputs of the slider-crank mechanism. The velocity is derived by applying a transfer function on input state. The four–bar linkage analysis is as follow. (see Figure 4) First, define a point ( , ) at the middle of the right side bar of four-bar linkage. Next, derive both clockwise and counterclockwise equations of the system. 90 )

( ( 

( 360 180 +

90 )

[

][ ̇ ]

(20)

[ ̇ ] Combining the clockwise with counterclockwise equations, we can derive (21); ̇ (21) [ ] [ ̇ ] [ ][ ̇ ] ̇ Where [ ] [ ] [ ].However, We care about the four-bar linkage output; therefore, the (21) can be simplified to ̇ ̇ [ ] [ ][ ̇ ] (22) ̇ The left side of the equation is velocity output. Moreover, we can derive the output rate by applying a transfer function to the right side of the equation (22). The right side of (23) is output angle . The represents a fix angle of the triangle structure. (23) Taking the derivative state of (23), we can obtain the velocity state equation. Finally, we can derive the following equation by combining the previous state equations with (24), which represents the velocity variation of the output and input. [ ][ ̇ ] ̇ ̇ ̇ [ ][ ] (24) ̇ According to this modal analysis, we can derive the angle variations which are driven by the difference inputs.

(8)

[

̇ [ ̇ ] ̇

90 )

̇ [

(7)

(

90 )

̇ =

̇

(

90 )

(

̇ ̇

90 )

(

3. Structure simulation

(13)

During surgery, the scalpels are used to contact the infected areas to excision. Due to the bendable scalpels are usually lack of stiffness and the infected areas are usually tougher than other human tissues, the structure of bendable scalpel needs to be designed strong enough when bending to ensure the safety of the operation. Also, a carefully-designed structure of bendable scalpels may avoid the angle error due to stress, and the problem of force inaccuracy may be kept off.

(14)

) (15) (16) (17) (18)

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In this study we designed a new high-stiffness scalpel , its structure and size are shown in (see Figure 2). The multi-crossed structure is designed to enhance the structure toughness. This scalpel is made from stainless steel which is human body acceptable. First, we take 0.6rpm as an angular velocity input and give a pull-up 5lbf force on the end of the scalpel. (the blue arrow in (see Figure 5)), observing the stress distribution when the time is at 0s, 0.5s, 1s, 1.5s, 2s (see Figure 6-10 ).

Figure 9. The stress distribution caused by 5.4°

Then we take 0°,1.8°, 3.6°, 5.4°, 7.2° as the input angle, observing the dynamic stress in the front part caused by these five kinds of inputs.

Figure 10. The stress distribution caused by 7.2° As shown in the figures above, by observing the yield strength, we may conclude that when we take 51lb as an input force, the stiffness of the structure is good and the maximum stress on the material is more less than the failure stress . By observing the results , show that the designed structure could sustain sufficient forces and remains its shape in any bending angle, indicating that our design owns good stiffness.

Figure 5. initial conditions of structure on schematic diagram

4. Conclusion Minimally invasive surgery (MIS) has always been a major development at the surgical department due to a small wound and fast recovery time. However, the operation range of the practical surgical tools were often restricted by less degree-of-freedom. Although there were several bendable surgical tools, there were still some problems of micro-designed structure and stiffness needed to be solved. Therefore, this study presents a novel design, using linkages composition to construct an able-rotated mechanism. The actuators and linkages can design independently so that it is easily to achieve a minimal design at the forward part of the surgical tools; moreover, it satisfies the dimension requirement of surgical MIS tools. For the stiffness property, these tools are made with stainless steel. Having a high-stiffness property, this tool did not have a destruction and failure by stretching and slicing during the surgery. Comparing with other single-structured able-rotated surgical tools on the market, this design is easier to be used on operation. In mechanism design, this study not only minimizes the linkages dimension, but also analyzes the kinematics of combination linkages; with the stress distribution status, we can verify the design which had both a minimal structure and high stiffness property.

Figure 6. The stress distribution caused by 0°

Figure 7. The stress distribution caused by 1.8°

Figure 8. The stress distribution caused by 3.6°

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In conclusion, this study presents a method to improve a stiffness problem of the surgical tools and combines with simulation analysis to verify the high-stiffness design.

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Acknowledgement This research is funded by the National Science Council, Taiwan under Project No. NSC 101-2221-E-002-133-MY3.

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