Optimization Model for Gas Spring of Endoskeletal

Proceedings of the Asia Pacific Industrial Engineering & Management Systems Conference 2012 V. Kachitvichyanukul, H.T. Luong, and R. Pitakaso Eds.

Optimization Model for Gas Spring of Endoskeletal Prosthetic Leg with Maximum Energy Storage Criteria Cucuk Nur Rosyidi† Production System Laboratory, Industrial Engineering Department, Faculty of Engineering Sebelas Maret University, Indonesia Tel: (+62) 271-632110 Fax: (+62) 271-632110 Email: [email protected] Putri Fitriawati, Rahmaniyah Dwi Astuti Work System Design and Ergonomics Laboratory, Industrial Engineering Department, Faculty of Engineering Sebelas Maret University, Indonesia Tel: (+62) 271-632110 Fax: (+62) 271-632110 Email: [email protected]/ [email protected]

Abstract. People with transfemoral amputation need above knee prosthetics. One of the important components of the prosthetics is the gas spring. The spring is applied to the knee-joint with a purpose to store the energy during flexion and release it during the extension. For the above knee prosthetics, it is important for the gas spring to have maximum energy storage. The energy will help the amputee in moving from one position to another. The aim of this research is to develop a gas spring optimization model with maximum energy storage criteria in a two bar mechanism of endoskeletal prosthetic leg. The constraints considered in this research are stroke, gas spring force rating, extended length, compressed length and gas spring characteristic. The design variables of the gas spring considered in this research are cylinder length (L), cylinder diameter (D), extension stroke (s2) and compression stroke (s2). These variables were used to define the geometry of the gas spring in the two bar mechanism of endoskeletal prosthetic leg. Keywords: gas spring, above knee prosthetics, energy storage, optimization

1. INTRODUCTION

In a normal leg, quadriceps and hamstring muscles are used as the extensor and flexor respectively. The prosthetic leg for people with transfemoral amputation, especially above knee amputee needs a component to replace those muscles. A spring, both mechanical or gas can be used as a component to replace the function of muscles in moving the knee joint. The application of spring in the knee joint is known as energy storing prosthetic knee (ESPK) (Symbiotech, 2009). Cherry et al. (2006) predicted that placing a spring in parallel with knee will result in a reduction of biological knee stiffness and muscle activation of the knee extensors. The system applied to the knee joint is used to transform the pressure from the body into an energy stored in the spring. The transformation is performed when the leg touch the floor. The energy is then released during the swing phase of cycle gait (Herdiman, 2010).

Nowadays, there are many people lost part of their body because of many causes. For example, people may experience transfemoral amputation due to an accident. Losing the lower limb will decrease ones flexibility in performing their daily activities. Design and set up of prosthetic leg for transfemoral amputation people will improve the level of flexibility and increase the level of life quality. In general, prosthetic systems can be differentiated in two types: endoskeletal and eksoskeletal with three main components, namely socket, suspension, and leg. In an endoskeletal system, a hollow cylindrical shaft (pylon) is used to connect the socket with the leg. The system is lightweight, adjustable, and modular. Eksoskeletal system used a rigid laminated cover to connect the socket with the leg (Haberman, 2008).

† : Corresponding Author 799

Rosyidi, Fitriawati, and Astuti

Energy storing is accomplished by devices or physical media that store energy to perform useful operation at a later time (Wikipedia, 2012). Symbiotech tech (2009) developed an ESPK, known as XT9 for sport activities ivities such as rock and ice climbing, ice skating, and surfing. Mechanical spring used in ESPK has a function to store energy given by the user body weight during flexion then released during the extension. The weakness of this design is the knee joint will respond too quickly, since it iss used for sport, and not for normal daily activities (Symbiotech, (Symbiotech 2009). The response will result in a larger force thann needed during the extension of the knee joint due to the large force resulted from the mechanical spring (Ultahar, 2011). For daily normal activities the knee joint needs to perform a smoother response using a gas spring. Ultahar (2011) conducted a research to verify a prosthetic knee joint design with energy storing system for a transfemoral amputee.. The research verified 2 and 6-bar design of endoskeletal prosthetic leg mechanism. The design used gas and helical spring as an energy storing components. The spring is an important component in a prosthetic leg. However, the research has not considered to find the optimum design parameter arameter of the spring. The aim of this research is to develop an optimization ation model for gas spring in 2-bar bar endoskeletal prosthetic leg. The objective function of the model is to maximize mize energy storing, considering extension and compression length, length cylinder length, stroke, piston displacement, and gas spring characteristic.

Figure 1: Knee joint with 2-bar 2 mechanism. Source: Ultahar (2011) Table 1: The components of knee joint with 2-bar mechanism. Part Name N

Part No.

Qty.

1

Body (right)

1

2

Body (left)

1

3

Adapter (lower)

1

B18.3.5M- 8 x 1.25 x 12 4

2. BACKGROUND 2.1 Endoskeletal skeletal Prosthetic Knee with 2-bar 2 Mechanism

3

5

Steel dowel pin

1

6

B27.7M – 3XM1-11 3XM1

2

7

Endoskeletal prosthetic is a lower-limb lower support consists of an internal pylon usually covered with a lightweight ight material, such as plastic foam (Mosby's Medical Dictionary, 2009). Prosthetic design in the research of Ultahar (2011) is a 2--bar above knee endoskeletal prosthetic using ESPK mechanism and double axis ankle joint system. A 2-bar bar mechanism has a two links connected with a joint. Double axis ankle joint system has an ability to move the leg in both dorsi flexion and plantar planta flexion directions. This system improved single axis system in which the leg can not move freely like a normal foot (Faiz, 2010). Endoskeletal letal prosthetic leg with 2-bar 2 mechanism is shown in Figure 1. The components of the prosthetic are shown in Table 1.

Socket FCHS – 161 N

B18.3.5M – 6 x 1.25 X 12 Socket

FCHS –12N

2

8

Pin energy storing

2

9

Energy storing

1

10

Patella

1

11

Adapter (upper)

1

2.2 Gas Spring Above knee prosthetic with energy storing is designed by adding a gas spring ing component. Gas spring consists of piston, piston rod, cylinder and end fitting. fitting Gas spring stores energy by compressing the gas inside the cylinder. The bigger the pressure, the air chamber inside gas spring will be reduced and accumulates accumulate the gas pressure and stores

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Rosyidi, Fitriawati, and Astuti

integration of equation (1).

larger energy. The advantage of the gas spring compared to mechanical spring is in its response. Gas spring tends to have a smoother response than a mechanical spring (Herdiman, 2010). Gas spring geometric elements are shown in Figure 2. In general, the spring geometric elements consist of cylinder diameter (D), piston rod diameter (d), extension length (La), compression length (Le) and stroke (s).

(3)

3.2 Constraints There are four decision variables in this research, which are cylinder length and diameter and extension and compression stroke. The following constraints must be satisfied to obtain optimal values of the design variables: 1.

Extension length (La)

The extension length is the gas spring length when the leg is in a straight position. In that position, the gas spring and body of the knee joint endoskeletal prosthetic leg forms an angle of 6 degrees as shown in Figure 3.

Figure 2: Gas spring geometric element Adapted from www. enidine.com (2009)

2.3 Energy Storing Device Energy storing device in a prosthetic leg has two functions. First, it replaces the quadriceps muscle used as an extensor in knee joint. Second, it replaces the hamstring muscle as a flexor on a normal knee joint. Energy storing device can store the obtained energy from pre-swing phase and release it in the initial-swing until the terminal swing. The force of the gas spring in the prosthetic leg reduces the amount of work done by the amputee leg muscles in the swing force when the amputee is walking (Herdiman, 2010). In other word, energy storing is functioned as actuator to perform automatic extension. According to Cortesi (2003), the energy of gas spring that occurs in the condition of adiabatic compression can be expressed in equation (1). ‫ܧ‬൫‫ݔ‬௙ ൯ =

௫ ‫׬‬଴ ೑ ‫ܲܣ‬௜

ቂቀ

௅

௅ି௫

ఊ

ቁ − 1ቃ ݀‫ݔ‬

Figure 3: Gas spring in extension position Source: Ultahar (2011)

(1)

Gas spring extension length is the resultant of body knee joint (h1) with the upper adapter length (h2). The gas spring extension length can be expressed in equation (4).

Equation (1) shows that gas spring energy is affected by piston area (A), pressure (P), cylinder length (L), piston displacement (xf), and ratio of the specific heats (γ). Ratio of the specific heats for diatomic gas (N2) is 1.4 (Miler, 1959). The piston area in equation (1) can be expressed as in equation (2), where D denotes the diameter of the piston. ‫=ܣ‬

గ஽మ ସ

‫ ݏ݋ܥ‬6 =

(2)

2.

3. FORMULATION OF THE OPTIMIZATION MODEL 3.1 Objective Function

௅௔ ௛భ

(4)

Compression length (Le)

The gas spring compression length is the length when the leg in a maximum flexion position. Position of the gas spring and upper adapter is in the position of a straight line inside the body in the knee joint endoskeletal prosthetic leg as shown in Figure 4. The gas spring compression length

The objective function in this research is to maximize the energy storage. Equation (3) shows the equation used for the objective function. The equation is resulted from the

801

Rosyidi, Fitriawati, and Astuti

need to have the same length with the knee joint body. Equation (8) determines the relationship among them. ‫ ܮ‬+ ‫ݏ‬ଶ + ℎଶ = ℎଵ (8)

can be expressed in equation (5). ‫݁ܮ‬

= ℎଵ − ℎଶ

(5)

In this research, the gas spring cylinder length is determined in a specific range value. Equation (9) shows the feasible range value for cylinder length. In this equation, Lmin denotes the lower limit of the range and Lmax denotes the upper limit of the range. ‫ܮ‬௠௜௡ ≤ ‫ܮ ≤ ܮ‬௠௔௫

(9)

Stroke length is also determined in certain range value as shown in equation (10). In this equation, smin and smax denote the lower and upper limit of the range. Figure 4. Gas spring in compression position Source: Ultahar (2011) 3.

‫ݏ‬௠௜௡ ≤ ‫ݏ ≤ ݏ‬௠௔௫

Cylinder length (L) and stroke (s)

4.

(10)

Piston displacement inside cylinder (xf)

The gas spring piston will slide to a certain position in the compression stage. Gas spring commonly capables to perform about 60% compression from its total length (Lift support Technologies, 2012). Equation (11) denotes the piston displacement.

The Cylinder length and stroke affect gas spring extension length and compression. Gas spring stroke extension length (s1) is longer than the compression stroke (s2) as shown in Figure 5 and Figure 6. Extension length (La) is the sum of cylinder length (L) and extension stroke (s1), while the compression length (Le) is the sum of cylinder length (L) and compression stroke (s2). Equation (6) and (7) show the extension and compression length respectively.

‫ݔ‬௙ ≤ 0.6 ‫ܽܮ‬

(11)

The piston displacement in gas spring directly affects the stroke when it is compressed (s2). Cylinder piston displacement is the difference between extension stroke (s1) and the compression stroke (s2). It can be expressed in equation (12). ‫ݔ‬௙ = ‫ݏ‬ଵ − ‫ݏ‬ଶ

Figure 5. Extension of gas spring.

(12)

The cylinder length can be found by substituted equation (6) and (7) into (12). ‫ ݁ܮ = ܮ‬− ‫ݏ‬ଵ + ‫ݔ‬௙ 5. Figure 6 Compression of gas spring. ‫ ܮ‬+ ‫ݏ‬ଵ = ‫ܽܮ‬ ‫ ܮ‬+ ‫ݏ‬ଶ = ‫݁ܮ‬

(13)

Cylinder diameter (D)

The cylinder diameter needs to be adjusted with the distance between the knee joint bodies since the gas spring is placed between both knee joint bodies. Equation (14) shows the feasible range value for spring cylinder diameter. In this equation, Dmin denotes the lower limit of the range and Dmax denotes the upper limit of the range.

(6) (7)

The compression length of gas spring in prosthetic leg will adjust the body length which is the main support of the knee joint. The stroke, cylinder length, and upper adapter

‫ܦ‬௠௜௡ ≤ ‫ܦ ≤ ܦ‬௠௔௫

802

(14)

Rosyidi, Fitriawati, and Astuti

6.

stroke

Gas spring characteristic (x)

Technologies (2012)

The gas spring characteristic (x) is defined as the ratio of the gas spring force at the compressed condition with the force at the extended condition (Stabilus, 1995). 1,01 < ‫ < ݔ‬1,6

smax

1000

mm

(2012) Compression

(15)

smin

10

mm

stroke The lower limit is obtained from the device geometry similar to equation (15), while the upper limit of gas spring characteristic depends on the stability of the components taking into account the necessary safety factors (Stabilus, 1995). x=

smax

80

mm

Dictator (2012)

Cylinder

(16)

୊భ

Dictator (2012)

Dmin

10

mm

diameter

୊మ

Dictator

Dictator (2012)

Dmax

43

mm

Ultahar (2011)

Force (F) in Equation (16) can be expressed as in equation (17). F(A, x) = AP୧ ቂቀ

୐

୐ି୶

Gas spring

Xmin

1,01

-

characteristic

ஓ

ቁ − 1ቃ

(17)

Stabilus (1995)

Xmax

1,6

-

Stabilus (1995)

Equation (17) shows that force is affected by piston area (A), pressure (P), cylinder length (L), piston displacement (x) and ratio of specific heat (γ).

Force

Fmin

10

N

Dictator (2012)

Fmax

4. NUMERICAL EXAMPLE AND ANALYSIS

1000

N

Dictator (2012)

Parameter data for numerical example can be seen in Table 2. Table 3 shows the gas spring geometric elements in Ultahar (2011). We used Lingo 9.0 to find the solution of the optimzation model. The result of the optimization is shown in Table 4.

Table 3: Gas spring geometric element measurement Variable Cylinder length

Table 2: Model parameters Parameter Extension

Compression

Value

Units

Source

La

160,59

mm

Ultahar

Extension stroke Compression stroke

(2011) Le

140,47

mm

length Cylinder

Cylinder diameter

Notation

length

32

mm

length 100

mm

Dictator

Design Variable Cylinder length Cylinder diameter Extension stroke Compression stroke

Dictator (2012)

Extension

smin

0.6 L

mm

Unit

L

118,1

mm

D

15,1

mm

s1

71,7

mm

s2

51,8

mm

Table 4: Optimization results

(2012) Lmax

Value

Ultahar (2011)

Lmin

Notation

Lift support

803

Not ation L D s1 s2

Optimal Value (mm) 80.15 29.57 80.44 47.32

Rosyidi, Fitriawati, and Astuti

This paper proposed an optimization model for gas spring of endoskeletal prosthetic leg with maximum energy storing criteria. Some constrains are considered such as extension length, compression length, cylinder length and stroke, piston displacement inside cylinder, cylinder diameter, and gas spring characteristic. For further study, another objective function can be considered such as minimum weight. Multi objective optimization can be used as a method to solve the problem. We also have to conduct verification and validation of the model through real application or simulation.

pada Pengguna Prosthetic atas Lutut Endoskeletal dengan Sistem Energy Storing Mekanisme 2-Bar pada Aktivitas Berjalan Cepat. Universitas Sebelas Maret Surakarta. Skripsi. Haberman, A. 2008. Mechanical Properties of Dynamic Energy Return Prosthetic Feet, Master Thesis Queens University Kingston Ontario, Canada Herdiman, Lobes and Damayanti, Retno Wulan. 2010. Pengembangan Prosthetic Kaki Dengan Sistem Energy Storing Prosthetic Knee (ESPK) Bagi Penyandang Cacat Amputasi Atas Lutut. Lembaga Penelitian dan Pengabdian pada Masyarakat. Universitas Sebelas Maret Surakarta. Lift Support Technologies. 2012. Gas Spring Principle. Available in http://www.lstechnologies.ca/principles.html. [24 April 2012]. Mosby's Medical Dictionary, 8th edition. Elsevier. 2009. Endoskeletal Prosthesis. Available in http://medicaldictionary.thefreedictionary.com/endoskeletal-+prosthesis. [14 April 2012]. Stabilus. 1995. Gas Spring Technical Information. Stabilus GmbH: Koblenz. Ultahar, Ardian. 2011. Verifikasi Rancangan Prosthetic Knee Joint dengan Sistem Energy Storing bagi Penyandang Cacat Amputasi Trasfemoral. Skripsi S1 Jurusan Teknik Industri Universitas Sebelas Maret Surakarta. Wikipedia. 2012. Energy Storage. Available in http://en.wikipedia.org/wiki/Energy_storage. [21 June 2012].

ACKNOWLEDGMENT

AUTHOR BIOGRAPHIES

This research is funded by BLU UNS in Fundamental Research scheme, under contract No. 07/UN27.8/PN/2012. This research is also part of undergraduate thesis of Putri Fitriawati under Cucuk Nur Rosyidi and Rahmaniyah Dwi Astuti supervision.

Cucuk Nur Rosyidi is a lecturer in Industrial Engineering Department of Sebelas Maret University. He is the head of Production System Research Group in the same institution. His research interests include product design and development and quality engineering. His email address is

There are differences in design variables between the result of optimization and the existing gas spring geometric element in Ultahar (2011). The energy storing of the optimization in this research has a larger value than Ultahar (2011). Table 5 shows the comparison of the energy storing. Table 5: The comparison of energy storing D

L

xf

E

mm

mm

mm

J

Ultahar (2011)

15.10

118.10

19.90

486.29

This research

29.57

80.15

33.12

9957.40

Source

6. CONCLUSIONS

REFERENCES Putri Fitriawati is an undergraduate student in Industrial Engineering Department of Sebelas Maret University. She is also a research assistant in Work System Design and Ergonomics Laboratory. Her research interests include work system design and ergonomic. Her email address is

Cherry, Michel S., Choi, Dave J., Deng, Kevin J. Kota, Shidar., Ferris, Daniel P. Design and Fabrication of an Elastic Knee Orthosis Preliminary Results. Proceedings of International Design Engineering Techinical Conferences & Computers and Information in Engineering Conference: ASME, pp.1-9 (Philadelphia, USA, 10-13 September 2006). Cortesi, Roger. 2011. Gas Cylinder Spring. Available in http://roger-cortesi.com/ideas/public/gasspring.html. [12 March 2012]. Dictactor. Push Type Gas Springs. 2012. Dictactor Technik GMBH: Germany. Enidine. 2009. Industrial Gas Spring and Dampers. Available in http://www.enidine.com/EBDS/514-76.pdf. [29 March 2012]. Faiz, Zulfa Miftakhul. 2010. Kajian Dynamic Cycle Gait

Rahmaniyah Dwi Astuti is a lecturer in Industrial Engineering Department of Sebelas Maret University. She is the head of Work System Design and Ergonomics Laboratory in the same Department. Her research interests are in the field of work design and anthropometry applications. Her email address is

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