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부분적 절단 환자를 위한 손가락 의수의 모델링 및 시뮬레이션

김현호1, 루엥비엣1, 황재혁2, 장한뜻1,#orcid, 김영진1,#orcid

Modeling and Simulation of Finger Prosthetic for Patients with Partial Amputation

Hyunho Kim1, Quoc Viet Luong1, Jai-Hyuk Hwang2, Handdeut Chang1,#orcid, Yeongjin Kim1,#orcid
Journal of the Korean Society for Precision Engineering 2022;39(9):669-674.
Published online: September 1, 2022

1 인천대학교 기계공학과

2 한국항공대학교 항공우주 및 기계공학부

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#E-mail: onemean@inu.ac.kr, TEL: +82-32-835-8413E-mail: Ykim@inu.ac.kr, TEL: +82-32-835-4112
• Received: May 24, 2022   • Revised: June 16, 2022   • Accepted: June 24, 2022

Copyright © The Korean Society for Precision Engineering

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  • The number of amputees is increasing globally due to various accidents or diseases such as diabetes. Among them, there are many patients with upper limb amputations, especially those with hand or finger amputations. As a result, it is highly possible that many people need prosthetic limbs. Most of the prosthetic limbs currently commercialized are products that implement only models without function. Additionally, prosthetic limbs, which have been actively studied in recent years, have many sensors and actuators, providing excellent capabilities inperforming various tasks. However, it is difficult for partial amputees such as finger amputations to use because it targets the entire hand under the wrist. Thus, we propose to develop a wearable finger that can be used by patients with partially amputated fingers. This paper designs the structure of the wearable finger prosthesis and performs the dynamic modeling of the linkage used in the structure. Also, simulation using RecurDyn software is conducted to estimate motion and contact force.
  • KEYWORDS: Prosthetics, Wearable finger, Cable driven
  • KEYWORDS: 의지, 착용형 손가락, 케이블 드라이븐

m

Mass of Link

I

Moment of Inertia of Link

L

Length of Link

θ

Angle of Link

θ˙

Angular Velocity of Link

θ¨

Angular Acceleration of Link

rc

Length to Center of Mass of Link

ks

Spring Constant

τ

External Force

R

Reaction Force at Joint

M0, M

Motor Torque and Equally Input Torque

T

Tendon Force

α

Contact Angle of the Pulley

β

Angle between the X-axis and RC, RD, T, F Respectively

r0, rp

Radiant of Pulley

s

Tendon’s Stroke
상지 절단은 교통사고, 산업사고 또는 당뇨와 같은 질환 등의 이유로 발생하며 국내에서는 매년 1만 2천여 건의 손가락 절단 사고가 새롭게 발생하여 누적 환자는 계속 증가하고 있는 실정이다. 또한 미국의 경우에는 절단환자가 매년 5만에서 10만명 이상 발생하며 그 중 80%가량이 상지 절단 환자이고, 이 중 70%가 손목, 손, 손가락 절단 환자이다[1]. 이에 따라 많은 사람들이 의수를 필요로 할 가능성이 크다.
세계 의수 시장은 2026년까지 2,014만 달러 이상의 규모로 성장할 것으로 예측되지만[2], 현재 상용화된 많은 의수들은 피부와 유사한 질감을 갖는 실리콘 기반의 모형만 구현한 제품이다. 최근에는 3D 프린터를 이용한 의수[3-5]들이 제작되고 있으며, 기술의 발전으로 많은 센서와 엑츄에이터를 포함하는 전자 의수들이 등장하고 있다. 이러한 로봇 손들은 실제 사람의 손과 비슷한 동작을 하며, 작업까지 수행할 수 있다. 예를 들면, Seppich 등은 지능형 의수를 개발하여 유저가 착용하고 임무를 수행하도록 하였다. 해당 의수는 Force-Sensing Resistor (FSR) 센서와 통합되어 형상 및 물체 재료를 추정하는 신경망 모델의 출력을 기반으로 유저에게 햅틱 정보를 전달한다[6]. Cho 등은 MSC 핸드라고 불리는 의수 플랫폼을 개발하여 실시간으로 다중 손가락의 동시 및 비례 제어가 가능하도록 하였고[7], Lu 등은 생체 모방 의수에 Liquid Crystal Elastomer (LCE)와 Liquid Metal (LM)을 조합한 텐던을 사용하여 움직임을 구동하는 연구를 제안하였다[8]. 또한 Kim 등은 링크 구동 메커니즘을 기반으로 작동하고, 촉각 감지에 필요한 모든 구성 요소를 통합하여 다양한 조작 기능을 보유한 ILDA 핸드를 개발하였다[9]. 이처럼 손목 아래를 목표로 한 전동 의수의 개발은 많은 연구팀에서 이루어지고 있는데 비하여, 일부 손가락만이 절단된 환자를 위한 전동 의수의 개발은 부족한 상태이다. 따라서, 우리는 부분적으로 손가락이 절단된 환자가 사용할 수 있는 착용형 손가락 의수를 개발하고자 한다.
해당 의수의 최종 형태는 의수, 케이블, 모터, 그리고 Electromyography (EMG) 센서로 구성된다. 의수는 Distal Phalanx가 절단된 혹은 Middle Phalanx가 절단된 환자가 필요한 개수에 맞게 사용할 수 있으며, 각각 케이블을 통해 모터와 연결된다. 모터는 EMG 센서의 신호에 따라 구동하며, 센서는 환자의 전완근에 다채널로 부착되어, 각각의 의수를 제어하고, 다양한 모션을 취할 수 있도록 한다.
본 논문은 앞에서 언급한 최종 형태의 첫 번째 단계로, 착용형 손가락의 구조를 설계한다. 또한, 그와 관련된 수식적 모델링과 운동학 시뮬레이션을 제시한다. 해당 논문은 다음과 같이 구성된다. 2장에서는 개발하고자 하는 손가락 의수의 구조에 대해 설명한다. 다음 3장에서는 동역학적 모델링에 대하여 다루며, 시뮬레이션 방법과 결과, 그리고 그에 따른 논의를 4장에서 설명한다. 마지막으로 5장에서는 결론과 추후 연구 계획이 제시될 것이다.
Fig. 1

Schematic representation of the concept of partial finger prosthetic

KSPE_2022_v39n9_669_f001.jpg
개발하고자 하는 의수는 3D CAD 프로그램인 NX 12 (Siemens PLM Software, USA)를 통하여 구조가 설계되었다. 착용형 손가락의 길이는 85 mm로 성인 중지의 길이와 비슷하며, 크게 4개의 링크 파트와 2개의 풀리, 그리고 케이블로 구성된다.
Fig. 2와 같이 베이스 링크는 손가락의 Proximal Phalanx 역할이며, 케이블의 위치를 손바닥 면에서 손등으로 변경해준다. Middle Phalanx 역할의 링크 1은 부분절단 환자가 의수를 착용했을 때, 직접 힘을 가해 능동적으로 의수를 움직일 수도 있게 하는 파트이며, 링크 2는 Distal Phalanx와 같으며, 케이블을 고정하고 풀리가 포함되어 있어 케이블 드라이븐 시에 힘의 방향을 변경시켜준다. 마지막으로 링크 3은 베이스 링크와 링크 2에 연결되어 링크 1에 힘을 가하면 Linkage 구조로 인해 의수가 손가락처럼 움직일 수 있도록 도와주는 역할을 한다. 스프링은 베이스 링크와 링크 3과 연결되어 자세 변환 뒤의 복귀를 도와준다.
Fig. 2

The structure of partial prosthetic finger

KSPE_2022_v39n9_669_f002.jpg
인간의 손가락은 Metacarpophalangeal (MCP), Proximal Interphalangeal (PIP), Distal Interphalangeal (DIP) 관절로 구성되어 일반적으로 PIP 관절은 약 100o 정도 굽힘하며, DIP 관절은 약 70o로 굽힘한다[10]. 본 논문에서 제안된 착용형 손가락 의수는 Fig. 3과 같이 PIP 관절에서 최대 90o의 굽힘 각도와 DIP 관절에서 최대 65o의 굽힘 각도를 가진다.
Fig. 3

Prosthetic finger movement

KSPE_2022_v39n9_669_f003.jpg
3.1 Linkage 구조의 동역학적 모델링
본 모션의 모델링은 Lagrange’s Equation을 사용하여 도출되었으며, 부분절단 환자를 위한 착용형 손가락의 Linkage에 대한 자유 물체도는 Fig. 4와 같이 표현되었다. 중력의 영향은 미미하기 때문에 무시된다고 가정하였고, Holonomic 속박 조건은 식(1)과 식(2)와 같다.
(1)
LABcos θBase+LBDcosθBase-θ3   =LACcos θ1+LCDcosθ1-θ2
(2)
LABsin θBase+LBDsinθBase-θ3   =LACsin θ1+LCDsinθ1-θ2
Fig. 4

Free body diagram of linkage

KSPE_2022_v39n9_669_f004.jpg
Lagrangian은 식(3)과 식(4)와 같다.
(3)
LAB-BD=12m3r3c2+I3θ˙32-12ksθ32
(4)
LAC-CD=12m1r1c2+I1+m2LAC2+r2c2+2LACr2ccos θ2+I2θ˙12                                   +12m2r2c2+I2θ˙22
Lagrange’s Equation을 적용하면 운동방정식은 식(5)부터 식(8)과 같다.
(5)
kSθ3=τSpring
(6)
m3r3c2+I3θ¨3=τLink21
(7)
m2r2c2+I2θ¨2+m2r2c2+LACr2ccos θ2+I2θ¨1                 -m2LACr2csin θ3θ˙1θ˙3=τLink22
(8)
m1r1c2+I1+m2LAC2+r2c2+2LACr2ccos θ2+I2θ¨1                 +m2r2c2+LACr2ccos θ2+I2θ¨2                -m2LACr2csin θ22θ˙1θ˙2+θ˙22=τLink 1
제안된 의수의 모션과 성능을 시뮬레이션 상에서 평가하기 위해 수행하였다. 본 시뮬레이션에서는 유명한 Multi-Body Dynamics 소프트웨어인 RecurDyn (FunctionBay Inc., Korea)가 사용되었다.
4.1 시뮬레이션 수행을 위한 구속조건
시뮬레이션을 위한 의수 구조의 구속조건은 Fig. 5와 같다. 베이스는 그라운드에 고정되며, 각 링크는 회전 조인트를 통해 다른 링크와 연결된다. 링크와 링크 간의 충돌을 선언하기 위해 솔리드 접촉이 설정된다. 또한 모델을 단순화하기 위하여 케이블 엑츄에이터 대신 토크 입력으로 설정된다. 토크 값은 Euler-Newton 방법을 사용하여 표현할 수 있다. Fig. 6은 케이블, 링크 3 그리고 링크 2 각각의 자유 물체도를 보여준다. 케이블의 힘 τ2는 다음과 같이 Euler 모델[11]을 사용하여 모델링할 수 있다.
(9)
T2=T1eα1+α2
Fig. 5

Constraints in simulation of prosthetic finger

KSPE_2022_v39n9_669_f005.jpg
Fig. 6

Free body diagram, (a) Free body diagram of cable, (b) Free body diagram of link 3, and (c) Free body diagram of link 2

KSPE_2022_v39n9_669_f006.jpg
케이블의 힘 T1은 모터의 토크로부터 결정할 수 있다.
(10)
T1=M0/r0
링크 3의 자유물체도로부터, 손 끝의 힘 F에 대한 방정식은 다음과 같이 성립할 수 있다.
(11)
RDcosβD+RCcosβC+T2cosβT+FcosβF=0RDsinβD+RCsinβC+T2sinβT+FsinβF=0T2rp+RDLCD+FLCFsinβCF=0
반발력 RC와 RD 및 힘 F는 식(11)을 풀어서 구할 수 있다. 링크 2의 자유 물체도에 따라 토크 값은 다음과 같이 나타낼 수 있다.
(12)
M=RCLAC sinβC-βA
4.2 시뮬레이션 결과 및 토의

4.2.1 Path 추정을 위한 모션 시뮬레이션

본 시뮬레이션의 목표는 의수의 경로를 평가하고 잡는 능력을 검증하는 것이다. 손가락 의수의 경로는 Fig. 7과 같으며, 실제 손가락과 유사하다는 것을 확인할 수 있다. 하지만 2장에서 설명한 것처럼 관절의 굽힘 각도는 실제보다 작기 때문에 Figs. 8과 9에서 볼 수 있듯이 링크 3의 End-Effect에서 작은 틈이 생긴다. 따라서, 사람의 손처럼 완전히 접을 수 없기 때문에 주먹을 쥐는 동작 등에서는 제한이 생긴다. 다른 중요한 매개 변수는 케이블의 스트로크 또는 선형 변위이다. 케이블이 항상 장력의 아래 있다는 가정[12] 하에 케이블의 변위는 풀리 D의 접촉각에 의해서만 영향을 받기 때문에 다음과 같이 주어질 수 있다.
(13)
s=rpα2'-α2π/180
Fig. 7

Finger end-effect’s path

KSPE_2022_v39n9_669_f007.jpg
Fig. 8

The roll angle of the links

KSPE_2022_v39n9_669_f008.jpg
Fig. 9

Final position of the finger

KSPE_2022_v39n9_669_f009.jpg

4.2.2 파지력 추정을 위한 접촉 시뮬레이션

본 시뮬레이션의 목표는 Fig. 10과 같이 물체를 잡는 동안 손가락 의수의 접촉력을 평가하는 것이다. 박스를 생성하여 그라운드에 고정시키고 링크 3의 End-Effect와 접촉시킨다. 토크의 입력은 1 N·mm로 일정하며, Fig. 11의 시뮬레이션 결과에서 볼 수 있는 것처럼 t = 0.05 s 시점에 접촉이 이루어진다. 접촉력은 대략 2N까지 증가하며, 해당 값은 식(9)부터 식(11)로 계산할 수 있다.
Fig. 10

Finger end-effect’s route

KSPE_2022_v39n9_669_f010.jpg
Fig. 11

Result of simulation. (a) Contact force and spring force, and (b) Roll angle of the links

KSPE_2022_v39n9_669_f011.jpg
본 논문은 부분적으로 손가락이 절단된 환자가 사용할 수 있는 착용형 손가락 의수 개발을 목표로 한다. 그 중 서론에서 언급하였던 최종 형태의 첫 단계로서 부분적 손가락 의수의 구조를 설계하였다. 또한 그에 따른 링크 구조를 Lagrange’s Equation을 이용하여 동역학적 수식으로 표현하였고, Multi-Body Dynamics 소프트웨어인 RecurDyn을 활용하여 운동학 시뮬레이션을 제시하였다. 시뮬레이션은 모션과 접촉에 대한 두 가지를 실시하였으며, 두 시뮬레이션 결과는 실제 사람의 손가락의 움직임과 유사하다는 것을 보여주었다. 하지만 의수의 PIP와 DIP 관절 부분에서 실제 손가락 관절과 굽힘 각도의 차이가 존재하기 때문에 의수가 최대로 굽었을 때, End-Effect의 최종 위치에서 약간의 차이를 보이지만 향후 개선될 수 있다. 마지막으로 Fig. 12와 같이 3D 프린팅을 이용하여 손쉽게 제작되어 성능을 평가할 수 있다.
Fig. 12

The prosthetic finger using a 3D printer

KSPE_2022_v39n9_669_f012.jpg
추후 금속 3D 프린팅을 활용한 강도 높은 프로토타입을 제작할 것이며, 실험을 통하여 시뮬레이션의 결과와 비교하여 모델링을 검증할 것이다.
이 논문은 2022년도 정부(산업통상자원부)의 재원으로 한국산업기술진흥원의 지원을 받아 수행된 연구임(No. P0008691, 2022년 산업혁신인재성장지원사업).
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Hyunho Kim
KSPE_2022_v39n9_669_bf001.jpg
Researcher in the Department of Mechanical Engineering, Incheon National University. His research interest is rehabilitation robotics, surgical robotics and soft robotics.
Quoc Viet Luong
KSPE_2022_v39n9_669_bf002.jpg
Postdoc researcher in Biorobotics Laboratory, Department of Mechanical Engineering, Incheon National University. His research interest is dynamic and vibration control theory, robotics, and the internet of things.
Jai-Hyuk Hwang
KSPE_2022_v39n9_669_bf003.jpg
Professor in the School of Aerospace and Mechanical Engineering, Korea Aerospace University. His research interest is dynamic and vibration control systems, and smart materials.
Handdeut Chang
KSPE_2022_v39n9_669_bf004.jpg
Assistant Professor in the Department of Mechanical Engineering, Incheon National University. His research interest is biomimetic robotics, variable impedance actuator, nonlinear dynamic system control, physical human robot interaction, and myoprocessor.
Yeongjin Kim
KSPE_2022_v39n9_669_bf005.jpg
Associate Professor in the Department of Mechanical Engineering, Incheon National University. His research interest is surgical robotics, rehabilitation robotics, and deep learning.

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Modeling and Simulation of Finger Prosthetic for Patients with Partial Amputation
J. Korean Soc. Precis. Eng.. 2022;39(9):669-674.   Published online September 1, 2022
DOI: https://doi.org/10.7736/JKSPE.022.067
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Modeling and Simulation of Finger Prosthetic for Patients with Partial Amputation
J. Korean Soc. Precis. Eng.. 2022;39(9):669-674.   Published online September 1, 2022
DOI: https://doi.org/10.7736/JKSPE.022.067
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Related articles

Modeling and Simulation of Finger Prosthetic for Patients with Partial Amputation
Image Image Image Image Image Image Image Image Image Image Image Image
Fig. 1 Schematic representation of the concept of partial finger prosthetic
Fig. 2 The structure of partial prosthetic finger
Fig. 3 Prosthetic finger movement
Fig. 4 Free body diagram of linkage
Fig. 5 Constraints in simulation of prosthetic finger
Fig. 6 Free body diagram, (a) Free body diagram of cable, (b) Free body diagram of link 3, and (c) Free body diagram of link 2
Fig. 7 Finger end-effect’s path
Fig. 8 The roll angle of the links
Fig. 9 Final position of the finger
Fig. 10 Finger end-effect’s route
Fig. 11 Result of simulation. (a) Contact force and spring force, and (b) Roll angle of the links
Fig. 12 The prosthetic finger using a 3D printer

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Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Fig. 11

Fig. 12

Modeling and Simulation of Finger Prosthetic for Patients with Partial Amputation
JKSPE : Journal of the Korean Society for Precision Engineering

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