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One of the major problems faced by hand amputees is the unavailability of a lightweight and powered multi-functional hand prosthesis. Under-actuated finger designs play a key role to make the hand prosthesis lightweight. In this paper, a hand prosthesis with an under-actuated and self-adaptive finger mechanism is proposed. The proposed finger is capable to generate passively different flexion/extension angles for a proximal interphalangeal (PIP) joint and a distal interphalangeal (DIP) joint for each flexion angle of metacarpophalangeal (MCP) joint. In addition, DIP joint is capable to generate different angles for the same angle of PIP joint. Hand prosthesis is built on the proposed finger mechanism. The hand prosthesis enables user to grasp objects with various geometries by performing five grasping patterns. Thumb of the hand prosthesis includes opposition/apposition in addition to flexion/extension of MCP and interphalangeal (IP) joint. Kinematic analysis of the proposed finger has been carried out to verify the movable range of the joints. Simulations and experiments are carried out to verify the effectiveness of the proposed finger mechanism and the hand prosthesis.

Hand prosthesis is an artificial device which replaces the missing hand of an amputee and is expected to fulfil the functional and aesthetic requirements of the amputated hand. The main problem that causes amputees not to accept the available prostheses is the unavailability of light-weight prostheses with acceptable controlling and functional properties [

Therefore, in this research a prosthetic hand comprises of under-actuated and self-adaptive fingers is proposed. The proposed finger is used as the index, middle, ring or little finger of the hand prosthesis. Modified mechanism of the proposed finger is used as thumb of the hand prosthesis which includes thumb opposition/apposition in addition to flexion/extension of MCP joint and interphalangeal (IP) joint. The proposed finger is capable of passively generating different flexion/extension angles for a PIP joint and a DIP joint for each flexion angle of MCP joint. In addition, DIP joint is capable of generating different angles for the same angle of PIP joint. In this study, abduction/adduction of MCP joint is not considered and only the flexion/extension is considered. The hand prosthesis assists user to grasp objects with various geometries by performing cylindrical grasp, hook grasp, lateral pinch and tip pinch and palmar pinch.

Next section of the paper proposes the under-actuated and self-adaptive finger mechanism. Section 3 presents the mechanical design and the mechanisms of the introduced hand prosthesis. Experiments and results are presented in section 4 and the last section concludes the paper.

Proposed finger can generate flexion/extension of MCP, PIP and DIP joints. It can be used as an index, middle, ring or little fingers of a hand prosthesis. Main structure of the finger can be simplified to a mechanism which consists of two four-bar mechanisms which are combined at PIP joint and with a coupling linkage as shown in

Initially, when the torque is applied by the driving bar the finger operates as a single rigid body due to second and third torsion springs. Then, first torsion spring which has lower spring constant than second torsion spring starts to compress and the spring resistance increases. When the spring resistance of second torsion spring is overcome by the first torsion spring middle phalanx starts to rotate relatively to the proximal phalanx. Once the middle phalanx motion is restricted by the grasped object, third torsion spring is compressed and side bar-1 starts rotating relative to middle phalanx. Then, distal phalanx

continues rotating relative to middle phalanx. In order to carry out the under-actuation properly second torsion spring should have the highest spring constant, first torsion spring should have the second highest spring constant and third torsion spring should have the lowest spring constant.

In order to carry out the proper under-actuation;

K ThirdSpring < K FirstSpring < K SecondSpring (1)

where K is spring constant.

Proposed finger incorporates self-adaptation ability which enables to grasp objects with different geometries.

Proposed finger mechanism shown in

spring resistance of second torsion spring is overcome by the first torsion spring, distal phalanx starts to rotate relatively to the proximal phalanx. The ratio of spring constants of first and second springs is 0.64:1.

In order to understand the kinematic behaviour of the finger mechanism kinematic analysis is carried out. As shown in

First, second and third springs are connected between, AB and the palm; AB and AC; and BD and BH. Initially even though the torque is applied to the AC, angle between AB and AC (θ) is kept constant due to the torsion spring between AB and AC. Then, angular velocity of AB becomes zero when its motion is restricted by the object. Initially, θ is known. Thus, β = 90 − (α + θ) for any α value. Assume that AC, AB, CD, DB, EF, BF, FG, BH, GH, HI, DE are l_{1} to l_{11} respectively. Considering ABDC four-bar mechanism;

l 1 sin α + l 3 sin γ = l 2 cos β + l 4 sin δ (2)

l 1 cos α + l 3 cos γ = l 2 sin β + l 4 cos δ (3)

From (2),

sin 2 δ = ( l 1 sin α + l 3 sin γ − l 2 cos β ) 2 ( l 4 ) 2

From (3),

cos 2 δ = ( l 1 cos α + l 3 cos γ − l 2 sin β ) 2 ( l 4 ) 2

γ can be found for the given α and β from the equation given below.

l 1 cos ( γ − α ) − l 2 sin ( γ + β ) = 1 2 ( l 3 ) [ ( l 4 ) 2 − ( l 1 ) 2 − ( l 2 ) 2 − ( l 3 ) 2 + 2 l 1 l 2 sin ( α + β ) ]

Similarly, solving (2) and (3),

l 2 sin ( δ + β ) − l 1 cos ( δ − α ) = 1 2 ( l 4 ) [ ( l 3 ) 2 − ( l 2 ) 2 − ( l 1 ) 2 − ( l 4 ) 2 + 2 l 1 l 2 sin ( α + β ) ]

The angle (δ) can be found from the above equation for the given α and β. Therefore, 𝜇 can be found using 𝛿 and angle 𝛾. Consider DE, EF, BF and BD.

l 11 cos γ − l 5 cos λ = l 4 cos δ − l 6 cos μ (4)

l 11 sin γ − l 5 sin λ = l 4 sin δ − l 6 sin μ (5)

Solving the above equations, λ can be found from the below equation.

l 4 cos ( λ − δ ) − l 11 cos ( λ − γ ) = 1 2 ( l 5 ) [ ( l 6 ) 2 − ( l 4 ) 2 − ( l 5 ) 2 − ( l 11 ) 2 + 2 l 4 l 11 cos ( γ − δ ) ]

µ also can be found similarly from the below equation.

l 11 cos ( μ − γ ) − l 4 cos ( μ − δ ) = 1 2 ( l 6 ) [ ( l 5 ) 2 − ( l 4 ) 2 − ( l 6 ) 2 − ( l 11 ) 2 + 2 l 4 l 11 cos ( γ − δ ) ]

Therefore, φ can be found using µ and η. Considering BFGH four-bar mechanism;

l 8 sin η = l 6 sin μ + l 7 sin φ + l 9 sin ϕ (6)

l 8 cos η = − l 6 cos μ − l 7 cos φ + l 9 cos ϕ (7)

From (6) and (7), φ can be found as below.

l 8 cos ( ϕ − η ) + l 6 cos ( ϕ + μ ) = 1 2 l 9 [ ( l 8 ) 2 + ( l 6 ) 2 + ( l 9 ) 2 − ( l 7 ) 2 + 2 l 6 l 8 cos ( η + μ ) ]

Similarly, φ can be found from the equation given below.

l 8 cos ( ψ + η ) + l 6 cos ( ψ − μ ) = 1 2 l 7 [ ( l 9 ) 2 − ( l 8 ) 2 + ( l 6 ) 2 − ( l 7 ) 2 + 2 l 6 l 8 cos ( η + μ ) ]

Considering joints of a finger fingertip “I”, position, (x, y) and orientation, (70+φ) with respected to the motor shaft A (0, 0) can be found.

x = l 2 cos β + l 8 sin η + l 10 sin ( 70 + ϕ ) (8)

y = l 2 sin β − l 8 cos η + l 10 cos ( 70 + ϕ ) (9)

(8) and (9) can be used to derived the position and orientation of the fingertip relative to the palm.

The proposed finger and thumb is used to introduce a multi-functional hand prosthesis shown in

The hand prosthesis consists of four main units: first finger unit, second finger unit, third finger unit and a palm [refer

Specifications | Quality |
---|---|

Finger length | 95 mm |

Palm width | 83 mm |

Palm thickness | 25 mm |

Flexion range of MCP joint | 0 to 90 Degrees |

fingers, worm and wheel gears (reduction ratio 35:1), and a motor. These three fingers correspond to the middle, ring and little fingers of the human hand [refer

All finger units are attached on the palm as shown in

Simulations and experiments are carried out to compare and verify the motion generation of the proposed finger. Furthermore, experiments are carried out to verify the adaptation ability of the finger and hand prosthesis. The kinematic model is simulated in MATLAB/Simulink environment to achieve the fingertip motion. Index finger motion of prosthesis is captured using a camera by placing passive markers to each joint and captured data is used to derive joint angles.

The experimental set-up is shown in the

Specification | Description |
---|---|

Maximum Speed | 400 rpm |

Stall torque | 1.58 kgcm |

Gear ratio | 75:1 |

Voltage | 6 V |

No load current | 70 mA |

Max. current | 1600 mA |

Weight | 10g |

Encoder resolution | 20 cpr |

displays the angle of PIP with respective to the proximal phalanx. The angle of DIP with respect to the middle phalanx is shown in

Fingertip trajectory for human hand [

Snapshots shown in

MCP joint [Degrees] | PIP joint [Degrees] | DIP joint [Degrees] | |
---|---|---|---|

Human hand [ | 0 - 90 | 0 - 110 | 0 - 70 |

Simulation results (with 3D model) | 0 - 90 | 3 - 104 | 0 - 82 |

Experiment results (with fabricated hand prosthesis) | 0 - 90 | 5 - 90 | 2 - 88 |

table for the comparison. MCP joint of the hand prosthesis have the same movable range as the human hand. However, motion range of PIP and DIP joints has slight variation. The fabricated proposed hand prosthesis is unable to achieve the exact ranges of the 3D model. These slight deviations cause due to friction between links and joints, dimensional accuracy and tolerances associated to fabrication process and actual spring constant ratios are different from calculated values.

An under-actuated and self-adaptive finger was proposed together with a hand prosthesis. The finger consisted of mainly two four-bar mechanisms. Modified mechanism of the finger was used as the thumb mechanism. Furthermore, a hand prosthesis with the proposed fingers and thumb was introduced in the paper. The finger was capable of generating different passive angles for a PIP joint and a DIP joint for each flexion angle of MCP joint. In addition, DIP joint was capable of generating different angles for the same angle of PIP joint. Thumb mechanism allowed for powered articulated thumb opposition/apposition. The weight of prototype hand prosthesis is about 250 g. Kinematic analysis and computer simulations displayed that the finger mechanism was capable of performing required motions. Simulations were used to validate the movable ranges of the joint angles of finger. The movable ranges obtained from the experiments are 0˚ - 90˚, 5˚ - 90˚ and 2˚ - 88˚ for MCP, PIP and DIP respectively. Joint angle variation for MCP, PIP and DIP joints of the finger was obtained using simulations

Prosthesis | DOF | No. of actuators |
---|---|---|

Proposed Hand prosthesis | 9 | 4 |

UOM Trans-radial Prosthesis [ | 7 | 3 |

DEKA RC Gen3 arm [ | 6 | 4 |

Vanderbilt Multigrasp Hand [ | 9 | 4 |

FluidHand III [ | 8 | 5 |

and experiments. The developed hand prosthesis offers a grasp adaptation using four actuators.

The hand prosthesis can be used to substitute a lost hand part of an amputee or can be used a terminal device for an arm prosthesis such as trans-radial prosthesis of trans-humeral prosthesis. Electromyography signals or electroencephalography signals of the wearer can be used to identify the motion intentions of the user to control the hand prosthesis, accordingly.

The authors would like to acknowledge the support given by Senate Research Council of University of Moratuwa, Sri Lanka (grant no: SRC/LT/2012/07).

The authors declare no conflicts of interest regarding the publication of this paper.

Gopura, R.A.R.C. and. Bandara, D.S.V (2018) A Hand Prosthesis with an Under-Actuated and Self-Adaptive Finger Mechanism. Engineering, 10, 448-463. https://doi.org/10.4236/eng.2018.107031